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Spectropolarimetry of the Jets of SS433

Permanent Link: http://ufdc.ufl.edu/UFE0041121/00001

Material Information

Title: Spectropolarimetry of the Jets of SS433
Physical Description: 1 online resource (352 p.)
Language: english
Creator: Charcos Llorens, Miguel
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: circe, jet, microquasars, relativistic, spectropolarimetry, ss433, wedowo
Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this thesis, we studied the stellar object called SS433. We investigated the composition and the geometry of outflows of gas, called relativistic jets, which are ejected from SS433 and the regions that contribute to the formation of these outflows. We used a new method of observation, namely spectropolarimetry, to study the emission of light from SS433, with the purpose of elucidating mechanisms of formation and evolution of relativistic jets. The physics of jet formation is largely unknown to astrophysicists. It is important to investigate this subject because the results will contribute to understanding the mechanisms underlying these outflows and more generally, physical laws governing the evolution of these stellar objects.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Miguel Charcos Llorens.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Eikenberry, Stephen S.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041121:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041121/00001

Material Information

Title: Spectropolarimetry of the Jets of SS433
Physical Description: 1 online resource (352 p.)
Language: english
Creator: Charcos Llorens, Miguel
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: circe, jet, microquasars, relativistic, spectropolarimetry, ss433, wedowo
Astronomy -- Dissertations, Academic -- UF
Genre: Astronomy thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In this thesis, we studied the stellar object called SS433. We investigated the composition and the geometry of outflows of gas, called relativistic jets, which are ejected from SS433 and the regions that contribute to the formation of these outflows. We used a new method of observation, namely spectropolarimetry, to study the emission of light from SS433, with the purpose of elucidating mechanisms of formation and evolution of relativistic jets. The physics of jet formation is largely unknown to astrophysicists. It is important to investigate this subject because the results will contribute to understanding the mechanisms underlying these outflows and more generally, physical laws governing the evolution of these stellar objects.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Miguel Charcos Llorens.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Eikenberry, Stephen S.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0041121:00001


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Manyyearsofpersonalandprofessionalexperienceshavesculptedthepersonthatiswritingthewordsexplainingthisdissertation.Itisdifculttothankanypersoninparticularfortheresultsoflongyearsoftrainingandexperiences.Manypeoplecontributedtothesuccessofthisthesisanditishardformetoenumerateallofthem.Firstofall,Ithankmyfamily,whosawmeleavinghometostartmyeducationandisstillawaitingtheendofmytraining.Thanksforwalkingwithmealltheseyearsandforsupportingmeinmypersonaldecisions.Inmyheart,therewillalwaysbeascarbecauseofallthetimethatIwasnotabletosharewithyou.Ialsothankallmyfriendsthataccompaniedmeallthewayuntilnow.Despitethelongdistancesbetweenus,Ihavealwaysfeltthemclosetome.Duringalltheseyears,Ihadthechanceofvisitingmanyplacesaroundtheworldandmeetingseveralpeople.IunderstandthatfriendsaretreasuresthataredifculttondandIfeelfortunatetohaveabunchofgoodones,eventhoughtheyarespreadaroundtheworld.Ithankallofthem,thosewhoarecloseandthosewhoarefaraway,fortheirsupportduringthisprocessandalongmylife.Manythingshappenedinthepastfewyears,goodandbadthings,anditwouldnothavebeenpossibletoreachthisstagewithouttheiremotionalsupport.IdeeplythankmyfriendDr.StephenS.Eikenberryforstronglyencouragingmetoendthisthesisandforhisguidanceasmyadvisor.Iespeciallythankhimforalwaysbeingsupportiveduringthebadtimesandfortrustingmyprofessionalismandmywork.IthankhimandDr.RebaM.Bandyopadhyayfortheirvaluablecommentsonmydissertationandforhelpingmetoimprovemywritingskills.Iamverythankfultoallmycommitteemembersfortheirgoodideasduringmyoralexamination,whichhelpedtopolishthiswork. 4

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page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 11 LISTOFFIGURES ..................................... 13 ABSTRACT ......................................... 18 1INTRODUCTION ................................... 21 2BACKGROUNDONRELATIVISTICJETSANDSS433 ............. 25 2.1RelativisticJets ................................. 25 2.1.1Denition,Properties,andEmissionofRelativisticJets ....... 25 2.1.2Formation,Acceleration,andCollimationofRelativisticJets .... 27 2.1.2.1Plasmacomposition ..................... 28 2.1.2.2Formationmechanisms ................... 29 2.1.2.3Accelerationandcollimationmechanisms ......... 30 2.1.2.4Propagationofthegasoutowsinrelativisticjets ..... 31 2.1.3ComparisonofRelativisticJetsinAGNandMicroquasars ..... 32 2.2JetsinMicroquasars .............................. 33 2.2.1DenitionandPropertiesofMicroquasars .............. 33 2.2.2ClassicationofMicroquasars ..................... 35 2.2.3PlasmaCompositionofJetsinMicroquasars ............ 37 2.3JetsinSS433 .................................. 38 2.3.1GeneralDescriptionofSS433 ..................... 38 2.3.2DynamicalMotionsofSS433 ..................... 39 2.3.2.1Orbitalmotion ........................ 39 2.3.2.2Precessionalmotion ..................... 40 2.3.2.3Nutationalmotion ...................... 41 2.3.3OpticalSpectrafromSS433 ...................... 41 2.3.3.1StationarylinesfromSS433 ................ 42 2.3.3.2MovinglinesfromSS433 ................. 43 2.3.4Jet-DiskInteraction ........................... 44 2.3.5DescriptionofSS433Jets ....................... 46 2.3.5.1EmissionofSS433jetsacrossthespectralrange:X-ray,radio,andopticaljets .................... 46 2.3.5.2StructuresofSS433jets:bulletsandcloudsofgas .. 47 2.4Summary .................................... 48 3SPECTROPOLARIMETRYOFSS433:OBSERVATIONS,DATAREDUCTION,ANDANALYSIS ................................... 57 3.1PolarimetricBasics:Concepts,PhysicsandMethods ............ 57 6

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.......................... 57 3.1.2SourcesofPolarization ......................... 59 3.1.2.1Electronscattering:Thomson,RayleighandComptonradiation ........................... 60 3.1.2.2Cyclotronandsynchrotronradiation ............ 63 3.1.2.3Cerenkovradiation ...................... 64 3.1.2.4FaradayrotationandFaradaydepolarization ....... 65 3.1.3Double-BeamSpectrographPrinciples ................ 66 3.1.4SourceofPolarizationMeasurementErrors ............. 70 3.1.4.1Atmosphereandpixeluctuations ............. 71 3.1.4.2Instrumentalpolarization .................. 71 3.1.4.3Simultaneoussourcesofpolarization ........... 73 3.1.4.4Interstellarpolarization ................... 74 3.2PolarimetryofSS433 ............................. 74 3.2.1PreviousPolarimetryObservations .................. 74 3.2.2ModelsofPolarizationfromThomsonScatteringfortheStudyofSS433 .................................. 77 3.3ObservationsandDataReduction ...................... 79 3.3.1DataReductionPipeline ........................ 80 3.3.2DatafromPalomar/DBSP ....................... 82 3.3.3DatafromMMT-Steward/SPOL .................... 83 3.3.4QualitativeAnalysis ........................... 84 3.4SpectralFitting ................................. 85 4DESPEJO:DYNAMICALEVOLUTIONOFSPECTROPOLARIMETRYEMISSIONOFJETOBJECTS ........................... 104 4.1IntroductiontoDESPEJO ........................... 104 4.1.1Overview ................................ 104 4.1.2HowToRunDESPEJO ........................ 105 4.1.2.1ScienticapplicationsofDESPEJO ............ 105 4.1.2.2Denitionofthedata:datalists ............... 105 4.1.2.3FitoftheStokesspectra:ttingpackage ......... 106 4.1.2.4DeterminationoftheISP .................. 107 4.1.2.5Intensityandpolarizationalongthejet ........... 108 4.1.2.6Particledensityoftheemittingandscatteringregions .. 108 4.2SoftwareDevelopmentConcepts ....................... 109 4.2.1DevelopmentStagesandHistoryofDESPEJO ........... 109 4.2.2DESPEJOv2.0:Object-OrientedProgrammingMethodology ... 110 4.2.3UniedModelingLanguage ...................... 111 4.2.4SoftwareTesting ............................ 114 4.3StructureofTheProgram ........................... 117 4.3.1DataDenition,ListofDataandDataFit ............... 117 4.3.1.1STOKES DATAclass .................... 118 4.3.1.2STOKES MODELclass ................... 118 7

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....................... 120 4.3.2ModelsandAnalysisoftheData ................... 121 5SPECTROPOLARIMETRYANDTHEACCRETIONDISKENVIRONMENTINSS433 ......................................... 127 5.1SystemInterpretationfromDynamicalBehavioroftheStationaryLines 127 5.1.1AnalysisoftheStationaryHLineProle .............. 128 5.1.1.1Questionone:generalstudyofthestationaryHlines. 129 5.1.1.2Questiontwo:relationbetweenstationarylines. ..... 130 5.1.1.3Questionthree:originofthestationaryHcomponents. 131 5.1.2TheoreticalDynamicalModelsofSS433AccretionDiskEnvironment ......................... 132 5.1.2.1Denitionofthecoordinatesystems ............ 133 5.1.2.2Motionsintheorbitalplane ................. 133 5.1.2.3Motionsinthejetdirection ................. 134 5.1.3DynamicalModelofTheCentralCoreandWingsofTheStationaryHLine ..................... 134 5.1.3.1DynamicalmodeloftheH1component ......... 135 5.1.3.2OriginoftheH1component:comparisonbetweenpreviousresultsandourspectropolarimetry ................. 137 5.1.3.3DynamicalmodelfortheH2andH3components ... 140 5.1.4StudyoftheGeneralStationaryHProle:ComparisonbetweenPreviousResultsandOurSpectropolarimetry ...... 141 5.1.5Summary:ModeloftheStationaryHComponents ........ 143 5.2PolarizationAnalysis .............................. 144 5.2.1DeterminationoftheInterstellarPolarization ............. 145 5.2.2IntrinsicSourcePolarization ...................... 147 5.2.3DynamicsoftheIntrinsicSourcePolarization ............ 149 5.2.3.1Analysisoftheeffectsoftheorbitalandprecessionalmotions ............................ 150 5.2.3.2Fourierdecompositionofthepolarizationevolution .... 152 5.3Electron-ProtonDensityandGeometryoftheAccretionDiskRegion ... 153 5.4SummaryandDiscussion ........................... 156 6EMISSIONFROMSS433JETS:STATEANDCOMPOSITION ......... 180 6.1OverviewoftheStateoftheOpticalJets ................... 181 6.1.1TheDynamicalModeloftheJetHEmissionLines ........ 181 6.1.2SpectroscopicPropertiesoftheRadiationfromtheJets ...... 183 6.1.3Discussion ................................ 185 6.2SpectropolarimetryfromtheOpticalJets ................... 187 6.2.1ConditionsoftheOpticalJetsfromMultiwavelengthObservations. 187 6.2.2TheOriginofthePolarizationfromtheOpticalJets ......... 188 6.2.3ConditionsoftheOpticalJetsfromSpectropolarimetry ....... 190 8

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...... 190 6.2.3.2Averagedprotondensityoftheopticaljetgas ....... 191 6.2.3.3Uncertaintiesontheelectronandprotondensities .... 193 6.2.4RadiationandParticlePopulationsalongtheOpticalJets ..... 196 6.2.4.1Intensityandpolarizationalongtheopticaljet ....... 196 6.2.4.2Protondensity ........................ 199 6.2.4.3Electrondensity ....................... 201 6.3ANewScenarioforSS433'sJetFormation ................. 203 6.3.1GeneralPicture ............................. 203 6.3.2WhoWasFirst,eore+p? ..................... 204 6.3.3AnePairJetDraggingae+pPlasma .............. 205 6.3.3.1Interactionbetweentheejetandtheaccretiondisk ... 205 6.3.3.2Basicequations ....................... 206 6.3.3.3Descriptionoftheinteractionregion ............ 208 6.3.3.4Annihilationintheopticaljet ................ 209 6.3.3.5Structuresintheopticaljet ................. 211 6.4ARevisedDynamicalModelforSS433 .................... 213 6.4.1PhysicsattheInteractionRegion ................... 214 6.4.1.1Interactionmechanismsbetweennormalandpairplasma 214 6.4.1.2Correlationbetweentheaccretiondiskpropertiesandthedeceleration-deectionofthejet ............ 215 6.4.1.3Instabilitiesinaccretiondisks ................ 217 6.4.2DopplerShiftResiduals ........................ 218 6.4.2.1Noisemodelsforresiduals ................. 218 6.4.2.2Correlationofresidualsandaccretiondiskwinddensity 219 6.4.2.3Atwomechanismmodelforresiduals ........... 222 6.4.2.4Physicaloriginofthetworesidualcomponents ...... 223 6.5Summary .................................... 224 7JETSINTHEINFRAREDWITHCIRCEATGTC ................. 241 7.1SS433intheInfraredwithCIRCE ...................... 241 7.2OpticalBenchDesignandMechanicalElements .............. 244 7.2.1FlexureandThermalCalculations ................... 245 7.2.2TheIDLThermo-MechanicalAnalysisSoftware ........... 247 7.2.2.1ITMASinterface ....................... 247 7.2.2.2InitialtestsofITMAS ..................... 248 7.2.2.3CIRCEandITMAS ...................... 248 7.2.3CADDesignofCIRCE ......................... 250 7.3Design,FabricationandAssembly ...................... 252 7.3.1DesignandFabricationAnalysisoftheRadiationShields ..... 252 7.3.2Design,FabricationandTestoftheOpticalBench .......... 253 7.3.2.1Machineandassemblyaccuracy .............. 254 7.3.2.2Stressdeformation ...................... 254 7.3.3DesignandFabricationoftheLN2Tanks ............... 256 9

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............. 256 7.3.3.2Half-cylindertankbeam ................... 257 7.3.3.3Cylindricaltankbeams ................... 258 7.3.4Design,Fabrication,AssemblyandTestoftheFilterBox ...... 261 7.4PolarimetryDesign ............................... 263 7.4.1DesignofthePolarimetry:FourBeamSpectropolarimeter ..... 263 7.4.2MaterialsofthePolarimetryOptics .................. 264 7.4.2.1AnalysisoftheIRmaterial:magnesiumuoride(MgF2) 265 7.4.2.2TheHWPandentrancewindowmaterials ......... 266 7.4.3OptimizationandPerformanceoftheWeDoWoGeometry ..... 267 7.4.4CalibrationRequirements ....................... 269 8CONCLUSIONS ................................... 282 APPENDIX ACOORDINATESYSTEMUSEDFORDYNAMICALBEHAVIOROFTHECOMPONENTSOFTHEHSTATIONARYLINES ................ 286 BANALYSISOFTHEOPTICALDESIGNWITHPOLARIMETRY ......... 289 COPTICALSPECTROPOLARIMETRYFROMSS433 ............... 293 DCIRCECADDESIGNS-SOLIDMODELS ..................... 305 EDESPEJOUMLDIAGRAMS ............................ 308 FMEASUREMENTOFPERFORMANCEOFSTEPPERMOTORSUNDERLN2TEMPERATURES ................................ 320 GFOCALPLANEMASKSFORPOLARIMETRY .................. 330 HFOCALPLANEMASKSFORPOLARIMETRY .................. 339 REFERENCES ....................................... 343 BIOGRAPHICALSKETCH ................................ 352 10

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Table page 3-1SummaryofOurSpectropolarimetry ........................ 89 3-2Propertiesofthedataandthettedlines ..................... 90 3-3LinetsusingI,Q,Ucombinationmethod ..................... 91 5-1FitofpeakvelocityshiftofHfromdatasetD1,D2,D3,D4,D5,andD6 159 5-2FitofpeakvelocityshiftofHandHeIfrom Giesetal. ( 2002b )data. ...... 160 5-3ResultsabouttheinterstellarpolarizationaroundSS433 ............. 160 5-4Linearapproximationvelocityshift=aorb+bofdynamicalbehaviorofH1,H2andH3components .............................. 161 5-5LinearapproximationP=acos2isdo+bofpolarizationofHandcontinuum. 161 5-6ApproximationofA(prec)=A0+A1cos2(2(precA))andB(prec)=B0+B1cos(2(precB)). ............................... 161 6-1ParameterofDynamicalModelsofSS433Jetsderivedfromtheopticaljets( Eikenberryetal. 2001 )[model1]andfromtheradiojets( Stirlingetal. 2002 )[model2] ........................................ 226 6-2Blue-JettoRed-JetIntensitiesRatio. ........................ 226 6-3DistancescalesoftheinteractionregionoftheeJetwiththeaccretiondisk. 226 6-4MovinglinesfromJet1andJet2( Panferovetal. 1997 ) ............. 227 7-1Concentratedloads ................................. 273 7-2Physicalvaluesoftheinstrumentstructure.ThesevalueswereobtainedfromCADdesign ...................................... 274 7-3DeectionofOpticalElementsobtainedfromanalyticalcalculationsassumingopticalbenchasacantileverbeam ......................... 275 7-4Collapsingpressuresofwallssubjecttovacuum ................. 275 F-1MOTOR1 ....................................... 321 F-2MOTOR2 ....................................... 322 F-3MOTOR3(day1) .................................. 323 F-4MOTOR3(day2) .................................. 324 F-5MOTOR4(day1) .................................. 324 11

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.................................. 325 F-7MOTOR5 ....................................... 326 F-8MOTOR7 ....................................... 327 F-9MOTOR8 ....................................... 328 F-10MOTOR9 ....................................... 329 12

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Figure page 2-1CatalogofknownmicroquasarsinourGalaxy ................... 50 2-2RadioobservationsofSS433from Jowett&Spencer ( 1995 ) .......... 51 2-3OpticalsynchrotronemissionintheradiojetofVirgoA(M87). .......... 52 2-4Astrophysicaljetformationscenarioswithmagneticelds. ............ 52 2-5DiagramofaLow-MassX-rayBinary(LMXB). ................... 53 2-6TypicalspectrumofSS433. ............................. 53 2-7Plotsillustratingmultiwavelengthcorrelationofthejet-diskinteractionregion. 54 2-8AverageofstationaryHvelocityprolesforvariousprecessionalphases. .. 55 2-9IllustrationofthejetsofSS433andthedynamicalmotions. ........... 56 3-1Linearlypolarizedelectricwavedecompositionalongthexandyaxes. ..... 92 3-2ElectronscatteringofanincomingelectricwaveEX 93 3-3IllustrationofthecalculationofQfromspectropolarimetryfromaDBSP. .... 93 3-4Spectraldistributionofsynchrotronemissionfromasingleparticle. ....... 94 3-5Cerenkovemissionwhenthevelocityexceedsthecriticalspeedvsofthemedium. .................................... 94 3-6Multiplescatteringinaannularcylinderscatteringregion. ............ 95 3-7InterfaceofreductionsoftwareusedtoprocessspectropolarimetryofaDouble-BeamSpectropolarimeter. ......................... 96 3-8LinearStokesParametersofD1set. ........................ 97 3-9LinearStokesParametersofD2set. ........................ 98 3-10LinearStokesParametersofD6set. ........................ 99 3-11LinearPolarizationofD1set. ............................ 100 3-12LinearPolarizationofD2set. ............................ 101 3-13LinearPolarizationofD6set. ............................ 102 3-14ShiftofHmovinglines. ............................... 103 4-1InterfaceofDESPEJO(listofdata). ........................ 123 13

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................... 124 4-3ActordiagramofDESPEJO. ............................ 125 4-4STOKES DATAandSTOKES MODELclasses. .................. 126 5-1TheorbitalphasesofdatasetsD1,D2,D3,D4,D5,andD6areoverplottedonthemeanV-bandlightcurve. ............................ 162 5-2SpectrumofdatasetD2(solidline)aroundthestationaryHline. ........ 163 5-3VelocityshiftofstationaryH1componentforvariousprecessionalphases. .. 164 5-4VelocityshiftofstationaryH1componentforprecessionalphases0.3
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.............................. 231 6-5I,QandUprolesalongthejetindatasetD2forapproachingandrecedingjets. .......................................... 232 6-6Modeledprotonandelectrondensitiesalongjetswithrespecttothereferencesegment. ....................................... 233 6-7Modeledprotonandelectrondensitiesalongjetsofthereferencesegment. 234 6-8Geometryoftheregionofinteractionbetweentheejetandtheaccretiondisk 235 6-9EquivalentWidthofthemovingHlineswithrespecttotheresidualsofthedynamicalmodel. ................................... 236 6-10EquivalentWidthofthemovingHlineswithrespecttoresiduals ...... 236 6-11EquivalentWidthofthemovingHlineswithrespecttoresiduals ...... 237 6-12EquivalentWidthofthemovingHlineswithrespectto 237 6-13ResidualsoftheDopplershiftofthemovingHlines. ............. 238 6-14CorrelationofresidualsoftheDopplershiftofthemovingHlinesofthetwojets. ........................................ 239 6-15DecompositionofresidualsoftheDopplershiftofthemovingHlinesofthetwojets. ...................................... 240 7-1CIRCEOpticalLayout ................................ 276 7-2EncircledenergydiagramofthelayoutofCIRCEexplainedby Edwardsetal. ( 2008 ). ........................................ 276 7-3TheIDLThermo-MechanicalAnalysisSoftwareInterface. ............ 277 7-4DeectionoftheBenchofCIRCEusingtheAUTOCADdesign. ......... 277 7-5CIRCEMechanicalLayout. ............................. 278 7-6Kcoefcientvaluesforpressurecollapsingpressureunderconditionsofradialexternalpressurewithsimplysupportededges .................. 279 7-7SectionofthevariousLN2tankcongurations. .................. 279 7-8FocalPlaneandDeckerMasks. ........................... 280 7-9Flexureofthebenchforthehalf-cylinderconguration. .............. 280 7-10SeparationofthefourbeamsintheWeDoWocongurationofCIRCEforasingleslotinJ-band. ................................. 281 15

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....... 290 B-2Spotdiagraminimagingpolarimetrymode(KBand) ............... 291 B-3Footprintdiagraminimagingpolarimetrymode(KBand) ............ 292 C-1LinearStokesParametersofD1set. ........................ 293 C-2LinearStokesParametersofD2set. ........................ 294 C-3LinearStokesParametersofD3set. ........................ 295 C-4LinearStokesParametersofD4set. ........................ 296 C-5LinearStokesParametersofD5set. ........................ 297 C-6LinearStokesParametersofD6set. ........................ 298 C-7LinearPolarizationofD1set. ............................ 299 C-8LinearPolarizationofD2set. ............................ 300 C-9LinearPolarizationofD3set. ............................ 301 C-10LinearPolarizationofD4set. ............................ 302 C-11LinearPolarizationofD5set. ............................ 303 C-12LinearPolarizationofD6set. ............................ 304 D-1CADdesignoftheinstrumentsviewfromthebackside. ............. 305 D-2CADdesignoftheinstrumentsviewfromthefrontside. ............. 306 D-3CADdesignofthelterbox. ............................. 307 E-1DiagramofthetreewiththedifferentpackagesofDESPEJOandthelistofactorsandactions .................................. 308 E-2Diagramofclasseswithsomeoftherelationsbetweentheseclasses ..... 309 G-1WedgedDouble-Wollaston(WeDoWo)prismwiththelabelsusedinZEMAXrepresentingthecongurationofeachray ..................... 330 G-2CongurationMask1:Patternofthefocalplanemask .............. 331 G-3SpotdiagramoftheimagesinJ-bandofthecongurationmask1. ....... 332 G-4SpotdiagramoftheimagesinH-bandofthecongurationmask1. ....... 333 G-5SpotdiagramoftheimagesinK-bandofthecongurationmask1. ....... 334 G-6CongurationMask2:Patternofthefocalplanemask .............. 335 16

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....... 336 G-8CongurationMask3:Patternofthefocalplanemask .............. 337 G-9CongurationMask4:Patternofthefocalplanemask .............. 338 H-1DiagramoftheZEMAXscriptanddenitionoftheinitialparameters. ...... 340 H-2ZEMAXsimulationresultsofthepolarizationsystemofCIRCE. ......... 341 H-3ExcelmacrofortheanalysisofthepolarizationsystemofCIRCE. ....... 342 17

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Inthisthesis,westudiedthemicroquasarSS433.Weinvestigatedthecompositionandthegeometryofitsjetsandjet-diskinteractionregion.WeusedspectropolarimetrytostudythestationaryandmovinglinesoftheemissionfromSS433,withthemoregeneralgoalofelucidatingmechanismsofformation,collimation,andaccelerationofrelativisticjetsinmicroquasarsandAGN. Thistechniqueallowedustodistinguishthreecomponentsofstationary(non-jet)linescomingfromthreeseparateemittingregionsneartheaccretiondiskatthejet-diskinteractionregion.WecreatedanewalgorithmthatusesinformationfromallthelinearStokesparameterstoseparateandttheemissionfromeachcomponent.Wecombinedthisinformationwithspectroscopyfromotherauthorsinordertoestimatethedynamicalbehavioroftheemittingregions.Fromouranalysis,themostlikelynatureoftheseregionsareaowfromthedonorstartotheaccretiondisk(regionone),andtwosymmetricwindsfromtheaccretiondisk(regionstwoandthree).WeestimatedthevelocityoftheorbitV=276102km=s,andthevelocityoftheaccretiondiskwinds1700km=s300fromtheemissionofregionstwoandthree.Thepolarimetryoftheemissionfromthewindsindicatesthattheyreachadistanceupto1011cm. WeusedspectropolarimetrytocalculatetheInterstellarPolarization(ISP)whichwasthemainunknowninthecalculationsfrompreviousauthors.Wefoundpolarizationanglesofabout35withtheSerkowskii'slawmaximumpolarizationofPmax1%at 18

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WecombinedanalyticalmodelsofscatteringgeometriesandourspectropolarimetrytocalculateelectronandprotondensitiesoftheopticaljetsofSS433.Wecomparedtheresultsfromspectroscopyofpreviousauthorswithourdata.Theanalysiswassupportedbythepolarimetrythatweobservedintheemissionlinesfromtheopticaljets.WeinvestigateditsoriginandweconcludedthatThomsonscatteringisthemostlikelymechanismproducingthispolarization.Assumingelectronscattering,ourresultsindicatedanexcessofelectron-likeparticleswithrespecttoprotonsinthejetsofSS433.Weconcludedthattheopticaljetsmustcontainasignicantpopulationofpositronparticlesarisingatthejetformationregion.Thisconclusionsupportsthetheoryofjetformationbasedonelectron-positronplasmawhich,inthecaseofSS433,dragsanormal-matterplasmaow. WedevelopedtheDynamicalEvolutionofSpectropolarimetryEmissionofJetObjects(DESPEJO)softwarefortheanalysisofourspectropolarimetry.DESPEJOincludesmodelsandtoolsfortheanalysisofspectropolarimetryfromSS433andotherastronomicalobjects.Weexplaineditsfunctionalities,thestructureofthecode,andthetestsofthecurrenttasks.DESPEJOwasimportantforthecurrentstudybutalsothissoftwarewillbenecessarytopursueouranalysisbystudyingthetime-evolutionofthepolarization. Finally,wedesignedtheCanariasInfraRedCameraExperiment(CIRCE)forstudiesofjetsofmicroquasarsinthenearinfraredrange.UsingCIRCE,weplantoobtaindataforfutureanalysisoftheSS433jetsanddisk-jetregionswithDESPEJO.BasedontheinitialopticaldesignofCIRCE,wedesignedthemechanicalstructuresupportingtheopticsandwestudiedfabricationandmanufacturingproblems.Wedevelopedacodeforthepreliminarythermo-mechanicalcalculationsandwetested 19

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Thisworkdescribesobservationsandinvestigationsofrelativisticjetsinastronomicalstellarsources.WeusedtheparticularcaseofthesystemknownasSS433becauseitpresentsauniqueopportunityforjetstudies.SS433isanX-raybinarysystemwithrelativisticjets,alsoknownasamicroquasar.SS433wasidentiedforthersttimeinasurveyofHemittingobjectswiththeBurrellSchmidtspectrographattheNassauAstronomicalStationandtheCurtisSchmidtspectrographatCerroTololoInter-AmericanObservatory( Stephenson&Sanduleak 1977 ).JetsfromSS433weretherstexampleofrelativisticradiojetsinourownGalaxy.ThecharacteristicsofSS433remainuniqueforthestudyofjetmechanismsandproperties.However,manyimportantquestionsaboutthisstellarobjectremainunresolved,eventhoughextensivedatafromSS433hasbeenobtainedoverthelast30yearscoveringmanywavelengthranges.Severalissuesthatarestillunclearincludethemassandnatureofthecompactobject;themassandthenatureofthemassdonorstar;thephysicalconditionsandaccelerationmechanismsinthejetformationregion;thephysicalconditionsinthejets;andthephysicalconditionsinthelineemittingregion. Inthiswork,weusedanewtypeofdataintheeldofmicroquasars,spectropolarimetry,inordertoexploretheseissues.Spectropolarimetryhasbeenshowntobeausefultoolforthestudyofthegeometryandthestateofanemittingregionaswellasitsinteractionwiththesurroundingenvironmentinothertypesofastronomicalobjects,includingAGN,cataclysmicvariables,theSun,andwhitedwarfs( delToroIniesta 2003 ).WeuseditintheparticularcaseofSS433inordertoanswerquestionsaboutthephysicshappeningintheopticaljet.Theresultswederivedareimportantforunderstandinggeneralquestionsaboutrelativisticjetsinotherobjects.Inaddition,spectropolarimetryofSS433illuminatesthescenariowherejetsareformedatthebase,neartheaccretiondisk. 21

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2 explainsthepresentknowledgeabouttheformationmechanismsandthepropagationofjets.Formation,accelerationandcollimationarethecentralissuesforunderstandingthesejets;theseprocessesarerelatedtothecompositionoftheow,whichmaybeelectron-protonorelectron-positronplasma.Propertiesofextendedjetsalsodependonthephysicsoftheinitialow,whichisrelatedtothenatureofthestellarobject.Wediscusshowthepropertiesofjetsarecommontodifferenttypesofobjects(AGNormicroquasar).Next,wedescribetheparticularexampleofrelativisticjetsinmicroquasarsandtheirgeneralproperties.Weshowthatjetsinmicroquasarsaregoodsourcesforunderstandinghowtheformationofjetsisrelatedtothecompactobjectandthustothedisk-jetinteractionmechanisms.TheparticularcaseofSS433isexplainedextensivelyinthelastsection( 2.3 ).DescriptionsofSS433includethedynamicalmodelsgoverningmotionofthesystemandthereforethemodulationoftheobservedemission;generalcharacteristicsofobservationsofitsjetsacrossthespectralrange;andtheresultingemissionfromthejet-diskinteractionregion. Chapter 3 presentsourspectropolarimetricobservationsofSS433.First,wedescribethegeneralbasisofpolarimetry,includingtheoreticalconcepts,theinstrumentsneededtomeasurepolarization,thesourcesofpolarization,andthetypicalmeasurementerrors.Then,wedescribethepreviouspolarimetricobservationsofSS433andtheradiativetransfermodelsthatcanbeappliedtosolvethepropertiesofSS433-likeobjects.Weexplainthemotivations,arisingfrompreviousimagingpolarimetryofSS433,forspectropolarimetryofthisobject.WedescribeourspectropolarimetrydatafromSS433inSection 3.3 .Weexplainthereductionprocessofthedataandthereductionpipelinewemadeforthispurpose.Wepresentaqualitativeanalysisofourdatawhichwillbecompletedinthefollowingchapters.FurtheranalysisrequiretechniquesofttingthespectropolarimetryfromSS433whichhasbeenshown 22

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Chapter 4 describesthetoolwedevelopedfortheanalysisofspectropolarimetryandmodelingoftheSS433emission.ThistoolwasimportanttostudytheperformanceofthetexplainedintheChapter 3 ,andwasessentialfortheanalysisoftheresultingdatashowninChapters 5 and 6 .WeintroducethesoftwarewemadethatwecalledDynamicalEvolutionofSpectropolarimetryEmissionofJetObjects(DESPEJO).WeshowhowtouseDESPEJOintheparticularcaseofSS433butalsoforotherastronomicalstudies. Chapter 5 isdevotedtotheanalysisoftheaccretiondiskemittingregion,includingourdynamicalmodelsofstationarylineemissionfromthisregion.Ourspectropolarimetrygaveanewperspectiveonthedataofpreviousauthors,resultinginnewinterpretationsofthemotionofemissionlinesandmodelsofthesystem.Modelsarediscussedbasedonthepolarizationstateandtheevolutionoftheseemissionlines.WecalculatedtheInter-StellarPolarization,acriticalquantitythathasbeenthenightmareofpreviousinvestigations.WeobtainedtheintrinsicpolarizationofSS433andwestudiedthebehaviorofthepolarizationwithrespecttothedynamicalmotionsoftheobject.WeusedFourierdecompositiontoseparateinthemeasurementsofpreviousauthorsbasedinimagingpolarimetry,theemissionfromthedifferentregionsthataredirectlyidentiedinourspectropolarimetry.Finally,wecalculatedthegeometryandthecompositionofthejet-diskinteractionregionbasedontheresultingmodelsofthedynamicsandthepolarizationoftheemissionlinesfromthejet-diskregion. Chapter 6 presentsourresultsontheopticaljetsinSS433.Werstcomparethegeneralresultsfromourdataandotherauthorsregardingthestates,thedynamics,andthestructuresofthejetsbasedonspectroscopy.Then,wediscussthepolarizationoftheopticaljetsofSS443,whichwasobservedforthersttimewithourdata,andweinvestigatethesourceofthispolarization.Weusedourspectropolarimetrytoestimate 23

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6.2.4 ,weexplainthemodelweusedtostudythegeometry,thepopulation,andthestructuresalongtheopticaljetsofSS433.Theresultsfromthesemodelsareatthebaseofimportantquestionswhichareexplainedinthischapter,aboutthecompositionoftheplasmajets.Weanalyzedthepossibilityofusingothertechniquestoderivethepropertiesofthejets,includingMonte-Carlossimulations.Weconcludedthatmorespectropolarimetryisnecessaryforthestudyofthedynamicalevolutionofthejetpolarizationwhichisrequiredtofollowupthepresentwork. Finally,wedescribethedesignofTheCanariasInfraRedCameraExperiment(CIRCE),aninfraredcameraandspectrographwithpolarimetriccapabilitieswhichisplannedforuseontheGranTelescopiodeCanarias(GTC).TheinstrumentisdescribedinChapter 7 .WestartthechapterbydescribingtheexistinginfraredspectroscopyandimagepolarimetryfromSS433.WeexplaintheimportanceofusingCIRCEtoobtainIRspectropolarimetryfrommicroquasars,particularlyfromSS433.WeshowhowCIRCEwillprovidetherequiredcapabilitiestoperformthepolarimetryofSS433whichisneededtopursuethestudydescribedinChapters 5 and 6 .ThemechanicalelementsofCIRCEaredescribed,withaspecialemphasisonthethermo-mechanicaldimensioningandthebenchdesign.Finally,thepolarimetrydesignanditsperformanceareexplainedinSection 7.4 .WeshowhowthespecicationsofthepolarimetriccomponentswereoptimizedforourscienticneedsforSS433. Thenalchapter( 8 )summarizesthemainconclusionsofthisworkanddiscussestheconsequencesoftheseresults.Weendthepresentworkbyexplainingourfutureplansforexploringthenewquestionsarisingfromourpolarimetricresults. 24

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Thischapterisdevotedtoexplainingthegeneralbackgroundofourpresentknowledgeaboutrelativisticjets.WeexplainthereasonswhythisthesisisbasedontheparticularastronomicalobjectSS433;andweillustratehowthepresentworkwillprovidenewinsightsintotheunderstandingofjetformationandpropagation.WedescribethenatureofSS433-likesystemsemphasizingthespecialcharacteristicsofSS433.Wesummarizethecurrentknowledgeaboutitsextendedjetsandtheirformationregionaswellasthefeaturesweobserveinitsopticalspectrawhichwillbethebasisofouranalysis. 2.1.1Denition,Properties,andEmissionofRelativisticJets 2-2 ).Inbothcases,theirsizeandcurvaturechangefromsourcetosource.Thegasisejectedinaspecicdirectiondenedbyanarrowcone.Theangleofthejetisanimportantcharacteristicinourworksincewewillneedittodeterminethegeometryofthejetsinourmodels.ConeanglesinAGNandXRBsareontheorderofafewdegrees.Ejectionmaybepoweredinonesingledirectionortwojetsinoppositedirections.Asacommondenition,jetsarecalledone-sided(seeFigure 2-3 )ifonesideismorethan4timesbrighterthantheother,althoughthiseffectisinmostcasespurelyobservationalduetoDopplerboostingoftheapproachingjetemission.Itisbelievedthatthesehighly 25

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Casse 2008 ). Theenergyofthematterthatthejetcarryawayfromthecentralsystemisanimportantparameterforunderstandingjetformation,aswewillseeindetailinSection 2.1.2 .Theenergyofjetsrangesbetween103040erg=sinXRBsand104050erg=sinAGN( Kordingetal. 2006 ),buttheintrinsicluminosityofthejetbecomesdifculttocalculateaccuratelybecauserelativisticeffectsboost(orweaken)theluminositybyafactor4(or4)whenthesourceismovingtowardtheobserver(orawayfromtheobserver).Itcanbeestimatedassumingequipartitionoftheenergythatisrequiredtoproducesynchrotronemission.Thisassumptionisusuallytrueforatypicalsysteminasteadystatebutrelativisticelectronsmaydominateovermagneticenergyduringknotejection( Homanetal. 2006 ).Theseauthorsestimatedthattheparticleenergyatejectiontimeis105timesgreaterthanthemagneticenergyduetoanimbalanceduringthistransientstatethatresultsininjectionofparticlesatthebaseofthejet.Inthisscenario,synchrotronemissionisabsorbedduetoanexcessofparticles,andtheenergyofthejetcanbecalculatedbyassumingself-absorptionintheknots. Relativisticeffectsalsoaffectotherobservationalsourceparameterswhicharerelatedtothephysicsofjetformation.Forinstance,thevelocityoftheoutowdependsontheformationandaccelerationmechanismofthejet.Intheframeworkofrelativity,themotionofthegasaffectthecalculationofaknotvelocityobtainedfromtheclassicaldistancetotimeratio.Infact,lightfromthegasemittedattwodifferenttimeshasdifferentdistancestotheobserversincethelengthofitspathduetoitsmotionduringtheinterveningtimecannotbeneglected.Theapparentdistanceisgreaterthanthedistancethattheknotactuallytravelsduringthisperiodoftime,resultinginanoverestimationoftheLorentzfactoroftheemittingplasmaandanapparentspeedoftheknotssometimeevenlargerthanthespeedoflight:upto45-60cinsomecases( Jorstadetal. 2001 2005 ).Wecanidentifytworelativisticmotions:theglobalspeedofknotsor 26

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Emissionfromrelativisticjetsrangesinenergyfromradioto-rays.Thisgiveustheopportunitytostudyalargenumberofphysicalphenomenonrelatedtothejetandtoinvestigatetheprocessesthatleadtotheformationoftheseoutows.ThebulkoftheX-rayemissionisattributedtoComptonradiationinasurroundingcentralregion.However,onlyafractionofthisemissioncomesfromthejetitself( Markoffetal. 2001 ).Radioemissionisproducedbysynchrotronprocessesfromtherelativisticparticlesintheinnerjet( Fender 2006 )nearthecenteroftheaccretiondisk,alsocalledthecore.Theoretically,verylowfrequenciesarisefromthesectionofthejetwithopticaldepth1wheremagneticandparticleenergydensitiesarethesame.Butotherphysicsinthecore,suchasshockscreatingknots,maymodifytheopticaldepthoftheemission.Highradiopolarizationandsynchrotronradiationobservedintheouterpartsoftheoutowsupporttheideathatmagneticeldsextendalongthewholejet.Magneticeldsandowstructuresareverydiversebuttherearetwomajorgroupsofradiosource( Bridle&Perley 1984 ).Intherstgroup,themagneticeldhasthesamedirectionallalongthejet-eitherparallelorperpendiculartotheow;inthesecondgroup,itisperpendiculartothejetnearthecentralengineandbecomesparallelattheedge.Typicalmagneticlinesofone-sidedjetsareusuallyparalleltotheowbuttwo-sidedjetsarecontinuouslyperpendicularorbecomeperpendicular.Asthegaspropagatesandcools,opticalandinfraredthermalemissionaddstosynchrotronradiation. 27

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Understandingthephysicsandtheroleofjetsinaccretingsystemsrequiresustoanswerquestionsaboutthenatureoftheplasma;theformationandconnectiontothecentralcore;theextractionmechanismofangularmomentumfromtheaccretingsystem;theaccelerationandcollimationmechanismsnearthecompactobject;andthemorphology,energyextraction,andinteractionwiththeenvironmentasthejetspropagate.Here,wewillexplainthekeyissuesaboutthesequestionsthatarerelatedwiththisthesis.Forthispurpose,wedividethisdiagnosisinfourparts:plasmacomposition,jetformationmechanisms,jetaccelerationandcollimationmechanisms,andpropagationofthejetgasatlongdistancesfromthecentralcore.Alongtheexplanation,wewillalsoseehowthesefoursubjectsarerelatedtoeachotherandhowcluesaboutanyofthemcanhelptounderstandthewholepicture. Theoriginofthenormalplasmadoesnotrepresentamysterysincetheaccretionprocessimpliesthepresenceofhydrogenowingtothecenteroftheaccretiondiskwherethejetsareformed.HydrogenemissionfromtheastronomicalobjectSS433hasbeendetected,agreeingwiththeexistenceofnormalplasmajets.However,e-p+jetsareheavyandtheaccretingowneedstobesuper-Eddingtoninordertoexplainhow 28

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Levinson&Blandford 1995 1996 )requirealimitingluminosityafactormp Ghisellinietal. ( 1992 )explainedthatepairsproducedintheinnermostregioncanbefoundintheextendedjetsundercertainconditions.Thenumberofeparticlesthatcanescapewiththejetowwithoutannihilationdependsonthesizeoftheregionwhereannihilationoccursandtheregionwherethe-raysofagivenenergycanescape.TheseargumentswillberecalledlaterwhenstudyingtheoriginoftheparticlesofSS433'sjets. TheplasmacompositiondeterminestheconditionswhichcanbemodeledusingMagneto-HydroDynamical(MHD)equationsnearthecentralcore.Theseequationsareattheheartofoutowphysicsandthemechanismsresponsiblefortheirformation.Boththemechanismsandthecompositionareintimatelyrelatedanddeterminationofoneislikelytoclarifytheother.Belowweexplainthemainissuesinourpresentunderstandingofthemechanismsofjetformationandevolutionnecessarytoelucidatethesequestions. 29

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2-4 ).Itcomeseitherfromtheinnerdiskortheergosphereoftherotatingblackhole(BH).Theformationmechanismsandthecompositionofthejetplasmadependstronglyonthemagneticeld.Wediscussbelowbothscenario. OnlythecaseofamagneticeldcomingfromtheergospherecanexplainhighLorentzfactors( Meieretal. 2000 ; McKinney 2006 )butitisdifculttoimaginehowparticlescrosseldlinesandmixwiththePoyntinguxintheergosphere.Pairplasmaisappropriateinthiscontextbecausephotonsfromtheaccretingregioncanhaveenoughenergytocreatepairs.Theparticleenergyrequiredtoacceleratepairplasmaissmallcomparedtothemagneticenergyattheergosphere,andtheplasmacanbelaunchedwithahighLorentzfactor.However,thismodelcannotexplainsomerandomvariationsofthejetdirectionatrelativelylongdistancesfromtheformationregionneartheradiusoftheBHmagneticeld( Jorstadetal. 2005 ). Analternativetothismodelinvolvesmagneticeldsintheinnerdisk.Extractionofangularmomentumfromtheaccretiondiskismorelikelythroughamagneticconnectionbetweenthediskandthejetthanthroughmagneticeldsatthesurfaceofthecompactobject.NormalplasmaislikelyintheframeworkofthismodelsinceitseemsdifculttoproducepairplasmaabovetheKepleriandisk.However,thismechanismisveryinefcient,requiringverystrongmagneticeldsinthedisktopropelprotons( deGouveiaDalPino 2005 ). Progaetal. 2000 )butmaximumspeedsareintheorderof5104km=s.Thus,themostpopularmodelsinvolveaccelerationfrommagneticeldsaloneorincombinationwithcentrifugalorthermalforces.TheBlandford&Paynemodelisthemostfrequentlyinvokedscenarioproducingasteadyoutowbycentrifugalforcesandapoloidal 30

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Blandford&Znajek 1977 ; Lovelace 1976 ).Toroidalmagneticeldscouldalsoacceleratetheplasmabuttheowbecomesunstablefurtherfromthecentralcore( Uchida&Shibata 1985 ).Asfortheformationprocesses,themagneticeldsparticipatingintheaccelerationprocessesoriginatefromthecompactobjectorfromthedisk. Analternativetothemagneto-centrifugalandtheradiativemodelsisthethermalmechanism.Inthismodel,theaccelerationisproportionaltothesquarerootofthecoronatemperature.Acoustic/Alfvenwavesorelectriccurrentsdissipateatthehotcoronaaroundthecompactobject,creatingwavepressurethatacceleratestheplasma.Numericalsimulationssuggesttwoows( Koideetal. 2000 )whenthermalandmagneticaccelerationsarecombined.Pressuregradientsforcetheoutowtocollimate,complementingthemildcollimationinducedbythepoloidaleld. Marscher&Gear 1985 ).Despitethepredictionsoftheory,polarizationobservationsshow( Lister&Homan 2005 )thatmostoftheshocksareneitherparallelnorperpendiculartothejetaxisbutinbetween( Alleretal. 2003 ). Analternativetotheshockmodelisamodelofbullet-likestructures.Theseareseparate3Dentitiesembeddedinthecontinuumow,eachwiththeirownmagneticeld.Concerningtheglobalmorphologyofthecontinuumow,theglobalmagneticuxdominatesoverpressureandcentrifugalforcesatlongdistances.Theirmorphologyisthusrelatedtoinnerelectriccurrentsandthecollimationdependsonthemagneticeldstructure.Ifapoloidalcurrentexiststhetubecollimatesintoacylindricalshape.Otherwise,thetubeisaparabola( Chiuehetal. 1991 ; Heyvaerts&Norman 1989 ). 31

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Then,theinitialquestionbecomeshowthemechanisms,power,timing,Lorentzfactorandcompositionsscalewiththeaccretormass?Someworkssupportsimilaritiesbetweenthesecousinobjects( Poundsetal. 1995 ; Samsetal. 1996 ; Falcke&Biermann 1996 ; Heinz&Sunyaev 2003 ).Thepowerofthecentralenginescaleswithaccretionmassrate( Kordingetal. 2006 ),meaningthattheratioofaccretedmasspercompactobjectmassisscalefree.Timingpropertiesalsoscalewiththemassofthecompactobject( Uttleyetal. 2005 )andsimilarphenomenaarefoundinbothtypeofobjects,asforexampleX-rayQPOsintheXRBGRS1915andtheAGN3C120( Fender&Belloni 2004 ).RadioandX-raycouplingofthefundamentalplaneofBHactivity( Merlonietal. 2003 ; Falckeetal. 2004 )aswellasLorentzfactorscales( Miller-Jonesetal. 2006 )suggestthattheresemblanceextendstotheaccretingprocesses.Thesupplyofaccretedmattercomesfromdifferentsources,buttheformationofjetstakesplacenearthecompactobjectanditpresumablydoesnotcarryanimprintofthesourceoftheaccretedmaterial. Amaindifferencebetweenthesetwotypesofsourcesconcernstheenvironmentsinwhichthejetspropagate.XRBsarelocatedinmuchlowerdensityandpressureenvironmentsthanAGN,especiallyforlowenergysources.Theinterstellarmedium(ISM)aroundXRBsiscleanerthantheIGMaroundAGN( Heinzetal. 2006 )and 32

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Mirabel 1994 ),oraresurroundedbyaradionebulaesuchasW50aroundSS433( Dubneretal. 1998 )andCirX-1( Stewartetal. 1993 ; Fenderetal. 1998 ). Hence,asaresultofthesimilaritiesoftheirmorphologiesandtheirphysicsthereisahopeofunderstandingmechanismsinjetsbycombininginformationfrombothtypeofstellarobjects.Bycomparingtheirpropertiesweobtaininformationondifferenttime-anddistance-scales.AGNcanbeexploredwithVLBIandtheirvariabilitytimescaleisuptoyears.Insuchsources,wecanstudyshort(comparewiththescaleofthesystem)periodandstructureoscillations.UsingdatafromXRBs,wecanstudylongertermevolutionbecauseoftheiroverallshortervariabilitytimescale.Inourwork,wewillobservethemicroquasarSS433,aparticularXRB,tostudyjetformationprocesses.Inthefollowingsection,wedenetheseobjectscalledmicroquasars,andweexplaintheirgeneralpropertiesandhowtheycanhelptounderstandjetformationmechanisms. 2.2.1DenitionandPropertiesofMicroquasars Mirabel&Rodrguez 1999 ).Theyarebinarysystemswithacompactobject-eitheraBHoraNS-andanormalcompanionstarthatprovidesaccretingmaterialtothecompactobject.Thecompanionstartypedifferencesresultintwomajorclasses,namelylow-massX-raybinary(LMXB)andhigh-massX-raybinary(HMXB)systems.LMXBshavelowmasscompanionsofspectraltypelaterthanBandmasstransferusuallyhappensthroughanaccretiondiskviaRocheLobeoverow.Incontrast,HMXBshaveinefcientmasstransferthroughwindsfromamassivestar(>5MSun)orearlytypestar(e.g.Be). 33

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2-5 )arecapableoflaunchingjets( Homanetal. 2008 )butmoredataisneededinordertoconrmthishypothesis.Asexamples,theLMXBsCirX-1,1E1740-942,andGRS1758-258exhibitradioemissionassociatedwithrelativisticoutows.Partofthematerialfallingontothecompactobjectisejectedintojets,removingsomeoftheangularmomentumcreatedduringaccretion.Thejetaxisandtherotationaxisofthebinaryareusuallymisalignedwithrespecttoeachotherbecausethetimescalerequiredfortheiralignmentisgreaterthanthelifetimeofthesystem( Maccarone 2002 ).Tidaleffects,precession,nutation,andwarpingofthediskcanresultfromthismisalignment,creatinganinteractionbetweenthejetoutow,thediskandthestellarwinds. Thenamemicroquasarcomesfromtheresemblanceoftheseobjectstoquasars.AcatalogofgalacticXRBsispresentedby vanParadijs ( 1995 ); Liuetal. ( 2000a 2001a ).Itisestimatedthatthereareabout700XRBsbrighterthan21034erg=s( Grimmetal. 2002 ; Paredes 2005 )butonly130HMXB( Liuetal. 2000b )and150LMXB( Liuetal. 2001b )areknowninourGalaxy,someofwhich(4050)areradioemittingsources.However,onlyasmallfraction(15)arerecognizedmicroquasarswithresolvedjets(seeTable 2-1 )and Paredes ( 2005 )estimated,basedonthetotalnumberofluminousXRBs,thattherearenomorethan100microquasarsinourGalaxy.Thestudyofthissampleofmicroquasarsprovidesuswiththeopportunitytoobservethephysicsoftheirjetswithinahumanlifetimeandtounderstandthemechanismsoperatingaroundthecompactsourceoveralongperiodcomparedwiththesystemtimescale(betweensecondstoafewhundredofdays). Inaddition,microquasarsareGalacticsourcesthataredetectedacrossalargewavelengthrange.Observationsatvariouswavelengthrangesshowamoreextendedpictureoftheirjetsthantheoneobtainedfromonlyoneofthewavelengthranges.Forinstance,CygX-1emitsfromlessthan1GHzradiowavelengthtohigh-energy-rays.Forsomeofthesources,radiosynchrotronemissionextendstotheinfraredor 34

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Brocksoppetal. 2001 ; Fenderetal. 2001 ).Asanexample,asimultaneousIRandX-rayvariabilitystudyoftheuxfromGRS1915+105( Eikenberryetal. 1998 )concludesthatsynchrotronemission,insteadofdiskreprocessingoftheX-rayradiation,istheoriginoftheobservedIRemissioninthissystem(seeFigure 2-7 ). Geldzahleretal. 1983 )tofullyrelativistic(0.9c)asforGRS1915+105( Mirabel&Rodrguez 1994 )andGROJ1655-50( Tingayetal. 1995 ; Hjellming&Rupen 1995 ).Theirclassicationisverycomplicatedbecausecalculationsofphysicalcharacteristicsofthesesystemsarestronglyinuencedbymodels.Forexample,asimplecalculationofthepoweroftheoutowfromGRS1915+105dependsontheplasmacompositionwhichisasyetunknown( Fender&Pooley 2000 ).StudyingdifferencesbetweenthosemicroquasarscontainingNSandBHcouldprovidecluesabouttheoriginofthemagneticeldwhichpowersthejets.Forinstance,BHbinarieshavehigherradiotoX-rayuxratiothanNSbinaries( Fender&Kuulkers 2001 ).RadioemissionisbelievedtoreectefciencyinproducingjetswhereasX-rayemissionisrelatedtoaccretionpower.Thisdifferencebetweentheradio/X-rayuxratioofBHandNSbinariesmeansthatBHsystemshavehigherefciencywhenlaunchingoutowsofgas,orthatX-rayradiationpropagationislessefcientthaninthecaseofNSbinaries.AcleardifferenceofthemechanismformingjetsexistbetweenmicroquasarswithBHandNS.WewillseelaterthatthenatureofthecompactobjectofSS433,themaincharacterofthiswork,isunclear.Forthisreason,itisimportanttohaveinmindthewholerangeofpossiblescenariosinordertoconsiderallthepossiblepicturesforthissystem.Next,weexplaintheclassicationinbothcases,NSandBHaccretingcompactobjects. XRBscontainingNSaredividedintotwodifferentclassesdependingonthestrengthoftheirmagneticeld.Therstclass,X-raypulsarsarehighlymagnetized 35

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Fender&Hendry 2000 ).Lowmagneticeldsources(<109G)includetheZsources(e.g.ScoX-1,GX17+2andCirX-1)thataccretenearEddingtonlimit,andtheloweraccretingAtollsources.Bothtypeoflowmagneticeldsourcesexhibitsynchrotronradioemissionthatmaybevariable.RadioemissionisstrongforZsourcesbutfaintforAtollsources(exceptforGX13+1). Ontheotherside,microquasarscontainingBHareonlycharacterizedbytheirmassandspin.Thus,theirclassicationisbasedonthestatesofX-rayemission:softandhardstates.AllBHmaybeatsomepointoftheirlifeinanyofthesetwostates.Thehardstateisdominatedbyanon-thermalpowerlawwithamaximumvalueinthehardpartofthespectrum(>50keV).Conversely,weobserveinthesoftstatethethermalemissionfromtheaccretiondiskwhichpeaksatlowtemperature(0.11keV).MicroquasarssuchasCygX-1,GX339-1,1E1740.7-2942,andGRS1758-258spendmostoftheirtimeinthisstate.Ingeneral,microquasarsinthehardstatehaveradiocounterparts( Pooleyetal. 1999 ; Mirabel 1994 ; Rodriguezetal. 1992 ).Incontrast,radioemissionisweakerorevensuppressed( Tananbaumetal. 1972 )insoftstateBH.AmongtheseclassestherearealsotransientstatesassociatedwithoutburstsofBHchangingfromhardtosoft( Hjellming&Han 1995 ; Fender&Kuulkers 2001 ).JetsfromBHintransientstatestendtobesignicantlyluminousandfast(>0.9c),whileBHinhardstatesorNScreatemoresteadyjets. MicroquasarswithBHaregoodtargetstostudythejet-diskcoupling.Forinstance,themicroquasarGRS1915+105( Mirabel&Rodrguez 1994 )canbeinabroadrangeofstates( Bellonietal. 2000 )anditsradioemissionshowscomplexbehavior( Pooley&Fender 1997 )withcorrelationsbetweenX-ray,radioandinfrared( Eikenberryetal. 1998 )althoughitsradioemissionisquenchedinthesoftstate( Galloetal. 2003 ; Maccaroneetal. 2003 ).Multiwavelengthobservationsareessentialforunderstandingthedisk-jetconnectionbecauseemissionfromthediskandjetcannotbespatiallyresolved.Models 36

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Fenderetal. 2004 2005 )showastrongcorrelationbetweentheX-rayemission,theluminosity,andthevelocityoftheoutow,suggestingthatoutowsformatthetimethatthematerialofthediskgetsclosetothecenternearthecompactobject.Consequently,exploringthejet-diskconnectionisimportantforunderstandingjetformationphysicsandtheresultingvelocity,thecollimation,andthegasstructures( Brocksoppetal. 1999 ; Corbeletal. 2000 ).Forinstance,thestudyofthejet-diskinteractionregionofourtarget(SS433)isimportanttounderstandtheresultsoftheopticaljetofthissource(seeChapter 6 )andthus,wewillexplorethisregioninChapter 5 Celotti&Blandford 2001 ).Inaddition,thecontentofoutowsinmicroquasarswilldiffuseintotheISM( Heinz&Sunyaev 2002 ; Fenderetal. 2005 ).Therefore,itwouldnotbesurprisingthatthesejetscouldcontributetotheoriginoftheGalactic-rayradiation( Johnsonetal. 1972 ).WhereasWolf-Rayetstars,novae,gamma-raybursts,supernovae,anddarkmatterarepotential-raysources,jetsfromLMXBsarealsooneofthemaincandidatesfortheoriginof-rays,especiallyiftheirjetscontainpairplasma.AnnihilationfromplasmainteractionwiththeISMorthecompanionstarwouldcreateadiffuse511keVlinethatistoobroadenedfordirectrecognition. Guessoumetal. ( 2006 )estimateda1041e+=scontributionfromLMXBtothegalacticbackground.Itwillbeinterestingtoconrmthisresultbycalculatingthenumberofpositronsinrelativisticjetsofmicroquasars.Inparticular,wewilldiscussduringouranalysisthecontributionfromSS433topositronsinourGalaxy. Forinstance,-rayradiationisdetectedusingEGRETfromthemicroquasarsLSI+61303( Kniffenetal. 1997 )andLS5009( Paredesetal. 2000 ).Awiderangeofjetformationmodelsbasedonpairplasmaowsexist( Bosch-Ramon&Paredes 2004b a ; Bosch-Ramonetal. 2005 ; Dermer&Bttcher 2006 ; Romero 2005 )buttheirexistence 37

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Margon&Anderson 1989 ).Modelsoftwo-plasmaowssuggestajetwithpairplasmasurroundedbyanelectron-protonregionthatmaybedraggedbyphotonorelectromagneticinteraction.Investigationoftheproblemofthecontentofjetsourceswillshowwhethertheoriginoftheemittinggasisatthebaseoftheformationoftherelativisticjetorifthegasisjustdraggedbytheleptonicplasmachannelingtheoutow.OurresultsbasedontheobservationsofSS433willbeamainstaytorejectorconrmedthesethreemodels.ThedescriptionsofSS433inthenextsectionwillbenecessarytounderstandourresultsabouttheopticaljetsofSS433(seeChapter 6 )andthejet-diskinteractionregion(seeChapter 5 ). 2.3.1GeneralDescriptionofSS433 vandenHeuvel 1981 )throughanaccretiondiskfromitsopticalcompanionviaRocheLobeoverow.Partoftheaccretedmass(107Msun=year)isejectedintorelativisticandhighlycollimatedasymmetricjets.Jetsextendtodistancesof1017cmfromthecore.TheyemitfromX-raytoradiowavelengths.ThedistanceofSS433hasbeenveryaccuratelydetermined(DSS433=5.50.2kpc)byobservingtimevariabilityinopticalandradioobservations( Lockmanetal. 2007 ).ItissituatedintheGalacticplane(l=39.7,b=2.2).SS433isaredobjectwithbolometricluminosityof1040erg=s( Cherepashchuk 1982 ),higherthantheEddingtonluminosityofthesystem. Goranskiietal. ( 1998a )determinedtheopticalmagnitudesofthishighlyabsorbedsource(Av8mag)tobeV=14.0magnitudes;with(UB)=0.8mag;(BV)=2.1mag;(VR)=2.2mag.ItsspectrumpeaksintheUVrange. SS433hasbeenstudiedsince1979andithasremainedafocusofinterestintheastronomicalcommunityeversince,notonlybecauseitwastherstjetsourcediscoveredbutalsobecauseatpresentitsjetsaretheonlyonesknowntoexhibit 38

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2.3.3 ).Theemissionlinesareclearindicationsofbaryoniccontentinthejets,andtheirDopplershiftsallowustoderivewell-denedsystemparameterssuchasjetvelocity.SS433isanexoticsourcethatwillhelpustodisentangleobservationaleffectsfromthedisk-jetinteractionandthecompositionofrelativisticjets. Katzetal. 1982 )describesthiseffect,predictinga6-dayperiodicmodulationofemissionfromSS433;thisperiodisindeedobserved.Thisthirddynamicalmotioniscallednutationornodding.Inthissection,weexplaineachofthesethreemotionsandsomeofthepropertiesoftheemissionderivingfromthem. Crampton&Hutchings 1981b ),whichistheonlylinereectingthemotionofthecompactobject.OpticaleclipsesofHeII4686andH( Goranskiietal. 1998a ),andX-rayeclipses( Kawaietal. 1989 ; Brinkmannetal. 1991 )conrmtheresultingperiodfromthekinematicsoftheHeII4686line.Inaddition,thetimedelaybetweendiskandstareclipsessuggestsaquasi-circularorbit(e<0.05)thatisstableoverdecadesbyPorb<2107( Fabrika&Bychkova 1990 ).Theeclipseoftheaccretion 39

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Gladyshevetal. ( 1987 )ephemeris.Thiswillalsobeimportantforourmodelsofthejet-diskinteractionregion(Chapter 5 ),whichwillconsideracircularorbitandthe Gladyshevetal. ( 1987 )ephemeristocalculatethepositionofthemass-donorstarwithrespecttotherestofthesystem.Wewillexplainmoredetailsduringthedescriptionofthesemodels. 2.3.3 ).Thekinematicmodelofprecessionhasbeenwellstudiedbyseveralauthors( Margon&Anderson 1989 ; Eikenberryetal. 2001 )usingH,themostprominentofthejetopticallines(seeSections 2.3.3 and 6.1 ). TheprecessionisverystablewithPprec<5105( Eikenberryetal. 2001 ).Wedenethreetypicaltimesofjetlinedynamics.Twoconcerncross-oversoftheredandbluelinesinthespectrumwhenbothjetsareintheplaneofthesky(T1atprec=0.34andT2atprec=0.66).Thethirdoneisthetimeofmaximumseparationofredandbluelines(T3atprec=0)whenthebluejetispointingtowardtheobserver.WeemphasizethesetimesbecausetheobservedemissionfromSS433atthesecongurationswillhavespecialcharacteristics.Forexample,theprojectedvelocityofthejettothelineofsightatT1andT2isnull.WewillexplainandusesomeofthesepropertiesduringouranalysisinChapters 5 and 6 ThedynamicalmodelfromopticalspectroscopymatchesthebehaviorofX-rayjetlinessuchasFeXXVK(7.06keV)( Migliarietal. 2002 )andthenon-eclipsedbluelineofFeXXV(6.7keV)( Watsonetal. 1986 ; Stewartetal. 1987 ; Brinkmannetal. 1988 ),whichsuggestsagasvelocityof=0.26990.0007withahighkineticluminosity, 40

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Stirlingetal. 2002 ).Therefore,weconcludetwomainissuesthatwillbeimportantforourmodelsthatwewillexplaininChapters 5 and 6 .First,theowsoftheradio,optical,andX-rayjetsareintimatelyrelatedandhavelikelythesameorigin.Secondly,themodelofthedynamicsofthejetisconrmedatvariouswavelengthrangesandsomeofthepropertiesoftheopticaljetsmaybeextrapolatedfromX-rayorradiojets. Photometricvariabilityshowsthesameperiodsasthedynamicalmotionfromspectroscopyconrmingthedynamicalmodelthatwewilluseinouranalysis.Forinstance,themeanbrightnessofSS433oscillateswithamplitudesof0.5magnitudeattheprecessionalperiod( Kempetal. 1986 ; Gladyshevetal. 1987 ). Collins&Scher 2002 )suggeststhatthestarrotatesintheoppositedirectionoftheprecessionalmotion.Nutationandsemi-synodicperiodshavealsobeenobservedat3.9,7.7,11.2and21.7GHzandmodeledfromradioobservations( Trushkinetal. 2001 ).Thedirectionoftheorbitalandprecessionalmotionwillchangethecongurationofthegeometryandthus,theresultsofourdynamicalmodelsbasedontheemissionlines(seeSection 2.3.3 ).OurmodelswilltakeintoaccountthedirectionofrotationandincludetheeffectofthenutationofthediskofSS433whoseexistenceisconrmedfrom5GHz-408MHz( Stirlingetal. 2002 ). 2-6 ).Linescomingfromitsjetsarecalledmovinglinesbecausethey 41

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2.3.2 .Otherlinesarecalledstationarylinesbecausethevariationsintheirwavelengthpositionsaremuchsmallerthanthoseofthemovinglines.Smallshiftsandintensityoscillationsareduetothedynamicalbehaviorofthebinarysystem.AmongthemovingopticallineswendH,HandHthatare10timesweakerthantheirstationarycounterparts.Forinstance,thestationaryHlineisthemostprominentemissionlineintheSS433spectrum. Murdinetal. 1980 ; Crampton&Hutchings 1981b ).Blueabsorptioninsomelineproles(inparticularFeII)andP-CygniprolesinHeImovewithprecessionalandorbitalphasesaroundtheirrestwavelength.ThePaschen,HandFeIIlineshavedouble-peakedstructures.TheseparationofthesestructuresmatchesKeplerianvelocitiesexpectedfromtheaccretiondisk.TheHeII4686alsoshowsadouble-peakstructurethatblendswithaFWHM950km=scentralcomponent( Goranskiietal. 1997 ; D'Odoricoetal. 1991 ).Thedouble-peakstructuredisappearsattheprimaryeclipse.ItstypicalpeaktopeakseparationV1500km=sisfarfromtheKepleriandiskmotionvelocities.Wewillndinourworkadifferentexplanationforthisdoublepeakstructureandwewillcompareourresultsbasedonournewinterpretationandtheconclusionsoftheseauthors. Ingeneral,theintensityandtheshiftofthestationaryhydrogenandheliumlinesexhibitcomplexbehaviorduetothethreedynamicalmotions(precession,orbitandnutation)andthecomplexityofradiatinggeometries.Inaddition,physicalmechanisms 42

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2-8 .Presently,thereisnointerpretationtotheapparentrandombehavioroftheselines.Ourworkwillshowthattheposition(andmaybetheintensity)oftheselinesdependsontothemotionandgeometryoftheSS433. Grandi&Stone 1982 ).Theprolesoftheselinesareunpredictablebecausethematerialdoesnothaveahomogeneousdistributionalongtheopticaljetsanditsradiationisnotisotropic.Globally,eachproleiscomposedofabrightmaincomponent(FWHM1001500km=s)andoneortwosecondarycomponents.Movinglinesofbothjetsoscillatesymmetricallyaroundacentralposition(0)withmirroredproles.Theydisappearsporadicallyfromtheobservedspectrumatpassivestatesandappearagainattheirexpectedpositionwhenthesteadyoutowstartsagain. Flarescreatealsorandomvariationsofthewavelengthpositionofthesameorderasnutation.Theserandominstabilitiesrangeintimescalefromweektomonths,appearinbothquiescentandactivestates,andtheyarealsophotometricallyobserved( Goranskiietal. 1998b ).Presently,thereisnotanexplanationofthesearesbutthey 43

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6 Filippenkoetal. 1988 )arepresentlythebestmodels.WithourspectropolarimetryofSS433,weexpecttoelucidatethescenarioaroundthejet-diskinteractionregionandtherefore,itisnecessarytoreviewthecurrentunderstandingaboutthisregion.Below,weexplainthepresentmodelsofthewindsobtainedfromoptical,UV,andX-raydataandwetalkabouthowX-raydatasuggesttheexistenceofahotcoronaatthebaseofthejet,neartheaccretiondisk.Theseregionsmaybethesourceofdraggedmaterialasexplainedbysomejetformationmodels,especiallymodelswhereapairplasmaowdragsprotonsofthedisk.Wealsodescribethecurrentknowledgeofthemass-donorstarbecause,eventhoughifthestarisunlikelyparticipatinginthejet-diskinteraction,itwillbeimportantforourmodelsinChapter 5 tounderstandhowthestarcontributetotheobservedemission. ThebehavioroftheFeIIabsorptionlines( Fabrikaetal. 1997 )supporttheexistenceofaccretiondiskwindsbecausetheytendtoblueshiftasthediskprecessestofacetheobserver.Variationsinthephotometryandradialvelocitysuggestthepresenceofanabsorbingregion( Crampton&Hutchings 1981a )thatmayberelatedtotheseaccretionwindswhosepresenceisconrmedbythebehavioroftheX-rayandopticalux,which 44

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Dolanetal. 1997 )andwhichmayberelatedtoabsorbingmaterialowingperpendiculartothedisk.Theproleoftheowvelocity,withanglewindfromthediskaxis,obtainedfromHandHeIforarange60
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2.3.5.1EmissionofSS433jetsacrossthespectralrange:X-ray,radio,andopticaljets 2-9 )startingfromX-raythermalemissionofgasatT108Kwhichprogressivelycoolsdownasitexpandsandemitsinoptical,infraredandradiorangesasittravelsfurtherfromthecentralcore.Inthissection,wedenetheoptical,X-ray,andradiojets,inparticularwedescribethemainpropertiesnecessarytounderstandtheevolutionoftheowalongitspath. TheintensityoftheX-rayemission(110keV)is1036erg=s( Brinkmannetal. 1991 ; Kotanietal. 1996 ). Kotanietal. ( 1996 )calculatedtheinitialtemperatureoftheX-rayjetsbeforetheemissionlinesstart(1012cm)byttingtheparametersofamodeloftheplasmatothevalueoftheFeXXVKtoFeXXVIKratio(FeXXVK=FeXXVIK=0.480.1).Theyestimatedaveryhighinitialtemperatureof22keV,muchbiggerthanthetemperaturewheretheX-rayjetends(231013cm)whichis1keV.Assumingadiabaticexpansiontheopeninganglejet=2Cs=Vjet=1.230.06( Marshalletal. 2002 )oftheX-rayjetisgivenbythewidthofjetemissionlines.Theopticaljetsextendfrom1.51014cmto31015cm,emittingbyde-excitationofHandHeatomsatT104Kwhicharecontinuouslyheatedbysomeunknownmechanism.Theradiojetsextendtodistanceslargerthan1017cmfromthecompactobject,coincidingwith 46

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Hjellming&Johnston 1981 )decaysexponentiallyalongtheopticaljetanditisintensiedatthebrightnesszone( Vermeulenetal. 1987 1993 ).Itisbelievedthattheemissionisstrengthenedbyanincreaseofrelativisticparticles,buttheradioemissiondoesnotexhibitanysignoftheshocksthatwouldresultfromthismechanism.Itisreasonabletothinkthattheheatingmechanismalongtheopticaljetandphysicalphenomenainthebrightnesszonearecorrelated. Wenowconcentrateontheopticaljetsthatarethefocusofthisthesis.Narrow(11.5)opticaljetsappearbetween13daysafterejectionofthegas.TheseopticaljetsarethesourceoftheHmovinglinesthatarecontinuouslyemittingalongtheopticaljet,requiringacontinuoussourceofheating.Gaspropagatesintheopticaljetsataconstantspeedof0.26cinagreementwiththespeedofX-rayjets,withadecelerationalongtheopticaljets,surprisingly,smallerthan1%( Kopylovetal. 1986 ).SS433'sjetsareasymmetricandthetimedelaybetweentherecedingandtheapproachingjetisnegligible(0.2days)withrespecttotheerrorsinthekinematicalmodel.Thecompositionofandphysicalconditionsinthejetsthemselveshaveneverdirectlybeenobserved.Mostoftheresultsaremodeldependentorbasedonextrapolationsfromotherwavelengthrangesandassumptionsaboutthemechanismsfromwhichthelineprolesoriginate. 47

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Davidson&McCray 1980 ; Begelmanetal. 1980 ).Thermalinstabilitiesleadingtotheformationofthesecloudsarepredictedbysimulationsofconditionsatthebaseofthejet( Brinkmannetal. 1988 ; Kotanietal. 1996 ).TheseresultsagreewiththeHlineprolemodels( Panferov&Fabrika 1997a )whichimplyallingfactorof106atadistancefromthecentralsourceof1014cm.Computationalsimulationsofradiationthroughauniformlayerofgas( Drake&Ulrich 1980 )predictthepresenceofdense(1013cm3)cloudsofthissizeandllingfactor. Thesecondstructures,calledbullets,arebiggerandappearasfeaturesofthelineprole( Borisov&Fabrika 1987 ; Vermeulenetal. 1993 )withafrequencyof2-3perday.Ignitionofopticalemissionisfast(6-10h)comparedwiththewholelifetimeofthebullet.Afterignitiontheirlightcurvesobeyexponentialintensicationfollowedbyexponentialdecaywithamaximumintensityatadistanceof41014cmfromthecentralsource( Kopylovetal. 1987 ; Borisov&Fabrika 1987 ).Theirintrinsiclightcurveisanisotropic( Panferovetal. 1997 ; Asadullaev&Cherepashchuk 1986 ).Theanglebetweenthedirectionofmaximumradiationandthejetisabout35towardtheprecessionalmotion.Bulletextinctioncoincideswiththebrightnesszone( Hjellming&Johnston 1981 ; Romneyetal. 1987 ; Vermeulenetal. 1993 ).Thesymmetryofthebulletpopulationinbothjetsisconserved,buttheH=Hratiodecreasesasthegastravelsinthejet( Panferovetal. 1997 )indicatingadecreaseofatomdensity.Wewillbeusingthelightcurvemodelofthebulletstostudythepropertiesofthegasalongtheopticaljet. 48

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ThecaseofthemicroquasarSS433wasextensivelyexplainedbecauseitisatthebaseofthisthesis.Overthepast30yearsmultiwavelengthobservationshaveprovidedsomeinsightintothenatureofthesystem.Forinstance,itisrmlybelievedthatSS433isamicroquasar,andtheparametersdescribingprecessionofthedisk,orbitofthebinarysystem,inclinationofprecessionalandorbitalaxes,andspeedofthejetarewell-known.However,intheparticularcaseoftheopticalrange,eventhoughthebigamountofimagingandspectroscopydataofSS433,theparametersoftheopticaljetsandthejet-diskinteractionregionarenottotallyclear.Forexample,wedonotknowthegeometryoftheaccretiondisk,thestructuresandthegeometryofthejet,thepopulationdensityintheaccretiondiskandthejets,andthenatureofthestarsinthesystem. Inthefollowingchapters,wewillshowthatspectropolarimetryfromSS433couldbethetechniquewhichmaysolvetheseunknowns.PolarimetryofSS433alreadyexistsintheliterature.However,aswewillexplaininSection 3.2 ,resultsfrompreviousauthorsarelimitedbythefactthattheyarebasedonbroad-ornarrow-bandimagingpolarimetry.Weprovidetherstopticalspectropolarimetrywhichisthekeyforstudyingthegeometryandthedensityofopticaljetsandthedisk-jetinteractionregion.Thenextchapterexplainsthebasisofpolarimetry,ourspectropolarimetricdatafromSS433,andtechniquesusedtoextractinformationfromthesedata. 49

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CatalogofknownmicroquasarsinourGalaxy.(a)NS:neutronstar;BH:blackhole.(b)p:persistent;t:transient.(c)jetinclination.(d)Prec:precession;XRJ:X-rayjet.Credit:Table1by Paredes ( 2005 ). 50

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RadioobservationsofSS433from Jowett&Spencer ( 1995 )usingtheMulti-ElementRadioLinkedInterferometerNetwork(MERLIN)at5GHz.Thetopdiagramsshowcontourmapsoftheradioimagesthatareshowninthebottom.Knotsofthejetsareindicatedwithletters.ThesequenceshowtheevolutionoftheseknotswithrespecttothecentralcorethatisindicatedasCore 51

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OpticalsynchrotronemissionintheradiojetofVirgoA(M87).Theobjectisobservedasaonesidedjetduetotheboostingeffects.Credits:NASAandTheHubbleHeritageTeam(STScI/AURA) Astrophysicaljetformationscenarioswithmagneticelds.(A)Dipoleeldofanaccretiondisk.(B)Acollapsingobjectwithaslowlyrotatingdensestellarcore.(C)Accretiondiskwithpoloidalmagneticeldaroundacompactobject.(D)Magneticeldfromtheergosphereoftheblackhole.Credit:Figure4from Meieretal. ( 2000 ). 52

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DiagramofaLow-MassX-rayBinary(LMXB).ThediagramshowthemainpartsofaX-raybinarysystemastheaccretiondisk,themassdonorstar,andthejets.Thecompactobjectisnotlabeledbutitisatthecenteroftheaccretiondisk.Otherregionsthatareshownarethewindsfromtheaccretiondiskandtheregionwherethegasfromthestarow(accretionstream)andencountertheaccretiondisk(HotSpot).TheregionofX-rayheatingcorrespondtothesurfaceofthestarthatisradiatedbytheaccretiondisk.Credit:hea-www.harvard.edu/garcia/nerabam/ TypicalspectrumofSS433.ThespectrumwasobservedinMarch20th1979attheLickObservatory3mShanetelescope.Thestationaryandmovinglinesareidentiedwiththeirnames.Theprexes+and-ofthelabelsdenotestheredorblueemissionlinesfromthejets.Theselinescorrespondtoshiftsofz1=0.090andz+2=0.019.Thetelluricabsorptionfeaturesarealsoshown.Credit:Figure1of Margonetal. ( 1979 ). 53

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Plotsillustratingmultiwavelengthcorrelationofthejet-diskinteractionregion.ThegraphicsshowsixsimultaneousX-rayandIRobservationsofthemicroquasarGRS19151105.ThediagramshowcorrelationbetweenIRandX-rayaresthatpeakwithsametimeoffset.Credit:Figure2of Eikenberryetal. ( 1998 ). 54

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AverageofstationaryHvelocityprolesforvariousprecessionalphases.Thelineisplottedwithrespecttothecentroidoftheprole.Theintensityisscaledincontinuumunits.Eachproleislabeledwiththemeanprecessionalphase.Credit:Figure4by Giesetal. ( 2002b ) 55

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IllustrationofthejetsofSS433andthedynamicalmotions.Intheleftpanel,weshowajetpropagatingfromthecentralcorewithascaleofthedistanceswherethedifferentemissionofSS433jetshappen.Thebluesquareregioncorrespondstotheopticaljets.Intherightpanel,weshowthecoordinatesystemofthegeometrydescribingthemotionofthesystem.Creditofrightpanel:Figure1of Collins&Scher ( 2002 ) 56

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Themaingoalofthischapteristointroducethebasicconceptsofastronomicalpolarimetry,ourspectropolarimetricdataforSS433,thetechniquesweusetotthedata,andtheinitialresultsfromouranalysis.Westartthechapterwithsomebasicsaboutpolarimetrywhicharenecessarytounderstandthespecialissuesofthistechniqueandhowitwillcontributetosolvethequestionsposedinthisthesis.Inordertounderstandourdatawedescribetheobservationaltechniques,thedataanalysis,andthemeasurementerrorsofgeneralspectropolarimetry.Wereviewthephysicalmechanismswhichproducepolarizedlight,particularlyfocusingonThomsonscatteringasitislikelytoplayamajorroleinthepolarizationforSS433.OurspectropolarimetryisabletoseparateforthersttimethepolarizationoftheopticalemissionlinesdescribedinSection 2.3.3 .Theresultsofthischapterareessentialfortheanalysiswhichwepresentinthefollowingchaptersofthegeometryanddensityofthejet-diskandjetregions. 3.1.1TheoreticalConcepts 57

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3-1 ).Theelectricvectortracesanellipseinthe(~X,~Y)plane.Insomecasesofparticularinterest,oscillationsof~Earelinear(X=Y)orcircular(YX==2),andanymonochromaticwavemaybedecomposedintoacombinationoftwolinearly-polarizedortwocircularly-polarizedelectriccomponents.Classicalimagingorspectroscopyconsistsofmeasuringthetotalintensityofthetwoelectricvectorsversusthepositionontheskyand/orthewavelength.Withpolarimetry,weobtaintheintensityofeachperpendicularcomponent(E0X,E0Y)andtheirphaselags. Variousmathematicalformalismsexistinordertosimplifythestudyofpolarimetry.TheStokesformalismprovidesagooddescriptionoftheelectromagneticwaveviatheStokesvector~S=(I,Q,U,V)T.Iisthetotalintensity,whichismeasuredinclassicalimage/spectroscopymodes;QandUrepresentthelinearpolarization;andVrepresentsthecircularpolarization.TheStokesvectorandtheelectriccomponentsarerelatedasfollows: Theoverallfractionalpolarizationofelectricwavesisdenedas~p=(q=Q=I,u=U=I,v=V=I)T.Q,UandVarepartialmeasurementsoftheintensity,sotheStokesparameterssatisfytheSchwartzinequalityI2Q2+U2+V2(Poincareequation)or,writtenanotherwayjj~pjj1.I2=Q2+U2(orI=V)correspondstoapurelinearly-polarized(orcircularly-polarized)wave.Inthecaseoflinearpolarization,wedeneitsdegreeofpolarizationP=p 2arctan(u q). Inthegeneralcase,thewavedoesnotpropagateinavacuumbutinadispersivemedium,andMaxwell'sequationsare~5~E=@~B 58

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Here,wepresentanoverviewofthemechanismsproducingandchangingpolarization.Firstly,weexplainthreemechanismscreatingpolarizationduetolinearaccelerationofelectrons:Thomson,Rayleigh,andComptonscattering.Then,weintroducethemechanismsofpolarizationduetocircularmotion:cyclotronandsynchrotronradiation.WegiveabriefdescriptionoftheCerenkoveffectwhichinvolvespolarizationfromnon-acceleratedparticles.Finally,wedescribeFaradayrotationand 59

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3-2 ).Theelectromagnetictheorypredictsradiationbyanoscillatingparticle,withintensityproportionaltotheprojectedoscillationsintheplaneperpendiculartothelineofsight.Accordingto Jackson ( 1975 ),theelectriceldemittedbyanacceleratedchargedparticleintherelativisticregimeis: where0isthepermissivityoffreespace;=1~n~isthefactorthataccountsfortheparticlemotion;Risthedistancefromthechargetotheobserver;~nistheunitvectordirectedfromtheparticletotheobserver;and=v=cisthevelocityoftheparticlerelativetothespeedoflightc. Therearetwoeffectsduetotherelativisticmotionoftheparticle:theeldisevaluatedataretardedtimetret=ttwithrespecttotheemissiontimetbecausethepropagationdelayt=R=coftheelectricwaveisnotnegligiblecomparedtothetimescaleoftheparticlemotion;andtheangulardistributionoftheradiationdependsonthespecicrelationshipbetweenthevelocityandtheacceleration.Forinstance,thefactorisexpressedintheretardedframeas=1+1 dt( Jackson 1975 ). Weconsideraparticlehavingintheobservercoordinatesystemaposition~r,avelocity~r=c~,andanacceleration~r=c~asfollows, ~r=x~Xmot+y~Ymot+z~Zmot ~r=x~Xmot+y~Ymot+z~Zmot 60

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Therefore,theEquation 3 oftheelectricvectoriswritteninthe(~X,~Y,~Z)coordinatesystemas, Intheparticularcaseoflinearaccelerationalong~Zmot,Equation 3 isstronglysimpliedbecause~k~(seeEquation 3 ).Foranoscillatingchargewhosemotionisrepresentedbytheequations(x(t)=0;y(t)=0;z(t)=z0ei!0t),theStokesvector(seeEquation 3 )inthecoordinatesystemofthepropagationisasfollows, 6!!400BBBBBBB@11001CCCCCCCA(3) Thomsonscatteringisaparticularcaseofoscillatingchargedparticles(seeEquation 3 )whosevelocityremainsnon-relativistic(!1).Aparticlethatisexcitedbyanelectromagneticwaveoscillatesintheplaneperpendiculartothepropagationdirectionoftheinputwave.Theaccelerationamplitudeoftheoscillationsisproportionaltotheincomingwaveamplitudeandtothecharge-to-massratio(!20z0/e mk~Ex,yk).Infact,aninputelectricwave~Excreatesanelectricforce~Felec=e~Ex,creatingamotionoftheparticlethatisdescribedbyNewton'slawmx=Felec. 61

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3 .ThomsonscatteringismathematicallyrepresentedbythefollowingMuellermatrix, whereT=8 Insomecases,electronsofanatomalsocreateanelasticdispersionofincidentphotonswithoutionizingorexcitingtheatom;thisiscalledRayleighscattering.Inthatcase,thescatteringcross-sectiondependsontheincidentradiationenergyandtheatomicnumber,decreasingas/4. Comptonscatteringtheorywelldescribesthescatteringofthephotonwhentheenergyoftheattachedorthefreeelectronsisofthesameorderastheincidentradiation.Atincidentphotonenergiesbetween50keV10MeV,themomentumexchangebetweenelectronsandphotonscannotbeneglected.Thephotonlosesenergyas wherehoutandh0arepost-andpre-scatteringphotonenergyintheelectronrestframe. 62

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dt=e~~Bresultsinacircularperiodicmotionthatintherelativisticregimehastheangularfrequency!C=eB Theenergyspectrumwouldbeasinglelineatthegyro-frequencyC=2!Cbecausetheelectriceldvariationsaresinusoidal.However,thepoweroftheemissiondependsontheangleoftheaccelerationoftheparticlebecausetheradiationisboostedbyafactor2inthedirectionofthemotion.Furthermore,theemissionisstronglybeamedalongthesamedirectionwithinaconeofhalf-angle1 Rybicki&Lightman 1979 ). ThecriticalfrequencyofthesynchrotronemissionisS=42BMHz.TheenergyofthespectrumdecreasessharplybelowCandthecriticalfrequencyaccountsfortheenergydistributionofthespectrumthatpeaksatpeak=2.82BMHz(seeFigure 3-4 ). ThepositionofanelectronatatimetturningatafrequencySinthecoordinatesystem(~Xmot,~Ymot,~Zmotk~B)is(x(t)=acos!t,y(t)=asin!t,z(t)=0).Theelectriceldradiatedduetothecircularaccelerationaround~BisobtainedusingEquation 3 .Finally,thesynchrotronradiationisdescribedbytheStokesvector: 63

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TheenergyradiatedbytheelectronswithspeedinamagneticeldofenergydensityUBisWsynchr=4c Ginzburg 1979 ). ItiscommoninnaturethatsynchrotronandComptoneffectscombineinmagnetizedrelativisticplasma.Inverse-Comptonscatteringbooststheobservedsynchrotronradiation.Thiseffect,calledSynchrotronSelf-Compton,happenswhenthelightisscatteredbythesamerelativisticelectronsthatproducedthesynchrotronradiation.TheelectronsbecomeopaquetotheirownradiationincreasingtheirtemperatureTe=mec2 Readhead 1994 )whereTmistherest-framebrightnesstemperature. 6.2.2 ).TheCerenkovradiationoccurswhenthevelocityvpartoftheparticleisgreaterthanthephasevelocityc nofthemediumofrefractionindexninwhichtheparticlemoves(seeFigure 3-5 ).Ithappensbecausetheelectriceldofthemovingparticledisruptsthepropagationmediumandtheelectronsofitsatomsaredisplacedandpolarized.Theradiationoccurswhentheelectronsofthemediumrestorethe 64

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whereeistheelectricchargeoftheparticlethatpropagatesinthemedium. dt=e~Ee c~v~B.Aninputcircularpolarizedwave~E(t)createsamotionoftheelectron~v(t)=ie m(!+!C)~E(t)thatvarythephaseofthewave.Theparameterisdifferentforright-(=+1)andleft-handed(=1)polarizedwave.TheFaradayrotationresultsfromthedifferenceoftheleft-andright-handedmodes.Anylinearlypolarizedwaveismathematicallyequivalenttothesuperpositionofaleft-andaright-handcircularlypolarizedwavesofequalweight.Theangleofrotationofthewavedependsonthewavelength,theopticalpathofthewaveLintheplasma,themagneticeld,andtheelectrondensityneasfollows, Faradayrotationconvertslinearpolarizationtocircularpolarizationbecausethecomponentsofalinearlypolarizedwavechangetheirphaseasitcrossesthemagnetizedplasma.Inaddition,theintegrationofthelightthroughvariousopticalpathsresultinanapparentdepolarizationduetothecancellationoftheemissionarisingfromdifferentdirections.Thiseffect,calledFaradaydepolarization,isthe 65

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m.FaradaydepolarizationisrepresentedbythefollowingMuellermatrix, Depolarizationeffectsaredominatedbyelectronsandpositronsbecausegandpareinverselyproportionaltotheparticlemassm.However,apureelectron-positronplasmadoesnotcreatedepolarization.Infact,Faradaydepolarizationdependsontheparticlecharge(g/e).IftheMuellermatrixoftheelectronisgivenbytheEquation 3 ,wherethetermgispositive,theMuellermatrixofthepositronis, TheeffectofaplasmawiththesamenumberofelectronsandpositronsisgivenbythemultiplicationoftheMullermatricesoftheelectronandthepositronswhichistheunitmatrix. 66

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ADouble-BeamSpectropolarimeter(DBS)isaninstrumentthatmeasurespropertiesofboththeordinary(o)andextraordinary(e)raysinasingleshot(seeFigure 3-1 ).Themostversatiledesignconsistsofaspectrographwithasplitterelementinthepupilplanethatdeviatesoandecomponentsandaretardernearthetelescopefocalplane.Commonretardersarehalf-waveplates(HWPs)andquarter-waveplates(QWPs).QWPscreatea1=4wavelengthphaseshifttransformingcirculartolinearpolarization.Itallowsthemeasurementofcircularpolarizationwithinthesameopticalsystem.AHWPcreatesahalfwavelengthshiftthatrotateseachlinearcomponentwithrespecttoareferencepositionbytwicetheangleofthefastaxis.AHWPattheentranceoftheinstrumentrotatesthecoordinatesysteminwhichthelightissplit.AWollastonPrism(WP)isusedtoseparateoanderays.ThisopticaldeviceconsistsoftwocementedprismsofanglePthataremadeofbirefringentmaterialandhavetheirfastaxesperpendiculartoeachother.Theseprismshavearefractiveindexdifferencen=nenobetweenoandethatdeviatesbothbeamsinthepupilbyanangle=ntanp,creatinganimageofeachraySe()andSo()atsymmetricpositionsonthedetector.Wecallthesetwoimagestopandbottom.Similarly,inspectroscopymodeweobtainatopandabottomspectrum. MeasurementofoandewithaDBSat=0givestheIandQStokesparametersinthecoordinatesystemoftheWP.Anadditionalmeasurementat=22.5isrequiredtogettheinformationgivenbytheUStokesparameterofthephasedifferencebetweenorthogonalcomponents.Intheory,thesetwomeasurementsgivealltheStokes 67

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3-3 ).Usingthesefourmeasurementswith=0,=22.5,=45,and=67.5thatresultin8spectraSo,e(0),So,e(22.5),So,e(45),So,e(67.5),thegaindifferencesbetweenoandeimagesduetoopticalorelectroniceffectscanberemovedfromthecalculatedStokesparameterswhentheyarecombinedasfollows: (3) (3) Asforregularimageorspectroscopymodes,polarimetricdatamayincludemultipleexposures.WedeneNasthenumberofexposures.Eachexposurei2[1,N]ofpolarimetryobservationsmustincludeallthe8spectraSo,e(i)(0),So,e(i)(22.5),So,e(i)(45),So,e(i)(67.5).Forsteadysources,theyarecombinedinordertoincreasethesignal-to-noise.Polarimetrydatamaybecombinedintwodifferentways.ArstapproachistocombinethespectraSo,e(i)foreachbeforecalculatinganyoftheStokesparameters.Weassumethat,nqk(i)=So(i)(0)Se(i)(45),nq?(i)=Se(i)(0)So(i)(45),nuk(i)=So(i)(22.5)Se(i)(67.5),nu?(i)=Se(i)(22.5)So(i)(67.5).nkandn?correspondtothenumberofcountsofthewaveintwoperpendiculardirectionsinthesky.Eachspectrumhastobecorrectedbyascalefactoraithataccountsforthedifferencesintheairmassesandtheexposuretimesbetweeneach 68

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Hence,theerrorsofthescalefactoraffectthenalresultandcanintroduceundesiredfeaturesinthedata. ThesefeaturesaremostlyremovedfromtheindividualexposuresusingEquations 3 ,and 3 .Therefore,amorereliablemethodconsistsofcalculatingtheqanduofeachframeiandthencombinetheresultingnormalizedStokesvectors.TheStokesvectorresultingfromthecombinationofalltheframesis: Todemonstratetheefciencyofthetwomethods,weinvestigatetheeffectonthenalmeasuredqanduusingEquations 3 3 3 ,and 3 withPoissoniannoiseintheobserveddata.Theerrorpropagationformulagivestheuncertaintyf(x1,x2,...,xn)ofnaldataf(x1,x2,...,xn)resultingfromthecollectionofparameters(x1,x2,...,xn).Thetotalerror2f(x1,x2,...,xn)=Pni=12i@f(xi) 69

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Inthecaseofframeswithsameexposuretimeandsamesignal-to-noise,wecanassumethatq=qiandI=Ii.Inthiscase,theratio1 whereMdet,Mspec(),Mpol(),Mtel,andMatmarethetransferlinearfunctionsofthedetector,thespectrograph,thepolarimeter,thetelescope,andtheatmosphererespectively.TheMuellermatricesoftheinstrumentdependontheangleoftheHWP(seeSection 3.1.3 ).Below,weexplaintheimpactofthesesystemsontheobservedpolarization. 70

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delToroIniesta 2003 ), Thecontributionoftheskybackgroundmustberemovedfromdataatthebeginningofthereductionprocessbecauseitintroducesnon-negligiblepolarization. Ontheotherhand,theeffectsofpixelgainuctuationsbetweenframesonthemeasuredpolarizationarenegligibleifthegainofapixelq(t)=q0+q(t)atagiventimevariesslightlyaroundq0. delToroIniesta ( 2003 )estimatedthattheeffectofthegainuctuationcomparedwiththeeffectoftheatmosphereisabout102q=q.Thus,forreasonablystabledetectors,thatisthegainuctuationslowerthanthegainitself,itisnotnecessarytoapplyanycalibrationcorrectingthegainuctuationsofthepixels. 71

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7.4.4 TheIPfromthetelescopecomesmainlyfromreectionsfromtiltedsurfacesandpropagationthroughmaterialsthatbecomebirefringentduetomechanicalstresses.Mostoftheeffectsofthetelescopeareremovedusingthestandardpolarizationcalibration.However,cross-talktermsoftheMuellermatrixofthetelescopecancontributetomodifytheobservedlinearpolarizationofasourcethathasalsocircularpolarization.Thesetermsaregenerallyverysmallandwecanignoretheireffects.Nevertheless,accuratemeasurementsorobservationsofhighcircularly-polarizedsourcesrequiretomeasuretheMuellermatrixofthetelescopethatcanbeperformedbyobservingastandardstarwhichhaspurelycircularpolarization. Themainpolarizationerrorfromthespectrographcomesfromthedifferencesbetweenblazeangledistributionsofthetwoorthogonalcomponents~Exand~Ey.TheeffectsfromthespectrographaremostlyremovedusingEquations 3 ,and 3 .However,anaccuratestudyrequiresmeasuringparametersB,and1,2<<1ofthe 72

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Equations 3 ,and 3 alsoremovemostoftheeffectsfromthepolarimeter. Patat&Romaniello ( 2006 )describedanadditionalcalibrationofthepolarizationmeasurementsthatremovestheresidualpolarizationfromthepolarimeter.TheopticalelementsofthepolarimeterintroducemeasurementerrorsthatdonotalwaysfollowaGaussiandistributionandaparticulartreatmentisrequiredfortheHWPandtheWP.TheerrorsinducedbytheHWPcomefromachromatism,inhomogeneouslydistributeddust,defocus,pleochroism,andwavelengthfast-axisdependence.Ontheotherhand,theerrorsfromtheWParisefromdifferenttransmissionsofoandebeams,defocusandblurring.Weusedthetechniqueof Patat&Romaniello ( 2006 )tostudytheeffectsoftheDouble-BeamSpectrographatPalomarObservatorythatweusedtoobserveourdata(seeSection 3.3.2 ).Wefoundthattheerrorsinthemeasurementduetotheseeffectsarelowerthan0.5%.WeplantousethesametechniqueandtheEquation 3 tocharacterizethepolarizationofCIRCE(seeSection 7.4.4 ). 73

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Davis&Greenstein 1951 ).Galacticgrainsscatterradiation,creatingpolarizationasafunctionoftheiropto-magneticpropertiesandtheirdensity.SpectropolarimetricmeasurementsoftheISPinthevisiblerangefollowsSerkowskii'slaw( Coyneetal. 1971 )describedbytheempiricalformula Coyneetal. 1971 )butitislinearlyrelatedtomax( Wilkingetal. 1982 )atlongerwavelengths.ISPmeasurementsaretypicallyconstantontimescalesofafewyearsandonlyvaryspatiallyfromstartostardependingonthedirectionoftheobservation.Thus,theISPmaybedeterminedfrompolarizationoftheeldstars.However,theISPdependsonthedistanceofthestarswhichareusuallynotwellknown. 3.2.1PreviousPolarimetryObservations Hjellming&Johnston ( 1981 )measuredanon-thermalpower-lawspectrumcomingfromsynchrotronradiationofthejets,and Seaquistetal. ( 1980 )observedadecreaseoftheradiouxofSS433atfrequencylower 74

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3.1.2.2 ).ThecircularradiopolarizationlevelinSS433radiojetsis0.36%at1-9GHz,indicatingmagneticeldsontheorderof50mG( Fenderetal. 2000 )whichcouldbehigheriftheoriginalemissionweredepolarizedbyjetplasma. Liebertetal. ( 1979 )foundnocircularpolarizationoftheopticalmovinglines,implyingtheabsenceofamagneticeldgreaterthan105Gintheopticaljets.Linearpolarizationfromtheopticaljetshasnotbeenreportedpriortothiswork. McLean&Tapia ( 1980 ); Dolanetal. ( 1997 )observedopticallinearpolarizationinthedirectionofSS433usingbroadbandlters,aswellasnarrow-bandlterscenteredonstationarylines.Thevariabilityofnarrow-andbroad-bandimagingpolarizationfromSS433suggestsintrinsicpolarizationfromtheobject.ThomsonscatteringisproposedtobethemostlikelymechanismproducingtheobservedlinearpolarizationintheaccretiondiskandthewindsofSS433.Ontheotherhand,UVpolarizationfromSS433inbroad-bandltersishigherthantheopticalpolarization( Dolanetal. 1997 )suggestingthatRayleighscatteringmaybepresentinadditiontothefree-electronscattering. However,itisnotpossibletodirectlyseparatethepolarizationfromdifferentoriginsinSS433frompreviousdatasincetheyarebasedonbroad-bandpassimagingpolarimetryratherthanspectropolarimetry.Moreover,theintrinsicvalueofthepolarizationisnotclearyetbecauseoftheuncertaintiesinthecalculationoftheISP.Usingnearbystars, McLean&Tapia ( 1980 )ndISPofmax=5500A,Pmax=1.5%2.7%andISP30. Dolanetal. ( 1997 )alsondsimilarresultsfrombackgroundstars(Pmax=2.10.6%,ISP=1010andmax=5240A). Emovetal. ( 1984 )estimatetheISPbycombiningzero-orderQandUvariationofthepolarizationinIlterandthepolarizationinUBVRIbands.TheresultingISPby Emovetal. ( 1984 )(Pmax=4.690.2%,ISP=3.62.8andmax=5860A)divergesfromtheotherworks. 75

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( 1984 )deducedtheintrinsicpolarizationfromthestudyoftheperiodicvariationsofthepolarization.Theorientationofthepolarizationandthevariationsofthepolarizationanglegiveinformationaboutthegeometryofthesystem.However,abadISPcorrectionmaychangetheintrinsicpolarizationangleandthustheconclusionsabouttheoriginofthescatteringregion.Forinstance,theirresultingISPlawonlytsRandIlterswell,andU,B,andVuxesarelowerthanexpectedfromtheirmodel.Inaddition,theyassumethattheintrinsicpolarizationfromSS433doesnotdependonthewavelengthwhichisinconsistentwithUVpolarizationobservations( Dolanetal. 1997 ).Thusweseethattheirresultsarebasedonpoortstothedataandwrongassumptionswhichhaveastrongimpactontheirconclusions,andthereforewedonotconsidertheirISPresultsinourwork.However,wediscussandusetheiranalysistechniqueinSection 5.2 becausetheirmethod,ifproperlyimplemented,canprovidegoodinformationofthegeometryofthesource.FindinganaccuratevalueoftheISPisacriticalissuebecausewithoutitwecannotinfertheintrinsicpolarizationfromthesystemandthereforethegeometryand/orthepopulationdensityofscatteringregionsofthediskandthejets.WediscusstheISParoundSS433furtherinSection 5.2 McLean&Tapia ( 1980 )calculatedtheelectrondensityoftheaccretiondiskfromtheintrinsiclevelofpolarization.ThelevelofpolarizationfromThomsonscatteringisproportionaltotheelectrondensityofthescatteringregion.Thus,errorsintheISPresultsinthemiscalculationoftheelectrondensity.TypicalvaluesoftheISParePmaxequaltoafewpercentandmax6000A.Forthesevalues,variationsoftheestimationoftheintrinsicpolarizationlevelofSS433areabout0.2%,resultinginuncertaintiesintheestimationoftheelectrondensityof<10%.However,therearetwoothersourceoferrorsthatarenotnegligibleandaffectconsiderablytheresultsfromallpreviousauthors.Themostimportantconcernsthefactthattheirimagingpolarimetrydoesnotdistinguishthecontributionfromvariousregionsofthesystem.Secondly,theyassumethatphotonsscatteronlyoncebeforeleavingthescatteringregion.Becausemultiple 76

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3 ,theseauthorsignoretheeffectsofthesystemgeometryinthenalpolarization.Theseerrorshaveconsequencesontheirnalvaluesbuttheirconclusionsremainvalid.WewillusetheirresultsaftercorrectionoftheirdatawiththeISPthatweobtainedfromourspectropolarimetrybelow(seeSection 5.2.1 ). 3-6 ).Theelectrondensitydistributionisthelocaldensityofelectronswhichissituatedatananglewithrespecttotheaxisofsymmetryofthegeometryandadistancerofthescatteringsourcefromtheinitialemissionregion.Weusetheparameter=costosimplifythecalculations. Brown&McLean ( 1977 )studiedthepolarizationoflightoriginatinginapointsourceandscatteredbyopticallythinandaxis-symmetricregions.Theresultingpolarizationdependsonthedensitydistributionanthegeometryasindicatedbythefollowingequation: 32TZZn(r,)drd Theshapefactorrepresentsthecontributionofthesystemgeometrytothepolarization.Therefore,theseequationsaccountfortherelationshipbetweenthepolarization,thegeometry,andtheelectrondensitydistributionasexplainedabove. ItislikelythatthepolarizationregionsinSS433includedisk-likeandpolar-likegeometries(i.e.accretiondisks,outowsandjets).Thepolarizationofscatteredlightinjetscanbeapproximatedasarisingfromthepolarizationbyasingleelectronmoving 77

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Brown&McLean 1977 ).SincewewishtoconsiderpolarizationduetoscatteringintheSS433jetsand/oraccretiondisk,weassumejet-likeanddisk-likegeometrymodels;thatis,anannularcylindermodelofinnerradiusR1,outerradiusR2andheightH(seeFigure 3-6 ).Thefactorisexpressedintermsofinnerradiusunits(=R2 R1)as, Thetypicalvaluesofthe-factorarebetween0and1.Forexample,thevalueof-factorofaninnitelythinaccretiondiskis0.Ontheopposite,aninnitelylongstructurewouldhavea-factorof1=2. Wenotethattheobservedpolarizationdependsontheopticaldepthofthescatteringwhichchangesthenumberofscatteringsofthephoton.Thepreviousanalyticalsolutionisbasedonopticallythinregionswithsymmetricdensitydistribution.Theanalyticalsolutionsofsystemswithcomplexgeometriesanddensitydistributionsareveryhardtodetermine.ThepolarizationresultsincomplicatedscenariosthatrequireMonte-Carlosimulationsandradiativetransfermodels( Goosmannetal. 2007 )toderiveinformationaboutthesystem.Inputstosuchsimulationsincludethesize,theshape,andthedensityofthescatteringandtheemittingregion;thepositionoftheregionsin3Dspace;theemittedspectrumpower;andthewidthandintensityoftheemissionlines.Theseresultinmultipledegeneratesolutionsforthegivenobservedpolarization.Additionalhypothesesaboutthesystemarenecessarytocomputethesemodelsandtondphysicalmeaningfulsolutions. ThecurrentunderstandingofSS433doesnotprovidesufcientconstraintsonSS433tocalculatethegeometryofthesystemusingMonte-Carlosimulations.Ontheotherhand,theassumptionsaboutthescatteringregionsoftheanalyticalmodelarereasonable:axis-symmetricandopticallythinscatteringregions.Firstly,thenatureofSS433suggest,exceptforsomeparticularregions,thatthescatteringregionscanbe 78

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3-3 ). WewillusetheanalyticalmodeldescribedaboveforthestudyofthegeometryandthedensityofthescatteringregionsinSS433accretiondiskandjets.ThisanalysisisbasedonthepolarizationofthefeaturesintheSS433spectrumdescribedinthefollowingsections.Therefore,wewillbeabletoapplytheanalyticalmodeltoeachindividualregionsofSS433becauseourspectropolarimetryseparatedpolarizationcomingfromdifferentregions,contrarytothepolarimetryusedbypreviousauthors.Moreover,wewillcombinetheinformationfromlinesandcontinuuminordertocalculateanaccurateISPthatwewillusetocorrectpolarizationdataofpreviousauthorsandhaveamoreaccurateunderstandingofthesystem. 3-1 summarizesthedata.SpectropolarimetrycanresolvethepolarizationofeachsourceofemissiongivingdetailedinformationabouttheemittingorthescatteringregionsandamoreaccurateISPvalue.Importantly,theseobservationscoverarangeofprecessionalandorbitalphases.Wewillbeabletocomparetheobservedpolarizationatdifferentorientationsofthesysteminordertoinfertheoriginofthescatteringregions.Westartthissectionby 79

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3-7 )showsinputparametersdeningthereductionandtheresultingdataateachstepoftheprocess.TheseparametersdenehowSo,e(0),So,e(22.5),So,e(45)andSo,e(67.5)areextractedfromroughimages.Theextractionprocesslookslikeregularspectroscopicreductionbutweextracttwospectraperimageinsteadofone.TheaperturesizeusedtoextractthespectraandtheskyofeachsetdependsonthePointSpreadFunction(PSF)oftheimage.Thebadpixelremoval,theat-eldcorrection,andtheskysubtractionstepsarestillthesameasforregularspectroscopy.Theprogramsavestheparametersofreductionandresultingdataateachstepinalogle.ThispipelinereturnsthepolarizationfollowingtheprocessexplainedinSection 3.1.3 thatconsistsofcombiningeachsetof8spectratoobtainthenalpolarizationvector.Then,thepolarizationiscalibratedandcorrectedfromIPwhentheparametersofthestandardpolarizationstarsareintroduced. Thesoftwaregraphicalinterfaceisdividedintotwopanels(seeFigure 3-7 ).Therightpanelhasthreetabs:Actions,Images,andDirectories.ButtonsstartingeachofthereductionstepsareshownintheActionstab.Imagestabincludethewavelengthrangedenitionsinwhichtheuserdecidetoapplyallthetreatmentstothespectra.Thethirdbuttonincludesinformationofthedirectorieswheretheimagesaresavedateachstepofthereductionprocess.Theleftpanelincludesheighttabs.Sixtabs,calledprocesstabs,deneparametersnecessaryduringtheprocess:Images,BadPixels,FlatFields,Wav.Calib.,SpcExtraction,andPolarization.TheDisplaytabshowspectraorimagesduringtheprocessinordertovisualizeeachstep. 80

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Theparametersofthereductionprocessareintroducedintheprocesstabs.Theparametersthatarerequiredforthereductionofspectropolarimetryweredenedbyrstreducingmanuallyourdata.Forinstance,mostoftheprogrammingproblemsduringthereductioncamefromdenitionsofbadrows/columnswithdeadorsaturatedpixels.Theseregionscreateintheresultsprogrammingerrorsoraddarticialfeaturestothenaldata.Theparametersdeningthereductioninvolvethebadrows/columnsintheinitialimageandtheatelds;thepixelareasoftheateldcorrection;thewavelengthrangeofthewavelengthcalibration;theslitsrangesofspectrumextraction;andthewavelengthrangeofthepolarizationcorrection.Thenamesofthetles(images,ats,lamps,andpolarizationstandards)arealsodenedintheinputparameters. Thetasksofbadpixelcorrection,ateldcorrection,wavelengthcalibrationandspectrumextractionweretestedintwoways:(1)wecomparedmanualandautomaticresultsofourdata;and(2)usingsyntheticimages.Weveriedthatthesefunctionsperformedcorrectlytheexpectedrole.Functionscarryingoutpolarizationcalculationandcorrectionweretestedusingcalibrationstandardsofourobservations.Aftertestingtheproperoperationofthesoftwareweusedittoreducethedataandndtheappropriateparametersgivingtheoptimumsolutionofthereduction.Wepresentthedatainmoredetailedbelow.Thedatasetsarechronologicallynamedbuttheyaredividedintwogroupsdependingontheinstrumentusedfortheobservation.TherstgroupweconsiderD2,D3,D4,andD5wasobservedwiththeDouble-BeamSpectrographatPalomar(DBSP).Thesecondgroup(D1andD6)wasobservedbyourcollaboratorsGarySchmidtandPaulSchmidtwithSpectroPOLarimeter(SPOL).Foreachgroup,thefollowingsections(Sections 3.3.2 and 3.3.3 )explaindetailsoftheobservationandthereductionprocess. 81

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Oke&Gunn 1982 ).DBSPisatwo-channellow-resolutionDBS(seeSection 3.1.3 ).Weuseda316lines/mmgratingatrstorderandablazewavelengthof7500Aand2slit,providingaresolutionof4.9A=pixelover55008060A.Twodatasets(D2andD3)correspondtoJune9thandtwoothers(D4andD5)toJune10th1999withatotalintegrationtimeof2290sandseeingof1.8/2ontherst/secondnight.Thepolarizationismeasuredintheinstrumentcoordinatesystemwhichisrotatedwithrespecttothesky.Theangleofconversionbetweenbothcoordinatesystemsisrelatedtotheangleoftheinstrumentrotatorringatobservationtime.Eachsetcorrespondstoaspecicorientationoftheinstrument:0forD3/D5setsandunknownorientationforD2/D4. WavelengthcalibrationswereperformedusingaNeonlamp.Thelampproducesemissionlineswhosewavelengthhavebeenfoundinthelaboratory.ThemostextensivecatalogofthisexperimentaldataistheNISTAtomicSpectraDatabase(ASD).Werecordedthepositioninthedetectorofthelinesthatweobservedfromthelamp.Therefore,weobtainedforsomepositionsalongthedetectortheassociatedwavelength.Wettedathirdorderpolynomialtothesedatapointsandthus,weobtainedafunctionfp2givingtheassociatedwavelengthofeachpixel.Usingthisfunctionwecreatedanarrayarraywiththewavelengthsofthenalspectrum.Theinitialwavelengthisintherstcell(0)andweincreasedthewavelengthofthefollowingcellswitharegularstep().Eachpixelofthespectrumcontainstheuxobtainedfromtheinitialspectrumbetweenthetwoconsecutivewavelengthsofthearrayarray.Theuxofnalspectrumatthepositionnisthesumoftheuxoftheinitialpixelsthatareincludedinthewavelengthrange0+n.Therelativecontributionofthepixelsoftheinitialspectrumwascalculatedusingfp2. 82

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TheresultsarecombinedusingEquations 3 and 3 .TheintegrateduxinVbandI(V)=14.0m( Goranskiietal. 1998a )andextinctionofAv8( Wagner 1986 )areusedforphotometriccalibrationofI.Weusetheclassicalpolarizationestimatorp=p q)sincep<0.7( Simmons&Stewart 1985 ).TheFigures C-2 and C-8 (seeAppendix C )showtheStokesparametersandthepolarizationangle/levelrespectivelycalibratedintheplaneoftheskyofdatasetD2.Theotherdatasets(D3,D4,andD5)arenotcalibratedintheplaneofthesky(seeAppendix C ). C-1 C-6 C-7 ,and C-12 intheAppendix C ) 83

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Giesetal. ( 2002a )interpretedthisclassicalproleasarisingfromthegeometryoftheaccretiondiskandwindswhichareaffectedbytheprecessional,orbitalandnutationalmotions.Here,weclearlyrecognizedifferentcomponentsinQandUspectrawithdifferentpolarization(seeFigures C-2 C-1 ,and C-6 intheAppendix C ).SuchemissionlinesarealsoobservedinAGNsthatexhibitfeatureswithacentralcoreandbroadwings( Smithetal. 2005 ).Theyoriginateinrotatingdisksandfromscatteringinpolarorequatorialregions,creatingapolarizationproleaccordingtotheirgeometryanddynamics.Thecontinuumpolarizationisapproximatelyconstantandstationary,whiletheHpolarizationdeviatesfromthisattendencyindifferentdegreesforthecoreandwingsoftheprole,asexpectedforanaccretiondiskwithequatorialorpolarwinds.ThestationaryfeaturesHeI6678andHeI7065areexpectedtobeemittedfromthesameregionsasthestationaryHlineandthus,theyshouldhavethesamenumberoffeaturesintheirproles.However,theyaretooweakandwecannotseparatethecomponentsthatweseeintheproleofthestationaryHline.Therefore,weapproximatedthemwithauniqueGaussian.OtherlinesinthespectrumHeI7281,CII7231=7236andOI7772arebarelydetectedandwecannotstudytheirpolarization.ThemovingH+andHlinesagreewithexpectationfromthekinematicmodelintheirwavelengthposition(seeFigure 3-14 ). Insomecases,thesefeaturesareblendedinourdatawitheachotherandtheirstudyrequiresacarefulttingprocessinordertoseparatethecontributionofthedifferentlinesofwhichprolesarecomplex.Thetraditionalttingofcomplexlineprolesgivesmultiplesolutionssomeofwhichdonothaveaclearphysicalinterpretation.However,qualitativelywenotethatcombininginformationfromalllinearStokes 84

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Pix2i.Choosinganerrorfunctioniscomplexbecausethebestcriteriadependontheoptimizationproblem.Inthecaseofalinearestimator,theoptimalsolutionfromminimumquadraticerrorisnamedtheBayesoptimum.ItstheoreticalestimatoristhelikelihoodE[Y=X]thatrepresentstheconditionalprobabilityofseenYgiventhatthehypothesisXistrue.However,theanalyticalrepresentationoftheBayesoptimumisdifculttoobtain.ThemostpopulartheoryabletosolvethequadraticcriterionisthebestsquaretapproximationsuggestedbyGaussandLegendreattheendofthe18thcentury.Itisahandymethodtoestimatetheunknownparametersofattingmodel.WhilethismethodiscommonlyusedwithlinearestimationsitdoesnotalwayssolvesophisticatedproblemsofcomplexequationsasinthecaseofmultiplesuperimposedGaussian. Wetourdatawithalinearequationforcontinuumux(Fcont())andGaussianlineproles(Fline())usingtheminimumleast-squaresmethodwithinlocalregionsaroundeachemissionline.Weusetwoparametersofthettingfunctionsforthecontinuum(AandB)andthreeperline(F0,0,and)asshownbythefollowingequationsofthese 85

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20 Becauseofthenon-linearityoftheproblem,weapproachtheleast-squaressolutionwithaniterativeprocedure,Levenberg-Marquardtalgorithm(LMA).Iterativeproceduresrequireinitialguessesforeachparameterandthesolutionsaresearchedbylocallinearapproximationsuntiltheestimatorfunctionapproachaminimum.TheoptimizationofprolesascomplexasHincludesmultipleminimumerrorsolutions,andthealgorithmisverysensitivetotheinitialconditions.QualitativeanalysissuggestsanimprovementontheinformationwhencombiningdatafromIthathashighsignal-to-noise(SNR)withQandU,becausethelatteroftenhaveabettercharacterizationofthepositionandthewidthoffeatures.WethuschoosetosimultaneouslytI,QandU.WeusethesumofdeviationsbetweenI,Q,UspectraandtheirtmodelsrelativetotheircontinuumSNR.SNRperresolutionelementiscalculatedbetween5904Aand6151A:SNRI=7080;SNRQ=29andSNRU=0.54forI,QandUrespectively.Then,ourapproachofsimultaneousIQUtconsistsofminimizingthefunction, wherespcI(x),spcQ(x),andspcU(x)correspondtotheobservedI,Q,andUuxesatthewavelengthx;andtI(x),tQ(x),andtU(x)arethevalueofthetfunctionstothedataatthesamewavelengthx. WecomparethismethodtotheclassicalsimplespectrumttingbycheckingrepeatabilityofthesolutionusingMonte-Carlosimulations.Weinitiallytthedataandweusethissolutiontocreatesyntheticmodels,addingvariousamplitudesofwhitePoissoniannoise.Foreachnoiseamplitudewecreate100syntheticmodelsbasedontheinitialtting.Weapplythettingalgorithmtothesyntheticmodelsandwecompare 86

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Aswemovetheinitialguessesawayfromtheunderlyingmodel,weseethatthesolutionsusingthetraditionaltdeviatemorethanthecombinedIQUt.Thisimprovementtendtorapidlyincreaseasthenoiseofthesyntheticmodelincreases.Forinstance,wecalculatedtheaccuracyofbothmethodsassumingdeviationsofA,B&0of0.1%and&F0of10%betweentheinitialguessandthetruevalue.Wecalculatedtherelativeerrorbetweentheinitialparametersofthesyntheticspectrumandthenalparametersofthetspectrum.Weobservedthattherelativeerroris40timeslowerwhencombiningallStokesspectraforthesignaltonoiseofourdata. Hence,wechosetotourdatausingsimultaneousI,Q,andUspectra.Table 3-2 presentsthepropertiesoflinesofourStokesspectra.EachlineislabeledwithareferencenumberthatisusedintheTable 3-3 .Somelinesmaybettedwithinvariouswavelengthrangesbecauseeachrangemayincludedifferentkindsoflines.Alinewhichisttedwithintwointervalshastwolabelsinthetable.Thepropertiesofthelinesincludethedatasetofthespectrum,thelinelabelnumber,thetypeoftheregionemittingthisline(jetordisk),thedateandorbital/precessionalphaseattheobservationtime,andthenameoftheemittingatom.Table 3-3 showstheresultsfromthetsimultaneouslyusingI,Q,andU.Eachspectrumisnormalizedinordertosimplifythecalculations.Thephotometricscaleisshowninthetableforeachline.ThetableshowstheuxIoftheline,thenormalizedStokesparameters,theirangleandlevelofpolarization,theirwavelengthposition,andthelinewidth.Uncertaintiesofallparametersarepresentedaswell.ThistwasprocessedusingDynamicalEvolutionofSpectropolarimetryEmissionofJetObjects(DESPEJO).Wedevelopedthistoolinorder 87

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SummaryofOurSpectropolarimetry DataNameDateofObservationOrbitalPhasePrecessionalPhase 89

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Propertiesofthedataandthettedlines 1D1JetsJet2451080.00.6360.73Halpha-32D1Jet2451080.00.6360.73Halpha+-13D1Jet2451080.00.6360.73Halpha+-24D1Unknown2451080.00.6360.73Unknown5D1Disk2451080.00.6360.73HeI667816D1HeI7065Unknown2451080.00.6360.73Unknown7D1Disk2451080.00.6360.73HeI706518D1DiskDiskold2451080.00.6360.73Halphaold-39D1Diskold2451080.00.6360.73Halphaold-110D1Diskold2451080.00.6360.73Halphaold-211D1Disk(Hbeta)Disk2451080.00.6360.73Hbeta112D1Jet2451080.00.6360.73Hbeta+-113D1OnecomponentDisk2451080.00.6360.73Halpha114D1Disk2451080.00.6360.73HeI6678115D2RedJetUnknown2451340.00.2370.59Unknown16D2Jet2451340.00.2370.59Halpha-117D2Jet2451340.00.2350.59Halpha-218D2Disk2451340.00.2370.59HeI7065119D2Jet2451340.00.2340.59Halpha-320D2Jet2451340.00.2320.59Halpha-421D2HeI6678Disk2451340.00.2370.59HeI6678122D2BlueJetJet2451340.00.2350.59Halpha+223D2Jet2451340.00.2370.59Halpha+124D2Disk2451340.00.2370.59Halpha325D2Disk2451340.00.2370.59Halpha226D2Disk2451340.00.2370.59Halpha127D2Disk2451340.00.2370.59HeI6678128D3RedJetUnknown2451340.50.2400.63Unknown29D3Jet2451340.50.2400.63Halpha-130D3Jet2451340.50.2420.63Halpha-231D3Disk2451340.50.2400.63HeI7065132D3Jet2451340.50.2400.63Halpha-333D3Jet2451340.50.2380.63Halpha-434D3BlueJetJet2451340.50.2420.63Halpha+235D3Jet2451340.50.2430.63Halpha+136D3Disk2451340.50.2400.63Halpha337D3Disk2451340.50.2400.63Halpha238D3Disk2451340.50.2400.63Halpha139D3Disk2451340.50.2400.63HeI6678140D4RedJetUnknown2451341.00.2430.67Unknown41D4Jet2451341.00.2500.67Halpha-142D4Jet2451341.00.2480.67Halpha-243D4Disk2451341.00.2430.67HeI7065144D4Jet2451341.00.2460.67Halpha-(Problem)345D4Jet2451341.00.2440.67Halpha-446D4Jet2451341.00.2420.67Halpha-547D4BlueJetJet2451341.00.2480.67Halpha+248D4Jet2451341.00.2500.67Halpha+149D4Disk2451341.00.2430.67Halpha350D4Disk2451341.00.2430.67Halpha251D4Disk2451341.00.2430.67Halpha152D4Disk2451341.00.2430.67HeI6678153D5RedJetUnknown2451341.50.2470.71Unknown54D5Jet2451341.50.2540.71Halpha-255D5Jet2451341.50.2520.71Halpha-356D5Disk2451341.50.2470.71HeI7065157D5Jet2451341.50.2500.71Halpha-458D5Jet2451341.50.2560.71Halpha-159D5BlueJetJet2451341.50.2540.71Halpha+260D5Jet2451341.50.2560.71Halpha+161D5Disk2451341.50.2470.71Halpha362D5Disk2451341.50.2470.71Halpha263D5Disk2451341.50.2470.71Halpha164D5Disk2451341.50.2470.71HeI6678165D6BlueJetJet2454740.00.1760.41Halpha-166D6Jet2454740.00.1730.41Halpha-367D6Jet2454740.00.1750.41Halpha-268D6Unknown2454740.00.1760.41Unknown69D6BlueJet(Hbeta)Jet2454740.00.1760.41Hbeta-170D6Jet2454740.00.1730.41Hbeta-371D6Jet2454740.00.1750.41Hbeta-272D6RedJetJet2454740.00.1760.41Hbeta+173D6Jet2454740.00.1750.41Hbeta+274D6Jet2454740.00.1730.41Hbeta+375D6DiskDisk2454740.00.1760.41Halpha176D6Disk2454740.00.1760.41HeI667877D6Disk(Hbeta)Disk2454740.00.1760.41Hbeta178D6Unknown2454740.00.1760.41ClII?

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LinetsusingI,Q,Ucombinationmethod

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Linearlypolarizedelectricwavedecompositionalongthexandyaxes.ThediagramshowsthepropagationalongaDouble-BeamPolarimeter.Thehalf-waveplate(HWP)hastwodifferentindexesofrefractionalongx(nx)andy(ny).TheWollastonprism(WP)hastwoprisms,namely1and2,withopticalaxes(OA)perpendiculartoeachother.Components~Exand~Ey,calledo-ray(ordinaryray)ande-ray(extraordinaryray)splitintothedetectoratdifferentanglesaftertheWP. 92

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ElectronscatteringofanincomingelectricwaveEX.Thisgureillustratesthescatteringprocessofaphotonbyanelectron.Theelectronisrepresentedwithablackdot.Theincomingphotoncomesfromthetopofthesketchoscillatingintheplaneofthedrawinganditencounterstheelectronwhichalsooscillatesinthesameplaneduetotheelectriceldcreatedbythephoton.Theamplitudeoftheradiationtothelineofsightontherightofthesketchistheprojectionoftheoscillationsperpendiculartothepropagationdirectionoftheelectron.Therefore,theangleofscatteringdenestheamplitudeoftheobservedradiationofthescattering. IllustrationofthecalculationofQfromspectropolarimetryfromaDBSP.Fromtwoimageswithhalf-waveplate(HWP)at0and45angles,weobtainthetwoimagespresentedintheleft.WeextracttwospectrafromeachimageS1(0),S1(45),S2(0),andS2(45)thatwecombineusingEquation 3 93

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Spectraldistributionofsynchrotronemissionfromasingleparticle.Thegyrofrequencyisnoted:c=42BMHz.Normalizeduxisplottedversusthenormalizedfrequencywithc.Thecharacteristicfrequencyoftheemission0=eB ThisillustratesCerenkovemissionwhenthevelocityexceedsthecriticalspeedvsofthemedium.ThesourceisshownatvariouspositionsSiaswellastheirwavefrontsWithatexpandatthevelocityvS.ThewavefrontoftheCerenkovradiationisalsoshowninthedrawing.Credit:http://www.physics.upenn.edu/balloon/cerenkov radiation.html. 94

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Multiplescatteringinaannularcylinderscatteringregion.Theguresketchesacylindricalregionwithscatteringparticlesandanemittingsource.Theinnerandouterradii(R1andR2)andtheheight(H)ofthecylinderaredenedinthesketch.Inthisparticularscenario,thesource(bluedot)emitsaphotonwhichsuffers5scattering.Thedashedlinetracesthepathofthephoton.Theelectronparticipatinginthescatteringofthisphotonarereddots.Atthelastscattering,weshowacoordinatesystembecausetheangleofthelastscatteringplaysaspecialrole.Forinstance,theorientationangleofthecylindricalregionwilldeterminetheobservedpolarizationwhichresultsfromthecontributionofallthescatteringphotonsasdescribedbyEquation 3 95

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InterfaceofreductionsoftwareusedtoprocessspectropolarimetryofaDouble-BeamSpectropolarimeter. 96

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LinearStokesParametersI,Q,andUofD1set.Thespectraarephotometricallycalibrated. 97

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LinearStokesParametersI,Q,andUofD2set.Thespectraarenotphotometricallycalibrated. 98

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LinearStokesParametersI,Q,andUofD6set.Thespectraarenotphotometricallycalibrated. 99

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LinearPolarizationofD1set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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LinearPolarizationofD2set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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LinearPolarizationofD6set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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ShiftofHmovinglines.Weshowthemain(diamonds)andsecondary(crosses)componentsofthemovinglinesindatasetsD1,D2,D3,D4,D5.ThedynamicalmodelbasedontheHmovinglinesvelocityshiftwithvaluesof Eikenberryetal. ( 2001 )isshownforbothjets(dashedlines). 103

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Thestudyofspectropolarimetryrequiresspecialtoolsforacompleteanalysisofthedata.Forinstance,weshowedinChapter 3 theimportanceofcombiningalltheStokesspectrainordertoobtainthemaximuminformationfromtheemissionlinesofSS433.Wedevelopedacodewithnewalgorithmsmanagingspectropolarimetry.Thiscodewillbeparticularlyusefulfortheanalysisoflargedatasets.Inaddition,wewillseeinthefollowingchapters(seeChapters 5 and 6 )howthisinformationcanbeusedinthecaseofThomsonscatteringfortheanalysisofemittingandscatteringregions.Weincludedinourprogramthetasksnecessaryforthisanalysisaswewillexplainbelow. 4.1.1Overview 4-1 ).AlthoughwedesignedthissoftwarespeciallyforthestudyofSS433,itincludesasetofgeneraltoolsforthetreatmentandvisualizationoflinearandcircularpolarizationthatcanbeusedfortheanalysisofspectropolarimetryofotherastronomicalobjects.DESPEJOisahandytoolforstudyingemissionandscatteringregionsinaccretiondisksandwinds. ThettingpackageofDESPEJOtsspectropolarimetryStokesspectraindividuallyorsimultaneously,andperformMonte-Carlossimulationsthattestthettingprocess(seeSection 3.4 ).DESPEJOalsocontainsmodelsusingtheresultingtsfortheanalysisofSS433thatwewillpresentinChapters 5 and 6 .Forinstance,thestaticanddynamiccharacterizationofthecontinuumandlinepolarizationisnecessarytocalculatetheISP(seeSection 5.2 )aswellasthegeometryandparticledensityoftheaccretiondiskandtheopticaljets(seeSections 5.3 and 6.2.3 ).Thegeometryandproton-electron 104

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3.2.2 .DESPEJOmanageslistsofspectro-orimaging-polarimetryforstudyingthedynamicalbehaviorofpolarizationandperformsFourierdecompositionofthepolarizationofthedatainthelist(seeSection 5.2.3.2 ).Thesetoolsareusedinthisthesisforstudyingregionsemittingthestationaryandmovinglines,andcalculatingtheparticlepopulationandgeometryalongthejets. 4.1.2.1ScienticapplicationsofDESPEJO 105

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4-1 ).WecreatedthelistofdatasetsD1,D2,D3,D4,D5,andD6explainedinSection 3.3 bypressingthe`Insert'databutton.Datamaybedeletedbypressing`Delete'.`RootPath'buttonintheleftpanelisusedtomodifytherootpathofthespectropolarimetrydata.Otherdirectorieswithtlesandmodellesaredenedintherightpanel. Afterthelistofdataisinsertedintothesystemwecanloadintotheprogramtheparticulardatawewanttoanalyze.Theanalysisincludefoursteps:thettingprocess,theISPdetermination,thedeterminationofuxcontributionalongthejets,andthecalculationofpopulationdensities.Thettingprocessisnecessarilyrst.Determinationofuxcontributionsofjetsegmentsmustprecedethecalculationsofpopulationdensitiesalongthejet.Otherthantheserequirements,theorderoftheanalysisisexible. 4-1 ).Byswitchingtothe`Spectra'tabweobservetheStokesspectraI,Q,andUsimultaneously.Wecanclickonanyofthesethreegraphicsanddragthemousearoundthelineregioninordertozoomtheareaandtovisuallylocatefeaturesinthewavelengthrange[6900A,7250A].Therststepconsistsofdeningthecontinuumandlinesforthesethreespectra. WedenethecontinuumoftheStokesspectrabyclicking`ModifyCont'.AsecondarywindowopenswiththeinformationofthelinearfunctionsforI,Q,andU.Wepress`Modify`andupdatethewidgetvaluesofI,Q,andUuxtoI=4.51050.2,Q=6.01070.003,andU=7.21080.005.WeaddalsofourHlinesandaHe7065lineatthe`Lines`tab.Itisveryimportantfortherestoftheanalysis 106

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4.3.1 .Wechangetheparametersinordertotqualitativelythespectrainthegraphics. Werecommendsavingthedatabyclicking`SaveFileAs'inthe`Action'panelbeforeproceedingtothetprocess.The`Action'tabalsocontainsthebutton`FitSpectra'whichstartsthetprocessofthespectra.Bypressingthisbuttonasecondarywindowshowsupinthescreenwiththeinformationofthet(seeSection 4.3.1.3 ).If`Fitstokes'ispressedthesecondarywindowdisappearsandanothersecondarywindowshowsinformationofthenewresultsbasedontheparametersfromthepreviouswindow.Wechoosethewavelengthrange[6700A,7400A]andthesimultaneoustofI,QandU.Theresultingvalues,andagraphicwiththedataandthenewtspectraareshowninanotherwindow.Becausenoerrorshappenedduringthettingprocessweconrmedtheupdateoftheinformation.Wecheckedthettingaccuracyandtheresultingpolarizationfromthenewvaluesinthe`Errors`and`Polarization`tabs. Weveriedtheveracityofthetbygoingtothe`FittingTest'tab.Anewwindowappearswiththesameinformationasthetprocesswindowplusanadditionalinformationofthenoiselevelofthesyntheticspectra,thenumberofMonte-Carlossimulations,andthedeviationoftheinitialvaluesofthettingparameters(seeSection 3.4 ).Theresultingdeviationofsixoftheparametersforoneparticularlineareshowninthe`FittingTest`panel. 5.2 .TheusermustdenetheparametersneededtottheStokesspectracontinuumandtheSerkowskii'slaw.OurinitialguessoftheSerkowskii'slawparametersforSS433wasbasedon McLean&Tapia ( 1980 ).WesubtractedtheintrinsicpolarizationofthesourceusingHe7065.Theresultingtofthecontinuumofqanduisshowninthe 107

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6.2.4 ).ThisanalysisonlymakessenseinthecaseofSS433becauseitistheonlyastronomicalsourcetoexhibitnarrowmovinglinescomingfromprecessingjets.Thus,thedefaultparametersofthedynamicalmodelarethoseofSS433anditsjetswhicharedenedinSection 2.3 .Theusercanchangethesevaluesinthe`DynamicalModel'tab.TheresultingcontributionofeachjetsegmentalongthejetisplottedforI,Q,andUatthe`JetLines'tab.AswewillseeinSection 6.2.4.1 ,ajetsegmentisanarticialsectionsofthejetthatwedeneinDESPEJOforcomputationalpurposes. 6.2.4 ).Itisimportanttocarefullydenesomepreliminaryinformationaboutthesystemincludingthecharacteristicoftheemittingatoms,thegeometryoftheemittingandscatteringregions,thephotometriccalibrationmagnitudes,andtheextinctionoftheemission.Thisinformationisdenedatthe`SystemModel'tabthatshowsthreetypeofmodels:theatommodels,theregionmodelsandthejetmodels.Theusercanadd,removeormodifyanyofthesemodels.WedenedtheatomandtheregionmodelsthatwewillexplainintheSections 5.3 and 6.2.4 .Then,wepressedthe`LinePopulation`and`JetPopulation`buttonsthatstartthecalculationsoftheelectronandprotondensities. Anatommodeldenesthecharacteristicoftheatomemittingaparticularline,theelectrontransitionresponsibleoftheemission,andtheprocessofexcitationoftheatom.Eachatommodelislabeledwithanamethatisassociatedtothettedlines.Theatommodelsareassociatedtoaregionmodelaswell.Theregionmodeldenesthe 108

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InSections 4.2 and 4.3 ,weexplaintheconceptofthesoftwareinordertounderstandhowithasbeendevelopedandtested;andthestructureofthesoftwarewhichisatthebaseofthefunctioningofeachtask.Thisknowledgeisnotonlyimportanttocheckifthesoftwarematchesspecicscienticneedsbutalsotoadaptthecodeinordertoimprovespecicproceduresforotheradditionalfunctionalities. 4.2.1DevelopmentStagesandHistoryofDESPEJO ThersttwostepswerefollowedbythedevelopmentofasecondversionofDESPEJO(`DESPEJOv2.0')withmoreoptimumalgorithms,calculations,andmemorymanagement.Inaddition,weimprovedthegraphicalinterfaceofDESPEJOv2.0allowingfriendlyandvisualinteractionwhenprocessingdata.Theinterfacehaseightgraphicalenvironmentsinthemainwindowthatareseparatedineightdifferenttabs.Secondarywindowsopentemporarilywhenanactionruns.Theyareusedtoavoid 109

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EachgraphicalenvironmentofthemainwindowofDESPEJOv2.0includesgraphicortextwidgetsthatshowintermediateornalresults.Somegraphicsareinteractiveallowingtheuserstodirectlymanipulateorzoom.Theuserscandenetheirowngraphicpreferencesincludingthelinestyle,thecolorsorthelabels.Thetextorthegraphicscanbesavedin'.dat','.ps'or'.sav'formats.Theprogramuses'.sav'or'.dat'lestoloadsavedinformationineachgraphicalenvironment.Thegraphicalenvironmentofthemainwindowarethefollowing, 1. Managedatalistanddeneles/directoriesofdata,tsandradiativemodels; 2. Atomandregionmodel(diskandjet)denitionsaswellasltersandphotometriccalibrationparametersinordertodeneemission; 3. Dynamicalmodelincludinggeometryorientationsandperiodsofmotionsofthesystem; 4. Spectravisualizationandline/continuumdenitionsforttingprocess; 5. Accuracyofttingresultsandreliabilityofttingparameters; 6. ISPcalculationandvisualization; 7. CalculationandvisualizationofcontributiontoI,Q,UandValongjets; 8. Densitycalculationsfromlineemissionsandscatteringandpopulationalongjet. Nevertheless,despiteofitsintuitivegraphicalinterfacethemainimprovementofDESPEJOv2.0liesintheprogramingmethodleadingtoanewstructureofthesoftwarethatweexplaininthenextsections. 110

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ThestructureofOOPprogramsgivesthechancetoseethegeneralpictureofthecodebyunderstandingthesmallentities(objects)thatformthesoftware.Ifthesoftwareiscarefullydesignedwithdiagramsshowinghowobjectsinteractwitheachother,theprogrammerwillhavethechancetoimproveordebugthesoftwareeasilyandefciently.Forthispurpose,itisnecessarytouseatoolhelpingtoorganizethesoftware.WeexplainbelowthemodelinglanguageandsoftwareweusedtodesignDESPEJO. 111

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4-3 )werewelldenedalongthedevelopmentofDESPEJOv1.0. Thestructurediagramsarethebaseofthesoftwarearchitecture.Theydenealltheobjectsinthesystemandhowtheseobjectsarerelatedtoeachother.AgooddenitionofparametersandfunctionswasthekeyforalgorithmoptimizationandthesestructurediagramsconstitutedthemainworkoftheoptimizationofDESPEJO.Themainprinciplesofthecalculationswerelocatedattherstversionbutitwasessentialtousethestructurediagramsinordertomaketheseconceptsuseful. WeusedArgoUMLsoftwaretomakethestructurediagramsofthesystem.ArgoUMLisanopenedsourceforUMLmodelingwhichsupportstandardUMLdiagrams.AlthoughitdoesnottranslatediagramstoIDLlanguage,weuseditasadevelopmenttoolbecauseofitspowerfulandfriendlygraphicalenvironment.Wefocusonclassandpackagediagrams.Thestructures,theattributes,andtherelationshipbetweenclassesaredescribedby`the`classdiagrams.Theclassesaregroupedintologicalelementsthatwedescribeusingpackages.TheArgoUMLprojectcontainsalldiagraminformationandotherdiagramswillbenecessaryforfutureimprovements.NinepackagesaredenedwithArgoUMLandtheirrespectiveclassesareasfollow, 1. Interface:interactswithuser Plot spc,plot windows,plot results,drawing events; io lines,io continuum,io stokes,io data list; io population,io model system,io dynamical model,io jet lines; 2. Fitting: 112

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line,stokes continuum,stokes model,lter emission t line range,stokes continuum range, tfun model,tfun test 3. ManageData: stokes data info,stokes data list, spectra photometry,stokes data 4. Dynamics: date dynamic state,dynamic model 5. widgets:widgetsofIDL widget base,widget undened widget slider,widget droplist,widget droplistNOFF, widget draw,widget text 6. interfaceactions: extract data list actions, t stokes data actions,t stokes data results,test t actions,modif modsys actions modifadd line actions,modifadd linerange actions,move line actions modif linear actions,modif linearrange actions plot setting actions,print stokes actions,modifadd plot results 7. population: model region,model atom emission,model system population emission 8. jetdecompose: model jet, jet line,jet population 9. InterstellarMedium:ISP ThefunctionsandparametersaredescribedindetailedinSection 4.3 .Therearesomecommontaskstoallclasseslikethefunctioncreatingordestroyingtheobjects(`INIT()',`CLEANUP()');andthefunctionschangingorreadingpropertiesoftheobjects(`SetProperty()',`GetProperty()',`ReturnResult()').Theinitializationofpropertiesofsomeobjectsaredoneusing`Reset Values()'.The`Scale Values()'functionmultipliesthevariablesofanobjectsbyascalar.The`Add Values()'functionaddsvariablesoftwoobjects.Theparametersoftheobjectcanalsobetranslatedtoastringoramatrix 113

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TheUMLdiagramshelptounderstandtheroleofeachobjectandthegoaloftheirfunctions.Theysimplifythecodingandthetestingofthesoftware.Verifyingthatobjectsfollowtheirindividualspecicationsisimportantwhentestinghowthesoftwareworksaswewillexplaininthefollowingsection. Oneofthemostimportantlessonsfromtherstversionistheimportanceofseparatingactionsthatareindependent.DESPEJOv1.0synchronizesactionsthatarenotcorrelatedrequiringpersistentupdatesofvariablesandwidgetsandtherefore,unnecessarycalculationsandmemoryaccess.ThegraphicalenvironmentsofDESPEJOv2.0simplifytheinterfaceaswellastheprogramstructurebecauseitseparatesindependentactions. 114

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2.3.2 )usinginformationfrompreviousauthorsreferredinSection 2.3 Theorientationofregionsofanastronomicalobjectdependsonthedynamicalmodelsgoverningthemotionsofthesystemandonthenatureoftheemittingregion.Forinstance,thesamedynamicalmodelofSS433isvalidforjetsanddiskbuttheemissionfromtheopticaljetsataparticularprecessionalphaseisshiftedwithrespecttothediskbecausethegastakesafewdaystogettotheopticaljetsafteritisejected.Weassumevariousgeometries,dynamicalmodelsandregions.TheorientationofthesystemhavebeentestedbycomparingtheresultsoftheDESPEJOv2.0,theanalyticalvalues,andtheresultsfromDESPEJOv1.0.Theanalyticalvaluesarebasedongeometricprojections.TheorientationinDESPEJOv1.0resultsfromrotationofthecoordinatesystemsexplainedinSection 5.1 .Therefore,thefunctionsofDESPEJOv2.0calculatingtheanglesofthesysteminclinationandtheorientationofthegeometriesintheskyweretestedintwodifferentways. Anothersensitiveissueconcernedthewavelengthrangesandresolutionsofthespectrathatarenotnecessarilythesameforallthedata.TheinformationofthewavelengthwereincludedintheobjectscontainingtheStokesspectra.Thefunctionsoftheseobjectstransformedthewavelengthscaleandrangewithoutchangingthephotometryofthespectra.Theseobjectsalsoincludedotherfunctionsrelatedtothephotometryofthespectra.AllthefunctionshavebeentestedusingsyntheticspectraandexistingspectrafromSS433. 115

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Emovetal. ( 1984 ). AsexplainedinSection 3.4 ,thetofthespectraisthebasisofouranalysis.Wetestedtwodifferentttingfunctions:mptfunandcurvet.Bothfunctionswereimplementedusingasinglestandardtortsbasedonanrecursivealgorithm.Therecursivealgorithmconsistedinttingcontinuumandlinesseparatelyforagivennumberofiterations.WetestedalltheoptionsusingsyntheticmodelsbasedonindividualordoubleGaussianswithwhitenoise.Weconcludedthatmptfunfunctionwithasingleiterationgavethemostaccurateandreliablets. Finally,otherfunctionalityofobjectsweretestedaccordingtotheirrole.Weexplainbelowthestructureofthesoftwareandgeneralfunctionsandparametersthatarenecessarytounderstandthecode. 116

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E DATA INFO')isessentiallyacollectionofstringwiththenamesofthelenameswhereimages,tparameters,andmodelsaresaved.Thesecondclass(`STOKES DATA')containstableswiththeStokesspectra(`SPECTRA PHOTOMETRY'),theparametersofthelinesandcontinuumoftheI,Q,U,Vspectratting(`STOKES MODEL'),thephotometricscale,andtheinformationofthenoiselevelatthecontinuum.Theinformationofalldatalesisstoredintheclass`STOKES DATA LIST'thatisalistof`STOKES DATA INFO'objects.`STOKES DATA LIST'and`STOKES DATA INFO'classesdonotneedanyspecialdescriptionbecausetheyonlycontaintheinformationwiththedataintheharddisk.Theywillbeimportantinthenextversionwhenimprovingthealgorithmofharddiskaccess.Therefore,inthissectionweexplainthe`STOKES DATA'classandtheclassesthatarecontainedinitsdenition.Inparticular,wedescribethe`STOKES MODEL'classthatisveryimportantfortheanalysiscarriedoutbyDESPEJO.Wealsooverviewthe`FITFUN MODEL'and`FITFUN TEST'whichareatthebaseofthettinganalysisofthedata.Thettingprocesscompetea`STOKES MODEL`usingtheinputdatastoredina`SPECTRA PHOTOMETRY'object. 117

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DATAclass DATA'.Anobjectofthisclassiscreatedwhendataisloadedintothesystem.Thisobjectwillbemanipulatedbydifferentobjectsandtasksalongtheanalysisofthedata.TheFigure 4-4 showstheclassdiagramof`STOKES DATA'.Itincludesatableof`SPECTRA PHOTOMETRY'objectswiththeStokesspectra(I,Q,U,V)[`spectra photometry`],theirttingparameters`t',andtheinformation`data info'oftheles. Thefunctionsrelatedtothisclassaremainlythebasicfunctionsdescribedaboveasloadingorcheckinganimage[`Load Image()',`Check Stokes Data()'];modifyingthescalewavelengthorthephotometry[`Match Spectra()',`Photometric Calibration()']orreturninguxorpolarizationofthecontinuum,thelinesorthespectrum[`Polarization()',LinePolarization()'].Theseprocessesmayusetheconceptoftheclass`FILTER EMISSION'thatdenethelterwavelengthrangeandcenterinwhichwecalibrateorintegrateuxes.Otherpossibleactivitiesconcerncalculatingthenoiselevelatthecontinuum[`Calculate SNR()'],returningasyntheticspectrumbasedonthet[`Calculate spc()']orinsertingaspecictmodel`STOKES MODEL'[`Insert Model()']. MODELclass MODEL'isalsoanimportantclassbecauseafteritiscompletedusingaspecicStokesdatatheinformationisusedfortherestoftheanalysis.Ithasacomplexstructurebecauseitincludesinformationofallthelines,thecontinuum,andtherangesoftheseparametersduringthettingprocess(seeAppendix E ).Thegeneralfunctionsthatapplytothisclassallowtomanipulatethelines[`Change numlines(),`Add Line()',`Remove Line()',`Select Line()',`Switch Line()',`Modify Lines()',`Return LineIndex()',`Move Lines()',`RemoveLast()',`InsertLast()',`ValidLine()'and`Import Lines()'],todoarithmeticoperationsbetweenobjects[`Reset Values()',`Add Values()',`Scale Values()',`Scale Values()',and`Copy Properties()'],save/loadinformationoftheobjectina 118

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Model()',`SaveFile()',and`LoadFile()'],andreturnpolarization,uxesorspectrum[`Calculate spc()',`Polarization()',`LinePolarization()',`Return Centroid()',`Return WavMinMax()',and`Scale Flux()'](seeFigure 4-4 ). Thedenitionofthe`STOKES MODEL'classisbasedonthefunctionsusedtottheStokesspectra.Thecontinuumisttedusinglinearfunctions.TheclassicaltofthelinesareGaussianfunctions,butDESPEJOgivestheopportunityofapproachingassymetricproleswithHermitefunctions.TheHermitepolynomialaredescribedrecursivelyas (4) (4) TheHermitefunctionsareusedforthestudyofstellardynamicsinellipticalgalaxies( vanderMarel&Franx 1993 )andsolarlineprolesinpolarizationtransfermodels( delToroIniesta&LpezAriste 2003 ).TheyaredenedfromtheHermitepolynomialasfollow, 2 Inourparticularcase,weuseda4thorderHermitepolynomialfunctiontottheproles.Therefore,thetconsistsinaleast-squareapproximationofthefollowingfunction, p 20 Theunknownsparametersofthisfunctionarethewidth,thedepth,andthecenter0oftheclassicalGaussianprole.Inaddition,fourotherparametersciareintroduced 119

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(4) (4) (4) (4) Thewidthandemissivityofthisproleisrelatedtotheparametersofthetasfollow, 4c4! A`STOKES MODEL'objectincludestheparametersofthettingfunction(`continuum'and`lines'),thescaleoftotalspectra(`photscale'),thettingproperties(`range',`contrange',`linesrange',`limits',`x'),thelistoflines(`linelist'),thetotalnumberoflines(`numlines'),andthenamesofthelines(`linename').Theerrorsofthetarealsoincluded(`conterror',`lineserror').Inthefollowingsectionweexplainthettingprocessthatisrequiredtocompletea`STOKES MODEL'objectfroma`SPECTRA PHOTOMETRY'object. 3.4 areperformedbyobjectsofthe`FITFUN MODEL'and`FITFUN TEST'classes.TheycontaintheinformationwiththerangeofPoissoniannoise,thenumberofMonte-Carlossimulationsforeachlevel,andthettingparameters.DESPEJOtseachsyntheticmodel,calculatesitsdeviationfromtheoriginalspectrumandreturnstheresultofeachparameter.Theseobjectsareassociatedtoanobjectofthe`STOKES DATA'classthatcontainthedataandthetmodel.Theyincludethewavelengthintervalinwhichwetthedata(`interval'),the 120

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Interval()'),calculatethecharacteristicoftheparametersduringthet(`Calculate ParInfo()'),andstartthettingprocess(`Fit Stokes()'and`Fit Continuum()')ThealgorithmsofthetandthetestofthesolutionareexplainedinSection 3.4 .MoredetailsabouttheseclassesareshowninAppendix E REGION'class.ThegeometryweusedfortheanalysisoftheSS433areannuluscylinders,thereforetheregionisfullydescribedgivingtheinnerradius,theouterradius,andtheheightofthecylinder. Themodeloftheatomemittingagivenlinearerepresentedbytheclass`MODEL ATOM EMISSION'.Thisclassincludestheinformationoftheatomresponsibleoftheemission,andtheprocessthatmakestheatomradiating.The`MODEL SYSTEM'classisacollectionofmodelsofregionsandatoms.Itassociatesobjectsofthe`MODEL REGION'classtoobjectsofthe`MODEL ATOM EMISSION'class.Thisclasswillbeveryimportantforthecalculationoftheparticledensityofregionsemittingspeciclines. Eachofthettedlinesislabeledaccordingwithitsnature(H,H+,H...).Thus,alineisdenedasacombinationofvariouscomponentsthatareassociatedtoanatomicprocess,aregionandadynamicalmodel.Particledensityiscalculatedfromrecombinationorcollisionalequationsdependingonatomicprocessesthatareassociatedtothespecicemittingregion.Electrondensitiesarecalculatedfromlinear 121

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5.2 and 5.3 Theclassesallowingthejetsegmentationprocess(seeSection 6.2.4 )are`MODEL JET',`JET LINE',and`JET POPULATION'.Theyareequivalenttotheclassesusedtocalculatethepopulationfromtheemissionlines.Theycontaintheinformationofthegeometryoftheregionsandtheemissionfromtheseregions.However,inthiscasetheregionsarealistofsegmentsoftheopticaljetobtainedfromthedynamicalmodelsofSS433. 122

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InterfaceofDESPEJO.Thecurrenttabshowthelistofdatathattheuserisanalyzing 123

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InterfaceofDESPEJO.Thecurrenttabshowthelistofspectratting 124

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ActordiagramofDESPEJO.Theactorsperformingeachtaskarerepresentedwithmangures.Thepackagerepresentingtheactionisshownwithanellipsecontainingthenameoftheaction. 125

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STOKES DATAandSTOKES MODELclasses.Thetoprepresentsthenameoftheclass,themiddleshowstheattributesoftheobjectsofthisclass,andthebottomenumeratesthenameofthetasksthatcanbeperformedbytheseobjects 126

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AsexplainedinChapter 3 ,ourdatafromSS433containstationaryfeaturesemittedbytheenvironmentinwhichjet-diskcouplinghappens.Thismicroquasarissubjecttothreemaindynamicalmotions:(1)theorbitofthebinarysystem;and(2)theprecessionand(3)thenutationoftheaccretiondiskandjets.Thesethreemotionsdominatetheappearanceofthestationarylines.Inthischapter,westudyanddescribethebehaviorofthestationaryHandHeIlinesinordertounderstandthecontextinwhichjetsformneartheaccretiondisk.Forthispurpose,wecomparecharacteristicsofthestationaryHlineinourspectrawiththoseofpreviousauthors.Weexaminepossibleoriginsofthelinecomponentsbasedontheirprecessionalandorbitalbehavior.Then,wediscusstheintrinsicpolarizationandthepolarizationbehaviorofthesestationaryHlinecomponentsinrelationtothemodelsobtainedfromthevelocityshift.Weobtainapicturefortheoriginofthesethreecomponentsthatweusetocalculatethegeometryandthedensityofparticlesoftheemittingandscatteringregionswhichareattheoriginofthelinecomponents.Inparticular,weareinterestedintheprotondensityoftheaccretiondiskregionsbecausewewillusetheseresultsinChapter 6 whenstudyinghowtheinteractionoftheX-rayjetswiththeaccretiondiskaffectstheobservedpropertiesoftheopticaljetsofSS433. Margon 1984 ; Crampton&Hutchings 1981a ; Giesetal. 2002b ),therearenomodelsaccuratelypredictingtheseprolesatagiventime(seeSection 2.3.3 ).OneofthemainreasonswecannotpredictthebehaviorofthestationaryHlineprolewellisthatwe 127

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5.1.2 ,wepresentthedynamicalmodelsthatwewillapplytondtheoriginofthecomponentsthatourspectropolarimetryreveals.Then,ouranalysisoftheoriginofthesecomponentscombineourdatawiththoseofpreviousauthors,resultinginamodelwhichincludesthreeows:aowintheorbitalplanefromthemassdonorstartotheaccretiondisk;andtwowindsparalleltothejetsofSS433arisingineachfaceoftheaccretiondisk.Sections 5.1.3.1 and 5.1.3.3 showthestudyofthevelocityofthesethreeows. 3.3 andTable 3-1 ).ThebinarysystemSS433hastwoeclipseswithdifferentamplitudes( Goranskiietal. 1998a ).Theprimaryeclipse,orb=0,occurswhentheX-rayemission(presumablyfromtheinneraccretiondisk)isobscured( Stewartetal. 1987 ),whereastheeclipseofthemassdonorstarhappensatorb=0.5.Ourdatacoversalargerangeoforbitalphasesaroundtheinferiorconjunctionoftheaccretiondisk.Figure 5-1 showstheorbitalphasesofourdatasetsinthelightcurveinV-bandofSS433.DatasetsD1andD6,whichareobservedatprec=0.64(edge-ondisk)andprec=0.17,respectively,haveorbitalphasesoforb=0.73andorb=0.41.DatasetsD2,D3,D4,andD5correspondtoobservationsaftereclipseofthemassdonorstar,withorb=0.590.71andprec=0.24.InSection 3.4 ,weshowedthatthestationaryHlinesshowthreecomponents,H1,H2,andH3(seeTable 3-2 ),indatasetsD2,D3,D4,andD5thatareclearlyseparated 128

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5-2 illustratesthetofthesethreecomponentstothestationarylineproleindatasetD2.Thewavelengthpositionsofthesecomponentsdependontheorbitalandprecessionalphases.Forexample,Figures 5-3 5-4 ,and 5-5 showstheevolutionofH1withrespecttotheorbitalphaseatvariousprecessionalphasesaswewillcarefullyexplaininSection 5.1.3.1 .Wenownotethat,ifthevelocityshiftsoftheseHcomponentsareindependentfromeachother,thegeneralproleofHmaylookrandomaswaspreviouslyobserved.Then,theexistenceofthesethreeHcomponentsraisesseveralquestionsaboutthecurrentunderstandingofSS433andprocesseshappeningnearitsaccretiondisk.Here,themainquestionsthatwewilltreatare: 1. Howdoestheexistenceofthesecomponentsexplaintheobservationsofpreviousauthors?; 2. Arethesecomponentsrelatedtoanyotherstationaryfeature?; 3. Finallyandmostimportant,whatarethephyscialoriginsofthesecomponents? Giesetal. 2002b ).Webelievethatthecombinationofemissionfromthreedifferentregionsresultsinthewingandcoreprolemorphology.ThesethreeregionscorrespondtotheregionsemittingtheH1,H2,andH3componentsthatarevisibleinourspectropolarimetry. Giesetal. ( 2002a )suggestedthatabsorptionfeaturesappearinboththeredandthebluewings(seeFigure 5-6 )buttheoriginofthesefeaturesisnotclear.Inourdata,wedonotseeanyindicationsfromthepolarizationthatthesefeatureshaveaphysicaloriginasabsorption.WebelievethattheabsorbingfeaturesappearwhentheemissionfromthecomponentswhichcreatethewingsoftheHlineproleareshiftedawayfromthecentralcoreoftheH

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Crampton&Hutchings 1981a ; Kopylovetal. 1989 ; D'Odoricoetal. 1991 ; Fabrikaetal. 1997 ).Inaddition,thedynamicsofCII7231,7236matchthegeneralbehaviorofHeII4686.Theirvelocitiesaremaximumatquadraturephase(orb=0.25andorb=0.75),haveanamplitudeof16030km=s,andanaveragevelocityof20020km=s( Giesetal. 2002b ). Conversely,thedynamicsandoriginoftheHeIlinesarenotasobvious.ThepositionsofthestationaryHeIlinesbestmatchthedynamicalbehaviorofthecentralcoreofthestationaryHline. Giesetal. ( 2002b )tracedthepositionofthecenterofthestationaryHbyusingthecentroidandthepeakintensity.ThewavelengthpositionsoftheH1componentinourdatacorrespondtothepeakofthestationaryHline.Thus,undertheassumptionthatthethreecomponentsalwaysexist,thepositionofH1followsthedynamicsofthepeakpositionstudiedby Giesetal. ( 2002b ).However,the Giesetal. ( 2002b )techniquedoesnotaccountfortheasymmetryoftheprole,leadingtoresultswhosephysicalmeaningisnotalwaysclear. Existingstudiesoftheglobalproleandradialvelocityoftheentirelineprovidecontradictoryresults.Forinstance,thecorrelationoftheHlineproletotheprecessionalandtheorbitalphase( Kopylovetal. 1989 ; Fabrikaetal. 1997 )suggeststhatH1originatesintheRoche-loberegion,whileotherauthorsconcludedthatitarisesinatwo-owregimeinthediskwhichincludesagastorusaroundthebinarysystem 130

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Giesetal. 2002b ).Therefore,wearenotabletohaveaquantitativeanswertoquestion(2).SolvingthisquestionrequiresamoreaccurateanalysisofthedynamicsofeachoftheH1,H2,andH3components.Inotherwords,agoodanswertoquestion(2)requiresrstsolvingquestion(3)abouttheoriginofeachcomponent. 5.1.3.3 and 5.1.3.1 ).Then,wewillanalyzeifthesemodelsverifytheobservedpolarizationandpolarizationanglesarisingfromH1,H2,andH3(seeSection 5.2 ).However,inordertoaccomplishtherststep,wehadtomeasurethevelocityshiftofeachcomponentofthestationaryHlineinallourdatasets(D1,D2,D3,D4,D5,andD6). WecalculatedthevelocityshiftoftheHcomponentsinthedatasetsD2,D3,D4,andD5withrespecttotheO2telluricabsorptionfeatures(andBO2atmosphericbands).Thepositionofthetelluricabsorptionfeaturesshouldremainconstantat=6276Aand=6867A( Grifn 1969 )overalltheobservationtimes.Therefore,variationsofthepositionofthetelluricabsorptionscomefromvariationsinthewavelengthcalibrationintimealongtheobservation.WeremovedthiseffectfromthevelocityshiftsoftheHcomponentsusingalinearwavelengthinterpolationofthevelocityshiftsobtainedwithrespecttoeachofthesetwotelluricabsorptionlines.WavelengthcalibrationofdatasetsD1andD6didnotrequireanyadditionalwavelengthcorrection. Figure 5-7 showstheshiftofthestationaryHlinecomponentsfordatasetsD1,D2,D3,D4,D5,andD6.Agoodunderstandingoftheregionsemittingeachcomponentrequiresmodelscorrelatingthedynamicsoftheregionandthevelocityshiftofthe 131

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InordertogiveaquantitativeanswertothebehaviorofH1,H2,andH3,weexplaininthissectiontheeffectofmotionsofdifferentpartsofthesystemonthewavelengthshiftoftheemissionlines.Then,wewillstateourdynamicalmodelsexplainingthebehaviorofeachstationaryHcomponent. 132

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5-8 andAppendix A ).TherstoneCobs=(~Xobs,~Yobs,~Zobs)istheobservercoordinatesystemwith~Xobspointingtothelineofsight.Then,Corb=(~Xorb,~Yorb=~Yobs,~Zorb)isthecoordinatesystemoftheorbitalsystemwith~Zorbperpendiculartotheorbitalplaneand~Yorbintheplaneofthesky.CobsisobtainedbyrotatingCorbbyanangleiorbaround~Yobs.ThethirdcoordinatesystemCprec=(~Xprec,~Yprec,~Zprec)rotatesaround~ZorbwithaprecessionalperiodPprec.~Zprecisrotatedbyanangleprecaround~Yprecthatcoincideswith~Yorbatprec=0.ThelastcoordinatesystemCnut=(~Xnut,~Ynut,~Znut)correspondstonutationalmotion.~Znutisrotatedbyananglenutaround~Ynutthatcoincideswith~Yobsatnut=0.Cnutrotatesaround~ZprecwithnutationalperiodPnut. ThegeneraltransformationfromCnuttoCobsofagivenvector~vow=(vX,ow,vY,ow,vZ,ow)isgivenbythelinearequationvX,obs=A11vX,ow+A12vY,ow+A13vZ,owwhereA11,A12andA13dependonthegeometryandthedynamicalstateofthesystem(seeAppendix A ).Alinecenteredat0isshiftedbyfromitsrestingpositionwhengasismovingatspeed~vow.ThewavelengthshiftofthelineiscalculatedusingtheclassicalDopplershiftequation 0=~vow~Xobs 2.3.2.1 ),thevelocityshiftatphaseorbisdescribedbyvlos=vsiniorbsin(2(0orb+orb))where0orbisthephasewhenmotionliesintheplaneofthesky.Thesecondorderapproximationtothisequationforsmallphasevariations(orb)aroundorbisasfollows, 133

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Katzetal. 1982 )proposedadiskprecessionandnutationdrivenbythetorqueofthemassdonorstar.Thenutational,precessional,andorbitalphasesarerelatedas(nut)=(2+Porb (5) Wenotethatintheabsenceofnutation(n=0)wendagainthewell-knowndynamicalmodelofHmovinglinesfromjets.Inthegeneralcase,variationsaroundaparticularorbitalphasearealsoinuencedbynutationalmotionbuttoasmalldegreecomparedwithothervariationssince=sin(20nut)issmall.Secondorderapproximationsresultinthefollowingequations, 134

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Giesetal. 2002b ).Weseparatetheresultsintwoparts.First,wewillexplainthemotionoftheH1componentthatresultsfromtheemissionoftherstregionhappeningintheorbitalplane.WewillshowtheresultingtofthedynamicalmodelexplainedinSection 5.1.2.2 andwewillstudytheeffectsoftheprecessionontheparametersofthemodel.Second,wewillcalculatetheorbitalvelocityandthespeedoftheaccretiondiskwindsusingtheotherstationaryHcomponents.ThevelocityshiftsofH2andH3resultfromthecombinationoftheorbitalmotionandandthewindspeed. ( 2002b )recordedpositionsofHpeakswithanaccuracyof=0.05A+7 Forthepurposeofseparatingtheeffectoftheprecessionalandorbitalmotions,wegroupedthedataaccordingtotheirprecessionalphasesasB0:prec=[0.,0.1[,B1:prec=[0.1,0.2[,B3:prec=[0.3,0.4[,B4:prec=[0.4,0.5[andB7:prec=[0.7,0.8[.Weobserveacosinusoidalpatterninthemotionofeachgroupwiththesameperiodastheorbitalmotion.Wettedeachprecessionalgroupwiththefollowingcosinefunction: 135

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Giesetal. ( 2002b ),weconsideredindependentamplitudesofthevelocityshiftsfordifferentprecessionalgroups.Infact,atdifferentprecessionalphasestheeffectsonH1duetotheorbitalmotionwouldbedifferentiftheobservedemissionalsodependsontheorientationoftheaccretiondisk.Thatisprobablythecasesinceeachgrouphasaclosebutdifferentwavelengthshiftpattern.TheirresultsandourtsareshowninTables 5-1 and 5-2 .Fromthesets,whichweshowinFigures 5-3 5-4 and 5-5 ,therearetwomainconclusions,aswewilldetailbelow:TheoriginoftheregionemittingH1isrelatedtoaowfromthestartothedisk;andtheowisaffectedbytheprecessionandthenutationoftheaccretiondisk. Therstconclusionisclearfromthetimeofzerovelocityoftheoscillations.ThemotionoftheregionemittingH1islikelyrelatedtotheorbitalmotionbecausetheresultingemissionismodulatedwiththesameperiod(Porb).However,themaximumblueshiftisnearinferiorconjunctionoftheaccretiondiskindicatingthatoscillationsofH1arenotstrictlyrelatedtothespeedofthestars,whosemotionwouldexhibitzerovelocityatconjunctionofthebinarysystem.Instead,theorbitalmotionofthebinarysystemwouldchangethedirectionoftheowofthegasemittingtheH1componentwhichlikelyhappensinthedirectionfromthemass-donorstartotheaccretiondisk.Infact,thisowwouldcreateamaximumblueDopplershiftwhenthemass-donorstarisbehindtheaccretiondiskandtheowmovestowardtheobserver,asweobservedinouranalysis. Thesecondconclusionisalsostraightforwardbecausetheparametersofthemodelchangewiththeprecessionalphase.Indeed,eachgrouphasadifferentresultingvalueofV0andV1fromthet.ThedifcultyliesinunderstandingthephysicaloriginofthecorrelationoftheseparameterstotheprecessionalmotionthatwestudyinordertondtheoriginoftheH1region(seeSection 5.1.3.2 ).Variationsoftheorbitalzero-phaseareontheorderoftheaccuracyofthetexceptfortheprecessionalintervalB1(seeFigure 5-5 ).TheH1componentisredshiftedbeforeorb=0.5comparedwiththe 136

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5-1 ).Thisvalue,0=0.005,isinagreementwiththezero-phaseobtainedby Giesetal. ( 2002b ).Wetagaineachgroupusingaconstantvalueofthezero-phase0=0.005,obtainingnewvaluesofV0andV1foreachrangeofprecessionalphases.WewillusethesevaluestostudytheoriginoftheH1componentandcompareourphysicalinterpretationwiththeconclusionsof Giesetal. ( 2002b ). 5-9 ).ItislikelythattheV0shiftisnotdirectlyduetotheowofthegasemittingH1becauseV0isnotmodulatedascosorbbytheorbitalmotion.Webelievethatthereissomekindofreprocessingbyscatteringoftheradiationbyanotherregion(thatwecallGrep)whosemotiononlydependsontheorientationofthedisk.Thisassumptionisconrmedbythepresenceofpolarizationofthelinethat,asweexplainedinSection 3.2 ,likelycomesfromThomsonscattering.Forinstance,equatorialwindsaredetectedfromradioobservations( Paragietal. 1999 ; Blundelletal. 2001 )whichcouldbeassociatedtoGrep.However,westudiedthispossibilityandequatorialoutowscannotexplainthebehaviorofV0withrespecttoprecaswewillseelater.Inordertoclarifytheoriginofthisregion,wetacosinusoidalfunctionV0=a+bcostoV0withabest-tformof, 137

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5-9 ),inotherwords,theredshiftishigheratedge-ondisk.Therefore,Grepisnotmovingneartheplaneofaccretiondisk.Theanglebetweenthemotionandtheaccretiondiskmustbehigherthan12(i.e.theinclinationofthebinarysystem90iorb;seeTable 6-1 )allowingtheredshifttodecreaseastheangledecreases.ThisrulesoutthepossibilityofGrepasequatorialoutows. Moreover,therearesomelimitationsofthegeometryoftheemissionandscatteringregionsinordertoexplainthesamevelocityshiftV0atanycongurationofthebinarysystem.Below,weexplainindetailtheselimitationsandwerecommendthereadertorefertoFigure 5-10 whichillustratesthescenariooftheemissionandscatteringregionsproducingtheobservedvelocityshift.Thescatteringgasmustexistinthewholeorbitormustorbitatthesameangularvelocityastheemissiongasbecausethescatteringproducesthesamevelocityshiftforanycongurationofthebinarysystem.Inaddition,V0isnotmodulatedbytheorbitalmotion,thereforethevelocityofthescatteringgaswithrespecttotheemittinggasaswellasthevelocityofthescatteringgaswithrespecttotheobserverdonotchangewiththeorbitalphase.Thesedirectionsonlydependontheprecessionalphase,meaningthattheowemittingtheH1componenthappensinaplaneperpendiculartothedirectionofthegasscatteringtheemission.Onthecontrary,thedirectionoftheemittingowwouldchangetheanglewithrespecttothedirectionofthescatteringowastheorbitalphasechanges;orthedirectionofthescatteringowwouldbedifferentwithrespecttothelineofsightatvariousorbitalphases(seeFigure 5-10 ). Ontheotherhand,theinterpretationoftheprecessionaldependenceV1istrickybecauseoftheapparentrandomvariationwithrespecttotheprecessionalphaseandofthesmallnumberofsamples.AswecanseeinFigure 5-11 ,thevariationsofV1

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Giesetal. ( 2002b )claimed,basedonthevelocityshiftsofthecentralpeakofHwhichcoincideswithH1,thatthestationaryHemissionlineisformedinthediskwindinavolumelargerthanthedimensionsofthebinarysystem.TheyarguedthattheradialvelocitycurveofH1isaffectedbythemass-donorstarthatevacuatesthesurroundingenvironmentoftheaccretiondiskwind.Inthe Giesetal. ( 2002b )model,theprecessionhasaneffectontheobservedvelocityshiftofH1componentbutdoesnotexplainhowthiscomponentisredshiftedbyanamountV0thatgraduallyblueshiftsastheaccretiondiskfacestheobserver.TheexistenceofthescatteringowfarawayfromtheaccretiondiskseemsunlikelybecausethereisnosourceofgasproducingtheV0velocityshiftthatisnotmodulatedbythestar.Nexttothemass-donorstar,thescatteringowwouldnotbeaffectedbytheprecession.Therefore,theemissionandscatteringhappensneartheaccretiondisk.Becausetheemittinggas,owingfromthemass-donorstartotheaccretiondisk,wouldconservethedirectionofitsinitialvelocityonlyneartheouteredgeoftheaccretiondisk,themostlikelyscenarioproducingtheH1componenthappensattheedgeoftheaccretiondisk,intheregionthatisclosertothemass-donorstar. WebelievethattheH1componentarisesduetotheinteractionoftheaccretedmasswiththeaccretiondiskinthehot-spotregion.Thehot-spotiscreatedwhenthestreamofgasfromthemass-donorstarstrikestheouteredgeoftheaccretiondisk,dissipatingthekineticenergygainedbythegasinashock.Theshockspreadsthegasaroundtheinteractionregion,thuscreatingthescatteringregionthatowsaway 139

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5-12 )willbediscussedagainwhenstudyingthepolarizationoftheH1component. 5-7 showsthevelocityshiftoftheHcomponentsindatasetsD2,D3,D4,andD5whichhavethesameprecessionalphasebutslightlydifferentorbitalphases.ThevelocityshiftsofH2andH3componentsarenearlysymmetricwithrespecttozeroshift.Theylikelyoriginateindiskwindswhichweassumetobecollimatedparalleltothejetdirectioninordertoestimatethewindvelocity.Inaddition,thediskorbitsaroundthecompanionstarandsooutowsfromthediskarealsosubjecttovelocitiesintheorbitalplane. Examiningtheradialvelocityoscillationswithrespecttoorbitalphaseprovidesinformationaboutthewindvelocityandorbitalspeed.However,duetothesmallamountofradialvelocityofH2andH3componentsandtheirhighuncertainties(seeTable 5-4 )thismethodisnotapplicablehere.Weassumesymmetryofwindsoneachsideofthedisk.Averagingbothcomponentsremovesthewindspeedcontribution,retainingonlyorbitalmotionshifts.Figure 5-4 containtheaveragedvaluesofthevelocityshiftsofthesetworegions.Theaveragedvalueiscloseto0atorbitalphaseorb=0anditfollowsalineartrendinrstorderapproximation.UsingEquation 5 andaddingthevelocityshiftofbothcomponentsweobtainedtheorbitalspeedof280km=s100km=s

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Giesetal. 2002b )andthevelocitycurveofHeII4686( Fabrikaetal. 1997 ). WettedthevelocityshiftsV2andV3oftheH2andH3componentswithalinearfunctionV2,3=aorb+b.Figure 5-7 showsthevelocityshiftoftheH2andH3components,aswellastheirtV2,3.Table 5-4 presentstsofH2andH3radialvelocityshifts.Thespeedoftheaccretiondiskwindsiscalculatedfromthelinearapproximationfunctionwhenthecontributionduetotheorbitalmotionisnull.AswecanseebylookinginFigure 5-7 attheaveragedlineartrendnearzeroshift,thishappensatorb=0(ororb=0.103),givingavelocityshiftVlosofH2andH3atthisphaseof35080km/sand38085km/sforH2andH3respectively.WeapplyEquation 5 tocalculatetheabsolutewindspeedVow,usingthepreviousvalueofvlosandtheparametersofthegeometryofthesystemobtainedfromthedynamicalmodelofjets( Margon&Anderson 1989 ; Eikenberryetal. 2001 ).Thevelocityoftheaccretiondiskwindis1700km=s300km=s,inagreementwithpreviousresultswhichestimateowspeedsof1500km=s( Goranskiietal. 1997 ). Giesetal. 2002b )andtheresultsfromourmodelbasedontheH2andH3components.Nevertheless,weshouldnotforgetthatthemeasuredFWHMandWmayalsobeaffectedbytheH1component.Westartthecomparisonofourresultswiththoseofpreviousauthors( Giesetal. 2002b )bystudyingthebehavioroftheFWHMofthestationaryHwithrespecttotheprecessionalandorbitalmotions.Infact,theseparationoftheH2andH3componentswillbroaden 141

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Previously, Giesetal. ( 2002b )measuredtheFWHMfromthewholeprole,simultaneouslyincludingtheH1,H2andH3components.Therefore,themeasuredFWHMdoesnotcorrespondtotheFWHMofanyindividualHcomponentbecauseitisoverestimatedwhenthecomponentsaremorespreadapartfromeachother.TheoveralltrendofFWHMisconstant(15A)exceptforB1andB3whichhaveabiggerFWHMneartheeclipseofthehot-spot.Thesystemisclosetoedge-on,meaningthatthecomponentsH2andH3arenotshiftedbecausetheaccretiondiskwindsowintheplaneofthesky.Therefore,thebroadeningoftheHlineprolecomesfromthebroadeningoftheH1component.Forthistohappen,theregionemittingtheH1componentmusthaveadifferentoriginthantheH2andH3components.ItisalsolikelythattheH1emissionisscatteredbyaccretiondiskwindswhichwouldbroadentheobservedemissionlinewhentheemittingregionisbehindthewindregionsinagreementwiththemodelwhichwestatedinSection 5.1.3.2 .Asareminder,themodeloftheH1componentconsistsofemissionfromaowatthehot-spotoftheaccretiondiskthatisscatteredbytheowofgasthatisejectedperpendiculartotheaccretiondiskduetotheinteractionatthehot-spotofthestreamofgasfromthemass-donorstarwiththeouteredgeoftheaccretiondisk. ConcerningtheevolutionofWofthestationaryHline,wedonothaveadenitiveconclusionaboutthecorrelationwiththegeometryoftheaccretiondiskandbinarysystem.Theradiation,thustheW,isexpectedtoincreaseastheinclinationangledecreasesbecausethefaceoftheaccretiondiskismoreopentotheobserver.Inorder 142

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5.1.3.1 ,ttingafunctiontoWwithrespecttotheorbitalphaseforgroupswithsameprecessionalphaseswithinarange.TheWofB0,B1,andB3suggestsinusoidaloscillations(seeFigure 5-13 ).Wettedacosinusoidalfunctiontotheequivalentwidthwithrespecttotheorbitalphaseasfollows, Then,wecomparetheparametersofthetforeachgroupandwestudytherelationoftheseparameterswithrespecttotheprecessionalphase.B2,B4,andB7haveveryfewdatapointsbutwenotethattheyspreadaroundacentralposition(seeFigure 5-13 )andmayalsobeperiodicwithrespecttotheorbitalphase.However,wecouldnotperformthetofthesinusoidalfunctiondescribedbytheEquation 5 becauseofthelownumberofdatapoints.Assumingthattheirevolutionisalsosinusoidalaroundacentralposition,thebestapproximationwecandoisusingthemeanandthestandarddeviationofB3,B4andB7asW0(prec)andW1(prec)respectively.Thislaterassumptionisverypoorbutithelpsustohaveareferenceoftheparametersofthesethreegroups(B3,B4,andB7).TherelationoftheparameterW1(prec)ofthetwiththeprecessionalphaseagreeswiththeexpectedincreaseofradiationatsmallinclinationangles(seeFigure 5-14 ).TheW1(prec)linearlydecreaseswithrespecttotheinclinationangleoftheaccretiondisk.However,theparameterW0(prec)doesnotshowanyobviouscorrelationwithrespecttotheprecessionalphase. 3.4 ).OurstudyofthevelocityshiftsofthesethreecomponentsindicatesthattheH1componentlikelyresultsfromaowfromthemass-donorstartotheaccretiondiskwhoseemissioniscreatedatthehot-spotandthenscatteredbysurroundinggas. 143

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UsingmodelsofthedynamicsoftheH2andH3componentswecorroboratedwindsfromtheaccretiondiskontheorderof1500km=sineachsideofthedisk.WewillseeinChapter 6 ,thattheexistenceofsuchwindsfromtheaccretiondiskhasastrongimpactontheevolutionoftherelativisticjetsofSS433whichinteractwiththewindneartheaccretiondisk.Therefore,itisimportanttoexpandourknowledgeofthegeometryandparticledensityoftheseregions.Aswewillseeinthefollowingsectionsofthischapter,thisispossibleusingourspectropolarimetrybecauseitseparatesthepolarizationofthedifferentsourcesofSS433aswellastheinterstellarpolarization(ISP). Giesetal. 2002a b ).Scatteringregionsplayanimportantroleinourmodels.ThisisconrmedbytheobservedpolarizationofH1,H2,andH3indatasetsD2,D3,D4,andD5.Wewillusethepolarizationofthesethreecomponentstoconrmthephysicaloriginoftheiremission.Forthispurpose,wewillusetheintrinsicpolarizationofthesecomponentsandtheevolutionoftheirpolarization.Wewillalsocompareourresultstothoseofpreviousauthors( McLean&Tapia 1980 )aftercalculatingamoreaccuratevalueoftheISPthatisonlypossibleusingourspectropolarimetry.Next,wewilldescribethecalculationoftheISP.Inthewholesection,wewillusethenotationsofpolarizationdenedinSection 3.1.1 andthenotationofthecomponentsexplainedinSection 5.1.1 144

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3 ,thedeterminationoftheISPisveryimportantbecauseitneedstobesubtractedfromtheoverallobservedpolarizationtoderivetheintrinsicpolarizationfromSS433.TheISPfollowsSerkowski'slawP()=Pmaxexp(1.15ln2(max Coyneetal. 1971 ).WeinvestigatedthestabilityoftheISParoundSS433butfewworksexistonthissubject. Wiktorowicz&Matthews ( 2008 )studiedthestabilityoftheISPoftargetscoveringalargerangeofeldsbuttheclosesttarget(HD157999)oftheirworkis26awayfromSS433.WecomparedstabilityofstarsintheeldofSS433instellarpolarizationcatalogs( Heiles 2000 )andpreviouspublications Krautter ( 1980 ).WefoundthatthepolarizationP=2.2%(within0.02%)andangleofpolarization=77.9(within3)ofHD179791werestablefor20years.HD179791isnearthelineofsightofSS433(within0.7)butmuchcloser(0.18kpc)thanSS433(5.5kpc).AnaccurateanswerrequiresobservingthestabilityofstarsnearSS433,sofarnowweassumeinthisworkthattheISPisstableforallthepolarizationdatathatwewilluse. Previously, McLean&Tapia ( 1980 )estimatedPmax=1.5%2.7%formax=5500Aandisp=30.Theyobservedlinearpolarizationwiththe2.3mand1.5mtelescopesattheUniversityofArizonaObservatoriesintheredlter(centeredat7000A),6500A7500Altersandanarrowband(FWHM32A)Hlter.Theymeasuredthepolarizationofstarswithin2'fromSS433tointerpolatethepolarizationofthetarget.Thesereferencestarsshowvaryingpolarizationlevelsfromnon-polarizedto1.5%andpolarizationanglesfrom352to165.ThespatialvariationsoflevelsandanglesofpolarizationaroundSS433arestrong,maybeduetovariationsofthedistancesofthereferencestarswithrespecttotheobserverbecauseISPisintroducedbythegrainsalongthelightpath(seeSection 3.1.4.4 ).Thus,thesestrongspatialvariationsinthepolarizationsuggestthatthelinearinterpolationoftheISPintheskybetweenreferencestarsaroundSS433isprobablyapoorassumption. 145

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McLean&Tapia ( 1980 )foundanupperlimitoftheISParoundSS433fromtheintrinsicpolarizationofSS433at2.2matprec=0.6( Thompsonetal. 1979 ).Basedonnon-detectionofpolarizationtheycalculatedanupperlimitofPmax=2.7%usingmax=5500A ( 1984 )observedUBVRIpolarizationofSS433withthe2.6mShaintelescopeandthe1.25mtelescopeattheCrimeanObservatory.TheyobtainedanISPangleISP=3.62.8fromIandRltersassumingthattheintrinsicsourcepolarizationiswavelengthindependent.TheyobtainedthelevelofpolarizationbyttingSerkowskii'slawtotheaveragedpolarizationofUBVRIlters.TheycalculatedtheISPinextremecasesofminimum[Pmax=2.81%andmax=5000A]andmaximum[Pmax=4.69%andmax=5860A]polarizationsbuttheirresultsarestillveryuncertainanddonotmatchalllters.Webelievethattheirassumptionsandtanalysisareproblematicandthisexplainswhytheirresultsdonotagreewith McLean&Tapia ( 1980 )and Dolanetal. ( 1997 ). WeuseourspectropolarimetryinordertosolvefortheISPandcorrecttheintrinsicpolarizationofSS433obtainedbypreviousauthors( McLean&Tapia 1980 ; Dolanetal. 1997 ).Forthispurpose,wesubtractedtheintrinsicpolarizationofthesourcetothecontinuumpolarizationobservedinourdata.WecalculatedtheintrinsicpolarizationofSS433usingthepolarizationoftheheliumlines.HeIlinesarelikelytooriginateinorneartheaccretiondisk( Crampton&Hutchings 1981b )wherethecontinuumemissionoccurs.Theheliumemissionlines(HeI7065andHeI6678)andcontinuumlikelyhavethesameoriginbecauseHeIhasalowionizationlevel.Thereforetheyhavethesamegeometry,densitydistributionofthescatteringregion,andgeometricalcongurationbetweenthesource,thescatteringgasandtheobserver.BecausethepolarizationfromThomsonscatteringdependsonthesethreeparameters,weassumethatthepolarizationoftheheliumlinesandthecontinuumisthesame. 146

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5-7 ).TheintrinsicpolarizationofHeIisobtainedfromthedifferentialpolarizationbetweentheHeIlinesandthecontinuum.Forinstance,thedifferentialpolarizationisfreefromISPbecauseSerkowskii'slawissmooth.WecalculatedtheISPsubtractingtheqanduStokesparametersofHeI6678andHeI7065emissionlinesfromthecontinuumStokesvector.Thus,theresultingStokesvectorSisp+linesisfreefromintrinsicsourcecontinuumpolarization;Sisp+linescontainsonlythecontributionfromtheISP,thestationarylines,andthemovinglines.Inordertoremovethecontributionoftheemissionlines,wettedSerkowskii'slawtoSisp+lines. TheISPfromHeI6678resultsinisp=327inthevisiblerangewithPmax=1.0%0.2%andmax7972A25A.Wendisp=376,Pmax=0.8%0.6%andmax=8180A14AusingHeI7065.ThemaximumpolarizationPmaxagreeswithresultsfromnearbystarsalthoughwedonotassumeanyparticularmaxwavelength.TheseresultsandtheISPfrompreviousauthorsaresummarizedinTable 5-3 .BothresultsareconsistentwitheachotherbutweadoptedtheISPobtainedfromHeI6678becausethelineisnotblendedwithotheremissionlinesandthesignal-to-noiseratioishigher.Ourresultssupporttheconclusionsof McLean&Tapia ( 1980 ).WefoundPmaxtobe0.5%lowerthantheseauthors,probablybecauseoftheirassumptionoflinearityoftheISPacrosstheeld.Weconrmedthatresultsfrom Emovetal. ( 1984 )arelikelytobeincorrect. 3.4 .Again,thedifferentiallinepolarizationcalculatedfromtheI,QandUuxabovethecontinuumisfreefromISPbecausetheISPvariessmoothly.WefoundinprevioussectionsofthischapterthattheHstationarylinehasthreecomponentsH1,H2,andH3.ThesecomponentswereclearlyvisibleindatasetsD2,D3,D4,andD5

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3.3.2 ).WewilluseD2fortheanalysisbelowofthepolarizationofthesethreecomponents. TheHcomponentsindatasetD2havedifferentpolarizations,indicatingdistinctgeometriesofthesource-scatteringregionscreatingH1,H2,andH3.Figure 5-12 illustratesthescenario,thatwestatedinSection 5.1 ,oftheregionswheretheH1,H2,andH3componentsareemittedandscattered.WecomparethepolarizationofthesethreecomponentsinordertoclarifythesimilaritiesbetweentheregionscreatingthestationaryHcomponents.WealsoincludeinthecomparisontheHeI7065andHeI6678withthepurposeofclarifyingquestion(2)inSection 5.1.1 .TheH1andH3componentshavesimilarorientation(H1=5.02.2andH3=1.60.9)andpolarization(PH1=1.8%0.4%andPH3=2.4%0.6%).ThepolarizationlevelofHeI6678isalsoofthesameorder(PHeI6678=2.1%0.6%)asH1andH3whereasthepolarizationofHeI7065(PHeI7065=1.1%0.6%)isconsistentwiththeminimallypolarizedH2component(PH2=0.9%0.1%).Ontheotherhand,H2hasthesamepolarizationangle(H2=17.02.6)asHeI6678andHeI7065(HeI6678=13.87.0andHeI7065=15.65.1). WerecommendthereadertokeepinmindFigure 5-12 duringthecurrentdiscussion.Thecongurationoftheemission-scatteringregionspolarizingH1andH3aresimilar.WenotethatourmodelsinSection 5.1 predictthatbothofthesetworegionsaresituatedonthesamesideoftheaccretiondisk(thesidewherethejetisapproachingtheobserver).ThiswouldexplainthatthepolarizationofH2,whoseemissionarisesintheothersideoftheaccretiondisk,isdifferentfromH1andH3polarizations.ThewidthsofthesethreelinesalsosupportthisideaconcerningthegeometryoftheH2regionwithrespecttoH1andH3.Infact,thewidthoftheH2component(600km=s)ismuchhigherthanthelinewidthsofH1andH3(200km=sand300km=srespectively).Inaddition,theH2emissionishighlyshiftedcomparedwiththeH1andH3components. 148

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Therefore,thestudyofthepolarizationofthelinessupportsourcurrentmodelwhichweobtainedfromthevelocityshiftoftheH1,H2,andH3components.However,thecharacteristicoftheregionscreatingtheselinescannotbesolelydeducedfromthemeasurementofthepolarizationataparticularprecessionalandorbitalphasebecausethepolarizationisrelatednotonlytothenatureofthescatteringregionbutalsototheorientationoftheemittingsource.ItisnecessarytostudythebehaviorofthepolarizationwithrespecttothedynamicalmotionsofSS433inordertoobtainmoredetailsofthesethreeregionsbecausetheseregionschangetheirpositionandorientationtotheobserverastheaccretiondiskandmassdonorstarmove. McLean&Tapia ( 1981 )foundagoodcorrelationofUwiththeprecessionalphase,buttheQvaluesdivergefromapureperiodicoscillation,probablyduetotheeffectsoftheorbitalmotion.TheyfoundamplitudesQ0.40.75%andU0.1%oftheQandUscatterfromapurecosinusoidalfunctionduetotheprecessionalmotion.However,theiranalysisdoesnottotallydisentangletheeffectsoftheorbitalmotionfromtheprecession.Here,weusethedataof McLean&Tapia ( 1981 )inordertostudytheeffectsoftheprecessionalandorbitalmotionsontheobservedpolarization.Wetthedatawithadynamicalmodelwhichde-correlatestheprecessionalandorbitaleffects.Although,morespectropolarimetryisrequiredinordertoconrmandne-tuneourmodel,weverifythatourmodeltsourspectropolarimetry 149

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Emovetal. 1984 ). 3 showsthatthepolarizationlevelPisrelatedtothescatteringangleiscatterasP/sin2iscatter.Theangleofpolarizationisrelatedtothegeometricorientationofthemainaxisinthesky.Wecorrectedthedatafrom McLean&Tapia ( 1980 )withtheISPvaluethatwefoundfromourspectropolarimetry(seeSection 5.2.1 ).Westudiedthedynamicalbehaviorofthepolarizationfromthesedatawithrespecttotheorbitalphaseorb.Thesedataarenotsufcienttodeterminethevariationsofthepolarizationwithrespecttoprecandorbindependently.Therefore,wefollowedasimilarapproachasfordynamicalstudy(seeSection 5.1 ).WegroupedthedataaccordingtotheirprecessionalphasedeningBP1asprec=[0.1,0.2],BP3asprec=[0.3,0.4],BP4asprec=[0.4,0.5],BP6asprec=[0.6,0.7],andBP8asprec=[0.8,0.9]. ThepolarizationofthegroupsBP1,BP3,BP4,BP6,andBP8ineachltertendtobeproportionaltocos2isdo,whereisdoistheanglebetweenthestar,thecenteroftheaccretiondiskandtheobserver.Wettedthepolarizationlevelofeachgroup(seeTable 5-5 )usingtheequation, Thepolarizationshowsalineartrendwithrespecttocos2isdo(seeFigure 5-15 and 5-16 )whichmeans,thatforeachorientationofthedisktheeffectoftheorbitaloscillations,atanyparticularprecessionalphaseprec,canberepresentedusingEquation 5 wherethepolarizationismodulatedbytheorbitalmotion.Foreachprecessionalphase,theeffectshavethesameamplitudeandmeanpolarization(A(prec)andB(prec)).Althoughwedonothaveenoughdatatoprovideanydenitiveconclusion,A(prec)andB(prec)mustoscillatewiththesameperiodastheprecessionbecausethescatteringalso 150

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Intherstcasewetriedcos(2(prec0))andcos2(2(prec0))functionsforbothA(prec)andB(prec).ThermsindicatesthatthebestapproximationsareA(prec)A0+A1cos2(2(precA))andB(prec)B0+B1cos(2(precB))(seeFigure 5-17 ).ThevaluesofthettingareshowninTable 5-6 .Inthesecondcase(A(prec)=A0),wecalculatedA0usingBP8groupthathavethemostnumberofdatapoints.TheparameterB(prec)isttedagainwithrstandsecondorderapproximations(seeTable 5-6 )usingthefollowingfunctions, (5) (5) TheresultsofthetsofA(prec)andB(prec)areplottedinFigure 5-17 .Thetotalnumberofdatapoints(25)isverysmallcomparedwiththenumberofparametersneededtocharacterizethedistribution.Therefore,thedegreeoffreedomofthedistributionislow,meaningthatthenumberofindependentobservationsissmall.Forinstance,thenumberofparametersintherstcaseforasecondorderapproximationofB(prec)isnine.Weadopttherstmodelbecausethenumberoffreeparametersisthehighest(18). Thepolarizationangleofeachgroupalsoshowsacosinusoidalvariationwithrespecttotheorbitalphase.WestudiedtheevolutionofB(prec)withrespecttotheprecessionalphasebyaveragingvaluesofeachgroupBP1,BP4,andBP6.ThegroupsBP3andBP8containmoredata,thereforeweobtainedB(prec)byapproximatingacosinusoidalfunction.Asforthesecondmethodforstudyingthelevelofpolarization,weobtainedtheevolutionofB(prec)fortheangleofpolarizationbyttingrstandsecond 151

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5 and 5 ) (5) (5) 5 arelargeduetothelowamountofdata.Inaddition,thepolarizationandangleofpolarizationobtainedinthismodelareaffectedbythepolarizationofthecontinuumandtheotherHcomponents.Werequiremorespectropolarimetrytoseparateeachindividualcomponentinordertoapplythecurrentmodelandtostudythecorrelationofthepolarizationtotheorbitalandprecessionalphases.AnaccuratestudyofthedynamicsofH1,H2,andH3regionswillgiveamoreclearpictureoftheaccretiondiskenvironment.Webelievethatwecanapplyourmethodforthestudyofthedynamicsoftheintrinsicsourcepolarizationtofuturespectropolarimetryobservationsinordertounderstandthemotionsoftheseregions.Forinstance,eventhoughthevaluesoftheparametersofourmodelwereobtainedwithlowamountofdata,weshowherethatitbettermatchesourresultsforthepolarizationoftheH1regionthanpreviousmodels( Emovetal. 1984 ). WecorrectedtheFourierdecompositionmodelof Emovetal. ( 1984 )usingtheISPobtainedfromouranalysis(seeSection 5.2.1 )andwecomparethisandtheintegratedpolarizationfromourmodeltothepolarizationofH1componentindatasetsD1,D2,andD6.TheintegratedpolarizationoverawholeorbitalperiodofaregionfollowingthemodelstatedbyEquation 5 is1 2A(prec)+B(prec).TheFourierdecompositionmodelof Emovetal. ( 1984 )consistsofttingtheobservedpolarizationvariationswith 152

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Figure 5-18 showstheFourierdecompositionmodelinthe(Q,U)polarizationplaneandtheH1componentsinourdatasetsD1,D2,andD6.Themodelof Emovetal. ( 1984 )beforecorrectionoftheISPisnotrepresentedbecauseitdeviatesconsiderablyfromthescaleoftheplot.ContrarytotheFourierdecompositionmodelaftercorrectionoftheISP,ourmodelisinagreementwiththeobservedpolarizationoftheH1component.Therefore,weplantofurtherinvestigatethegeometryoftheseregionsbyapplyingourmethodtofuturespectropolarimetry.ThisstudywillbeimportanttocompleteourresultsinthenextsectionabouttheparticledensitiesandthesizesoftheH1,H2,andH3regionsbecausetheirvaluesdependonthegeometry. Dolanetal. ( 1997 )estimatedthesizeoftheregionemittingtheblackbodycontinuumtobeL1.521012cm.Thepolarizationofthecontinuumsuggeststhatnearbydiskregionswiththistypicalsizehavene1.51010cm3( McLean&Tapia 1980 )although,thisresultissubjecttothedeterminationofthecorrectvaluefortheISP.Conversely,thepolarizationofstationarylinesindatasetD2giveselectronandprotondensitiesbetween281011cm3foraregionsize1012cm.Ascatteringgasthatisseparatedfromtheemittingregionwoulddilutethepolarizationatarateinverselyproportionaltothe 153

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Ontheotherhand,wecanestimatetheelectronandprotondensityusingequations, whereneistheelectronscattering,PistheobservedpolarizationfromthescatteringgasandIistheintensityoftheemission.Wedenethefraction=P2=Iwhichcanbemeasuredfromourspectropolarimetryandweassumethatne=npinthediskenvironment.Foranaxially-symmetricgeometry,thisratioisproportionaltotheparametergwhichwedenedas, whereHistheheightoftheaccretiondisk.Foranhomogeneousdensitydistributionne(r,z)=n0andifweassumethatthelightcrossthewholediskofradiusR2theparametergbecomes, Thus,wecalculatedtheheightsoftheemissionregionsusingg=H,andtheobservedintensityandthepolarizationoftheemissionlines.TheheightoftheHeIandHemissionregionsare109cmand5101010cmrespectively.Wecomparedthesevaluestotheheightofthediskfora10Msun-20Msunbinarysystem.Thecircularizationradius,wherethemostofthemassjointheaccretiondisk,isR2=0.07a=5.21011cm,whereaisthesemi-axisoftheorbit.TheheightofthewindsfromtheSS433accretiondiskisderivedfromtheeclipsesoftheX-rayemission,andisfoundtobeH0.4R22.081011( Stewartetal. 1987 ),tentimeshigherthanthesizeoftheHandHeI

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Westudiedtheinuenceoftheerrorsofthedifferentparametersusedinthecalculationoftheelectrondensity:thedistanceofSS433totheobserver;theintensityofI,Q,andUoftheemissionlines;andthegeometryanddensitydistributionofthescatteringregion.TheprotondensityisproportionaltoD2SS433,whichisknownwithin10%(seeSection 2.3.1 ).Therelativeuncertaintiesofthelineintensitiesaregenerallyhigherthan20%fortheHcomponents.However,themeasuredofHeIintensitiesareaccuratetoabout2%,thuswecannotneglecterrorsinthedistanceofthesystemwhencalculatingtheirluminosity. Thedensitydistributionalsoaffectsthecalculationsoftheheightofthescatteringregion.Forthepurposeofstudyinghowtheparticledistributionaffectsthenalresultfornon-homogeneouselectronandprotondensitydistributionsofanaxially-symmetricdisk,wedenetheparameterfas, Ontheotherhand,thedensitymayincreasesharplyattheedgeoftheaccretiondiskincreasingthegfactoranddecreasingthecalculatedheightoftheaccretiondisk.Anotherscenarioisoneinwhichahotspotlocallyincreasesthedensityatthediskedge 155

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wheredensityisevaluatedlocallyallaroundthedisk.Thisexpressionaccountsforthecontributiontothepolarizationofthescatteringregionsawayfromthelineofsight.Then,theeffectsoftheasymmetrydependonthedensity,requiringmodelingofthedensitydistributionsinordertoevaluateg.Whatseemsclearisthattheresultingpolarizationdependsontheenergydistributionandthegeometryofthebinarysystem. Theshapeoftheemittingandscatteringregionsisalsoanimportantfactorbecausepolarizationcarriestheimprintofthescatteringregion.Itsinuenceisestimatedforaxi-symmetricstructuresinopticallythinregions(seeSection 3.2.2 ).TheSS433accretiondiskhasradiativelydrivenoutowswithvw1500km=sformingaconearoundthejetsarisingfarfromthecentralsourceandextendingwelloutsidethedisk.Asidefromasymmetriesintroducedbytidalforcesandwindsfromthemassdonorstar,andthescatteringregionsoftheaccretiondiskarelikelyannularcylinders.Weassumethatwindsfromtheaccretiondiskarecollimatedinordertocalculatetheeffectsoftheshape,thusthisregionisalsoanannularcylinderforthepurposeofthisanalysis.TheinuenceoftheshapeofregionswiththisgeometryanduniformdensitydistributionsisgivenbytheshapefactorexpressedbyEquation 3 .ForR11.21011cmequaltotheexpellingdistanceofthewind( Begelmanetal. 2006 ),R2=5.21011cmandh 156

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Inaddition,wecalculatedtheorbitalspeedV=280km=s100km=sfromthesecomponentswhichisinagreementwiththeamplitudesoftheradialvelocityofCII7231,7236.Therefore,themassfunctionofthebinarysystemF=1.035107V3orbPorbisknownbecausetheorbitalperiod(Porb=13days)ofSS433hasbeenaccuratelydetermined(seeSection 2.3.2 ).Consideringtheuncertaintiesofthevelocityoftheorbit,theminimummassfunctionisFmin=7Msun.Themassratioisdenedq=MX Stewartetal. 1987 ).Theseauthorsndamassratio0.8
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McLean&Tapia 1980 ).Ourmeasurementssuggestthattheelectrondensityinaregionofsize21012cmisne281011cm3,morethanoneorderofmagnitudehigherthantheresultsfromtheseauthors.Theseauthorsmadesimpleassumptionsaboutthesizeofthescatteringregionwhichisintimatelyrelatedtotheparticledensity.Forinstance,thecalculatedparticledensityandsizeofthescatteringregiondependonitsgeometry.Wealsostudiedtheeffectsofthegeometryonthesizeanddensityoftheaccretiondiskwindsbecausetheseresultsareofextremeinterestforthestudyofthejet-diskinteractionwhichwepresentinthefollowingchapter. 158

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Fitofpeakvelocityshift(V)ofHvstheorbitalphase(orb)fromdatasetD1,D2,D3,D4,D5,andD6usingacosinuoidalfunctionV=V0+V1cos2(orb0).WegroupthedataaccordingtotheirprecessionalphasesasB0:prec=[0.,0.1[,B1:prec=[0.1,0.2[,B3:prec=[0.3,0.4[,B4:prec=[0.4,0.5[andB7:prec=[0.7,0.8[.Thistableincludesboth,ttingvalueswithallfreeparameters(Topofthetable)andassumingsamezero-phase0foralltheprecessionalgroupsB0,B1,B3,B4,andB7(Bottomofthetable). PrecessionalGroupV0(km/s)V1(km/s)0 159

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Fitofpeakvelocityshift(V)ofHandHeIvstheorbitalphase(orb)from Giesetal. ( 2002b )datausingacosinuoidalfunctionV=V0+V1cos(2(orb0)).Thedataisseparatedaccordingtherunnumberoftheirobservations.Credit:Table6 Giesetal. ( 2002b ) PrecessionalGroupV0(km/s)V1(km/s)0 Table5-3. ResultsabouttheinterstellarpolarizationaroundSS433 ( 1980 )[1.5,2.7]550030 ( 1984 )(1)2.8150003.6 ( 1984 )(2)4.6958603.6HeI66780.97797232HeI70650.81818037

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Linearapproximationvelocityshift=aorb+bofdynamicalbehaviorofH1,H2andH3componentsfromdatasetsD2,D3,D4,andD5.DifferentialvelocityshiftsusingandBbandsareused.ThetofmeanofH2andH3isalsoshownaswellasatoftheseindividualcomponentsusingtheresultingslopeofthemean(designatedby*) Componenta(km/s)b(km/s) Table5-5. LinearapproximationP=acos2isdo+bofpolarizationofHandcontinuumfromD1,D2,D3,D4,D5,D6,and McLean&Tapia ( 1980 )data. Binrefa(%)rms(%)b(%)rms(%) BP10.8309710.05587661.913040.0294487BP3-0.005851030.05065662.056920.0407214BP40.6206450.154151.422750.070641BP60.7634230.09068250.9380630.0512726BP80.4465330.07360971.262880.0468263 BP1(slopeBP8)0.4465330.07360972.289920.0149987BP3(slopeBP8)0.4465330.07360972.052450.0138567BP4(slopeBP8)0.4465330.07360971.674550.0328487BP6(slopeBP8)0.4465330.07360971.224740.0383256 Table5-6. ApproximationofA(prec)=A0+A1cos2(2(precA))andB(prec)=B0+B1cos(2(precB)).*correspondstocoefcientsobtainedassumingthattheslopeA(prec)=A0isconstant

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TheorbitalphasesofdatasetsD1,D2,D3,D4,D5,andD6areoverplottedonthemeanV-bandlightcurve.Credit:OurdatapointshavebeenoverplottedinFigure3by Kempetal. ( 1986 ) 162

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SpectrumofdatasetD2(solidline)aroundthestationaryHline.ThethreeH1,H2,H3componentsthatwettothedatainSection 3.4 arealsooverplotted(dashedlines).TheplotincludesalsotwomovingHlines(Halpha+)ontheleftofthestationaryHline,andtheHeI6678.Thenamesofthemovingandstationarylinesarelabeledonthetopofthewindow. 163

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VelocityshiftofstationaryH1componentforvariousprecessionalphases.Thedatafrom Giesetal. ( 2002b )areseparatedinthreeplotsaccordingtotheirprecessionalphaseasexplainedinSection 5.1.3.1 .FromtoptobottomprecessionalintervalsareB0:prec=[0,0.1],B4:prec=[0.4,0.5],andB7:prec=[0.7,0.8].EachplotillustratestheevolutionoftheH1velocityshiftwithrespecttotheorbitalphase(orb).Weoverplotthedynamicalmodel(dashedline)thatwettothedatainSection 5.1.3.1 .Foreachoftheseprecessionalranges,thevelocityshiftoscillateswiththeorbitalphasewithsameorbitalzero-phase. 164

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VelocityshiftofstationaryH1componentforprecessionalphases0.3
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VelocityshiftofstationaryH1componentforprecessionalphases0.1
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EvolutionofabsorptionfeaturesintheHlineprole.ThedashedcurveindicatesthepositionoftheHjetlines.Thebluedottedlinetracesthemotionoftheblueshiftedabsorption.Credit:Figure6by Giesetal. ( 2002b ). 167

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EvolutionoftheHlinecomponentsofdatasetsD2,D3,D4andD5.DatapointsarelabeledasDX YwhereXindicatesthedatasetnumberandYindicatesthecomponentnumber.ComponentsareH1(redsquares),H2(reddiamonds),andH3(bluetriangles).ThemodelobtainedinSection 5.1.3.1 ofthedynamicsoftheH1isoverplot(blackdots)fortheparticularcaseofprec=0.24. 168

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IllustrationofthecoordinatesystemsdenedinSection 5.1.2.1 .Thepurposeofthegureistosketchhowtheframesarerelatedwitheachother.Becausethesystemconsistofthreeframesthatarerotatedinspacewitheachother,itishardtoimagineit.Wewanttovisuallyillustratetheanglesofrotationbetweentheframes.Forthispurposeweshow2Dprojectionsontherightofthesketchanda3Dsketchofthegeneralpicture.Wedenedthefourcoordinatesystems:Cobs=(~Xobs,~Yobs,~Zobs)(observer),Corb=(~Xorb,~Yorb=~Yobs,~Zorb)(orbit),Cprec=(~Xprec,~Yprec,~Zprec)(precession),andCnut=(~Xnut,~Ynut,~Znut)(nutation).ThesecoordinatesystemsaredrawnoverasketchofSS433whichincludethemass-donorstar,theaccretiondisk,andthetrajectoryoftheorbit(dashedcircle).Thepatternoftheprecessionofthejetsisonthetopofthesketch.Weindicatetheorbitalinclination(iorb)andthenutationalamplitudeangle(nut)whicharepresentedinTable 6-1 169

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EvolutionofV0withrespecttotheinclinationofthejetsofSS433.V0resultsfromthetoftheV=V0+V1cos2(orb0)functiontothevelocityshiftstationaryH1component.WeshowthevaluesofeachgroupBiofprecessionalphasesintherange[i,i+0.1]B0:prec=[0.,0.1],B1:prec=[0.1,0.2],B3:prec=[0.3,0.4],B4:prec=[0.4,0.5]andB7:prec=[0.7,0.8].Theaveragedvaluesofthevelocityshiftin[0.5,0.6]and[0.6,0.7]intervalsarelabeledasB5andB6respectively.ThecosinusoidalapproximationV=250315cosisoverplotted(dashedline).ThisgureshowsthatthevelocityshiftV0isconsistentwithperiodicaloscillationswithrespecttotheinclinationangleofthejet,thereforeitmaycomefromtheprojectionofagasowvelocitytothelineofsight. 170

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Sketchofthescenarioaroundthehot-spotemittingH1.WeillustratetherelativedirectionsbetweentheV0ow,V1ow,andthelineofsight.V1representsthespeedofthestreamofgasgoingfromthemass-donorstartotheaccretiondisk.V0representstheaveragedvelocityofthegasthatisspreadatthehot-spotduetotheinteractionofthestreamwiththeouteredgeoftheaccretiondisk.Weshowtheopticalstar(yellow),theaccretiondisk(brown),thehot-spot(red),thecompactobjectregion(blue).Thesesketchesillustratethreedifferentscenariowhere:(1)1=\(V0,V1)6=90isconserved(topleft),(2)0=\(V0,l.o.s)=constant(toright),and(3)1=90(bottom).Thethreesketcheshavetwocongurationswiththeopticalstaratorb=0andorb=0.5.Scenario3istheonlycongurationinwhichboth0and1areconservedforanyorb. 171

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ThisplotshowstherelationofV1withrespecttotheprecessionalphase.V1resultsfromthetoftheV=V0+V1cos2(orb0)functiontothevelocityshiftstationaryH1componentforeachgroupBiofprecessionalphasesintherange[i,i+0.1]B0:prec=[0.,0.1],B1:prec=[0.1,0.2],B3:prec=[0.3,0.4],B4:prec=[0.4,0.5]andB7:prec=[0.7,0.8].WeseethatV1doesnotfollowanyclearlinearorcosinusoidalvariations. 172

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IllustrationoftheregionsemittingH1,H2,andH3.Thegureshowsthebinarysystem(compactobjectandmass-donorstar)andtheaccretiondisk.Intheouteredgeoftheaccretiondiskthegasatthehotspotisspreadduetostream-diskimpact.Thisgasowsawayfromthehot-spotandscattertheinitialemission.Theemissionfromtheaccretiondiskwindisshiftedbecauseofthegasmotionandtheorbitalmotionofthediskaroundthemass-donorstar. 173

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EvolutionofequivalentwidthofthestationaryHlineforvariousorbitalphases.Wegroupthedatafrom Giesetal. ( 2002b )accordingtotheirprecessionalintervalsareB0:prec=[0.,0.1](top),B1:prec=[0.1,0.2](middle),andB3:prec=[0.3,0.4](bottom).ThisplotillustratestheevolutionoftheHequivalentwidthwithrespecttotheorbitalphase(orb).WeoverplotthetsthatweobtainedinSection 5.1.4 ofthefunctionW=W0(prec)+W1(prec)cos2(orb0(prec))foreachgroup(dashedlines). 174

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EvolutionofW1withrespecttotheinclinationofthejetsofSS433.Weshowthevalues(bluediamonds)ofeachgroupBiofprecessionalphasesintherange[i,i+0.1]B0:prec=[0.,0.1],B1:prec=[0.1,0.2],B3:prec=[0.3,0.4],B4:prec=[0.4,0.5]andB7:prec=[0.7,0.8].W1ofgroupsB0,B1,andB3resultsfromthetoftheW=W0(prec)+W1(prec)cos2(orb0(prec))functiontotheEquivalentWidthofthestationaryHline.WeplotthestandarddeviationofthesamplesB4andB7whichwedonotseebecausetheyareverysmall.Wenotethattheequivalentwidthincreasesastheaccretiondiskfacestheobserverasexpectediftheradiationfromtheaccretiondiskwindsisanisotropic. 175

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Modelofthepolarizationversusorbitalphase:P=A(prec)cos2isdo+B(prec).PolarizationofcontinuumforprecessionalphaseintervalsBP1:prec=[0.1,0.2](top)andBP3:prec=[0.3,0.4](bottom).Thediamondsindicatebroadandnarrow-bandimagingpolarimetry( McLean&Tapia 1980 ).ThepolarizationofdatasetD2,D3,D4,andD5comefromH1(squares).ThepolarizationofdatasetsD1andD6arecalculatedfromasingleGaussiant(squares).Dashedlinesarelinearapproximations.SolidlinesshowlinearapproximationsusingsameslopeasBP8.Thecosistorelationsuggeststhatthepolarizationisduetotheorbitofthescatteringregionaroundtheaccretiondisk.However,itisnecessarytocompletethisanalysiswithmorespectropolarimetrywhichseparatesthedifferentcomponents. 176

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Modelofthepolarizationversusorbitalphase:P=A(prec)cos2isdo+B(prec).Polarizationofcontinuumforvariousprecessionalphases.FromtoptobottomprecessionalrangesareBP4:prec=[0.4,0.5],BP6:prec=[0.6,0.7]andBP8:prec=[0.8,0.9].Thepolarizationdata( McLean&Tapia 1980 )arecalculatedinbroadandnarrowbandimages.Dashedlinesarelinearapproximations.ContinuumlinesshowlinearapproximationsusingsameslopebaseonBP8whichhasthelargestsampleofalltheintervals.Thecosistorelationsuggeststhatthepolarizationisduetotheorbitofthescatteringregionaroundtheaccretiondisk.However,itisnecessarytocompletethisanalysiswithmorespectropolarimetrywhichseparatesthedifferentcomponents. 177

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Modelofthepolarizationversusprecessionalphase(A(prec)andB(prec)).Foreachprecessionalinterval,A(prec)(square)andB(prec)(diamonds)coefcientsareobtainedfromthepolarizationapproximationP=A(prec)cos2isdo+B(prec).TheplotshowstheevolutionofA(prec)andB(prec)withrespecttotheprecessionalphasefortwodifferentmodels.Therstmodel(top)assumesconstantA(prec)=0.446andB0+B1cos(2(precB)).ThesecondmodelassumesA0+A1cos2(2(precA))andB0+B1cos(2(precB)).OurmodelsforA(prec)andB(prec)arerepresentedwithsolidanddashedlinesrespectively.Weobservethattheyhaveaperiodictrendalthoughmoredataisrequiredinordertoverifythattheoscillationsarestatisticallyconsistent. 178

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ComparisonofourmodelandtheFourierdecompositionofthepolarization.Theplotshowstherst(solidline)andsecond(dashedline)orderFourierdecompositionof Emovetal. ( 1984 ).WeoverplottheH1componentindatasetsD1,D2,andD3aswellastheexpectedpolarizationattherespectiveprecessionalphasesofthesedatasets.Theexpectedpolarizationwascalculatedusingourdynamicalmodelofthepolarizationbasedondataof McLean&Tapia ( 1981 ).Thepredictedpolarizationfromourmodelatprecessionalphasesprec=0,prec=0.24,andprec=0.66andtheirerrorbarsareploted(largecrosses)andlabeledaccordingtoprec.WenotethatourmodelbettermatchespolarizationobtainedfromourspectropolarimetrythanFourierdecomposition. 179

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ThestudyoftheopticaljetsofSS433isatthecoreofthepresentthesis.InChapter 2 ,wediscussedtheissuesrelevanttorelativisticjetformation.Oneoftheimportantquestionsisaboutthecompositionoftheplasmathatisejectedintheow-eitheraproton-electronplasmaoranelectron-positronplasma.Knowingtheplasmacomposition,incombinationwiththeresultsfromChapter 5 aboutthejet-diskinteractionregion,willhelptoelucidatethephysicsofthejetformationandacceleration.Inthischapter,weanalyzethepropertiesoftheopticaljetsofSS433obtainedfromspectroscopyduringthepast30yearsandthepropertiesderivedfromthepolarizationofthejetsobtainedfromourspectropolarimetry.Inparticular,wewillstudytheevolutionoftheequivalentwidthofthemovinglines,andtheBalmerdecrementofthejetwithrespecttotheprecessionalphaseasadiagnosticofthephysicalconditionsofthegas(protondensity,temperature,llingfactor,opticaldepth),theanisotropyoftheemissionfromtheopticaljets,thesourceofheatingofthegas,andtheenvironmentaroundtheplasmajet.InSection 6.2 ,weuseourspectropolarimetrytothepurposeofcalculatingandcomparingtheelectronandprotondensitiesoftheopticaljets.Afterexploringtheoriginofthepolarimetry,wederivethegeometryandcompositionofthejetsfromthepolarizationofthemovinglines,andwepresentourmodelforthestudyoftheparticlecompositionalongthejetandtheresultsderivingfromthismodel.Finally,wediscusstheconclusionsfromthespectroscopicandspectropolarimetricstudies,andweexploretheconsequencesofourresultsonourunderstandingofSS433'sjetsandthecurrentmodelsofrelativisticjetformation.InSection 6.4 ,weinvestigatehowthecorrelationbetweenparametersofthedynamicalmodel,thejet-diskinteractionregion,andthejetregionpropertiesareconsistentwithourmodelofSS433'sjetformation. 180

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6.1.3 thephysicalconsequencesofthecurrentspectroscopicanalysis. 2.3.2 ,thepositionofthemovinglinesdependsonthejetinclinationanglewithrespecttothelineofsight.Thejetsrotateastheaccretiondiskprecesses,periodicallychangingtheirorientation.isdenedintermsofgeometryas, cos=sinprecsiniorbcosprec+cospreccosiorb(6) Margon&Anderson ( 1989 )and Eikenberryetal. ( 2001 )foundfromtheanalysisofthemovinglines(seeSection 2.3.3 onthespectraofSS433)theinclinationangleofthebinarysystemwithrespecttothelineofsight(iorb=78.05)andtheprecessionalconehalf-angle(prec=20.92).Theseauthorsdenedtheprecessionalphaseprec=2tt0

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3-14 ). InSection 2.3.5.2 ,wedescribedthestructureofthejetsofSS433.Theopticaljetsareformedofmaterialintheformofclumpsofgascommonlycalledbullets( Borisov&Fabrika 1987 ; Vermeulenetal. 1993 ).Theyappearasstructuresintheasymmetricjetlineproleswhicharegenerallycomposedofamaincomponentandtwoorthreesecondarycomponents. Panferov&Fabrika ( 1997a )studiedtheluminosityproleofthesebulletsalongtheopticaljetandnotedthatthesecomponentsappearwhenthebulletscooltoT104Katthebaseoftheopticaljetremainingatthesamewavelengthpositionfor23daysuntilbulletopticalemissionceases.Redandblueprolesareusuallyanti-symmetric( Kopylovetal. 1987 ).Clumpsofgasarealsoobservedinradioimages( Vermeulenetal. 1993 )athigherdistancesfromthecentralsource.Theyfollowthedirectionpredictedbythekinematicalmodel( Margon&Anderson 1989 )obtainedfromthemaincomponentsofthemovingHlines, where=v=c=0.26isthejetvelocity,=121=2istheLorentzfactor,precistheprecessionalphase,iorbistheinclinationofthebinarysystem,andprecistheinclinationofthejetwithrespecttoprecessionalaxis.Wepresentthevaluesoftheparametersoftheequationthatwerederivedusing20yearsofspectroscopyofSS433( Eikenberryetal. 2001 )andinradioobservations( Stirlingetal. 2002 )inTable 6-1 .ThecoherenceofopticalandradiokinematicmodelmakesitpossibletoestimatethedistanceDSS433=5.50.2kpcofthesystemfromtheEarthwithhighaccuracy( Lockmanetal. 2007 ). 182

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Panferovetal. ( 1997 )studiedtheangulardistributionoftheradiationfromthejets.Although,theHlightcurvesaresubjecttoassumptionsaboutabsorptionoftheISM,itisclearthattheintensityofthemovinglinesdependsonprecessionalphase.Themaximumintensityoftheradiationisobservedbeforeprec=0,suggestingthatthemaximumilluminationisabout3040fromthedirectionoftheowtowardprecessionalmotiondirection.Thefrontsideofthebulletsseemstobe1.7timesbrighterthantheirbackside. Wecalculatedinourdatatheratiobetweentheapproachingtotherecedingjetintensitiesattheprecessionalphasesprec=0.17andprec=0.24inordertoverifytheassymetryresults.Wedidnotcalculatetheratioatprecessionalphaseprec=0.63becausethecontributionfrombothjetsinthedatasetD1cannotberigorouslyseparated.TheresultingratiosforthemainandsecondarycomponentareshowninTable 6-2 .TheratiooftheintensitiesofbothjetswerecalculatedusingH Panferov&Fabrika ( 1997b )foundthatovertenyearsthehydrogenH 183

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Weuseddatafrom Asadullaev&Cherepashchuk ( 1986 )inordertocompleteourresults.TheystudiedtheevolutionoftheintensitywithrespecttotheorbitalandtheprecessionalphasesoftherecedingandapproachingHjetsseparately.Wecalculatedtheratioofintensitiesofthebluetoredjetlinesusingtheirdata(seeFigure 6-1 ).Weassumedthatthesameextinctionaffectsbothjetssotheratiodoesnotneedanyextinctioncorrection.Theratioishigherintherangeprec=[0.1,0.3]increasingnearprec=0anditisaboutonenearprec=0.5.Theaveragedvalueswithinintervals=0.1showa2ndorderpolynomialtendency withminimumH Wegroupedthedataaccordingtotheirprecessionalphase.WefoundnocorrelationoftheratioofintensitiesofHjetlineswithorbitalphaseorb(seeFigure 6-2 ),meaningthattheorbitalmotiondoesnothaveacleareffectontheobservedintensityofthemovingHlines.Theeffectsthatthenutationhasinthevelocityshiftofthemovinglines( Stirlingetal. 2002 )donotappearintheintensityoftheradiation.Forinstance,theangleofthenutationistoosmall(3)tochangetheopticalpathoftheemissionfromthejetbuthighenoughtochangetheprojectedvelocitytothelineofsightforsuchalargevelocity(v0.26c).Inaddition,wethinkthataninteractionbetweenthegasoftheopticaljetsandacontinuouswindfromthemass-donorstarisunlikelybecausetheorbitalmotionwouldmodulatetheobservedintensityoftheemission. Inordertocompletethepreviousstudyoftheintensityofjetlines,westudiedtheBalmerdecrementofthetwojetswhichistheratioofintensitiesbetweendifferent 184

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Panferov&Fabrika ( 1997b ).Theseauthorsfound[H] [H]=0.90.2and[H] [H]=0.80.1atprec=[0,0.2];and[H] [H]=1.60.2and[H] [H]=0.70.1atprec=[0.7,0.9].Ourresultsdivergefromtheirdata.Wecalculated[H] [H]=1.050.4atprec=0.63and[H] [H]=0.950.32atprec=0.17.WedonotseeanycorrelationbetweenHtoHorHtoHratiosandtheprecessionalphase.Therefore,theresultsoftheelectrondensity( Panferov&Fabrika 1997b ),whicharebasedontheevolutionoftheBalmerdecrement,aredoubtful,aswewilllaterdiscuss. Panferovetal. 1997 )whichsupportstheexistenceofnon-sphericalregionsemittinganisotropically. 185

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Panferovetal. 1997 ).Themainlimitationwhileinvestigatingtheinnerpropertiesofthejetfromtheintensityoftheemissionlinesisthatthesourceofenergyexcitingthehydrogenofthebulletsisnotasyetknown. Brown ( 1991 )reviewedthemechanismsheatingtheHbulletsofthejetandrestrictedthepossibleconditionsofthegas. Brown&Fletcher ( 1992 )and Brown ( 1991 )suggestedthatthemostlikelysourceofheatingiscollisioninteractionofthejetwiththegasowingfromtheaccretiondisk.However,thereareotherpossiblesourcesofenergyheatingthegasoftheopticaljetsincludingUVorX-raycollimatedradiationfromthecentralsource.UVradiationcanonlyheatthebacksurfaceofthecloud(nearerthecentralcore)whichcontradictsourresultsontheanisotropyofthebulletsabove.HeatingbyX-raysseemsplausibleonlyiftheX-rayradiationisbeamedalongthejetwhichmayhappeninthefunnelofthethickaccretiondisk.Forinstance, Panferovetal. ( 1997 )derivedtheelectrondensityne1013cm3ofbulletsllingafactor=106ofthetotaljetvolume.However,theoriginofthesourceofheatingofthebulletsisstillunknownandtherefore,anystudyofthepropertiesofthejetsassuminganyoftheheatsourcesisuncertain. Panferov&Fabrika ( 1997b )usedanotherwaytocalculatetheconditionsofthejet.TheycomparetheobservedBalmerdecrementfromthemovinglinesandthecomputationalsimulations( Drake&Ulrich 1980 )ofradiativetransferthroughauniformslab. Panferov&Fabrika ( 1997b )invokedelectrondensityne1013cm3andllingfactor=106ofthejet,assumingUVandcollimatedX-rayradiationheatofthebullets.Theseresultsdependonceagainontheoriginoftheheatingmechanismsofthegasoftheopticaljets.Inaddition,ourresultscontradicttheirmodelbecausewendnovariationoftheH=Hratiowhichwecalculatedatthesameprecessionalphasesastheseauthors.WedonotbelievethedensityderivedfromtheBalmerdecrement 186

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Drake&Ulrich 1980 )isnotaccurate,andtheirBalmerdecrementdonotmatchourobservations. Marshalletal. ( 2002 )foundthermalelectrondensitiesofne21015cm3atthebeginningoftheX-rayjetsandne41013cm3attheendoftheX-rayjets,whichextendtodistancesfromthecompactobjectuptod21011cm. Kotanietal. ( 1996 )conrmedelectrondensityofne1014cm3fromtheX-raySiXVIItriplet.Intheradiojetsatdistancesfromthecentralcorebetweend3.51015cm1017cm, 187

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Seaquistetal. 1980 ).Ifthejetsareexpandingasanadiabatically-coolingplasma,theelectrondensityshoulddecayasne/1 Thisvaluecanchangeaccordingtotheionizationfractionofthehydrogenatomsofthejetgas.ThegasistotallyionizedatthetypicaltemperatureoftheX-rayjets.TheionizationstateofthebulletsalongtheopticaljetisgivenbytheSahaequation, h23=2e13.6eV kT(6) wherenHisthetotalnumberofhydrogenatoms,fion=ne Thus,weestimatedfromtheobservedelectrondensityoftheX-rayjetsthat,ifthegasisadiabaticallyexpandingwhilethejetpropagates,theelectrondensityoftheopticaljetsisaboutne107cm3.However,theresultsofpreviousauthors( Panferovetal. 1997 ),basedonspectroscopy,suggesthighdensityne1013cm3.Theseresultsaremodeldependentbutourspectropolarimetricdataprovidetherstdirectmeasurementofphysicalconditionsintheopticaljet. 3.3 ,ourspectropolarimetryshowslinearpolarizationofthemovinglines.Forinstance,allourdatasets(D1,D2,D3,D4,D5,andD6)containemissionlinesattheexpectedwavelengthpositionfromthedynamicalmodelofthemovingHlines.Thelineproleslookliketheproleofthemovinglinesinpreviousspectroscopy.Therearepolarizedfeaturesinourspectropolarimetryatthesamewavelengthsatthe 188

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C )clearlyshowspolarizationfromtheopticaljets.WereferthereadertoSections 3.2 ,and 3.1.2 whilereadingthediscussionabouttheoriginofthepolarization. InSection 3.2 ,weexplainedthatarelativelyweakmagneticeldislikelyintheopticaljetsbecausenoopticalcircularpolarizationisobserved( Liebertetal. 1979 ).TheabsenceofastrongmagneticeldintheopticaljetsindicatesthattheopticallinearpolarizationisnotproducedbycircularlyacceleratedparticlesforwhichpolarizationistransformedintolinearpolarizationduetoFaradayeffectsintheplasma. PolarizationbytheCerenkoveffectisalsounlikely.Letusassumethatparticlesarepropagatedalongthejet,whichweconsidertobeanopticalmediumofrefractiveindexn.AsexplainedinSection 3.1.2.3 ,theradiationwouldhappeninaconeofhalf-anglec=acos(1 3 .Ifweassumethatthecharacteristiclengthoftheemittingregionis1014cm(whichisthesizeoftheopticaljets),theobserveduxfromtheCerenkovradiationwouldbeabout31027erg.Thisisaverylargeestimatebecausethecharacteristicsizeoftheemissionregionmustbemuchsmallerthanthejets.Furthermore,thevolumeweconsideredoftheemittingregionismuchlargerthantherealvolumeofthejetitselfthus,theresultingobserveduxisamaximumvalue.Asareference,theobservedemissionfromthejetsisabout21013ergwhichisafactor1014greater.TheemissionduetoCerenkoveffectsistoosmalltopowerthefeatureswhichareobservedinourspectropolarimetry. Comptonscatteringbyhigh-energyphotonsmayalsoproducepolarizationfromthejets.However,thelinewidthofthepolarizeduxisroughlyconserved,indicating 189

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Thomsonscatteringbyfreeelectronsofthehydrogenandheliumemissionlinesismorelikelyresponsibleforpolarizationofthejets.Therefore,weusedthesameanalyticalmodelsexplainedinSection 3.2.2 forthepolarizationoftheaccretiondisk.Theopticaljetsarelikelypolar-likegeometriescontaininggasinformofclumps.Next,weusetheresultsofhomogeneouscylinderstocalculatetheproton-electronpopulationofthejetandthen,westudytheinuenceofthellingfactorandthegeometryintheresultingparticledensities. 6.2.3.1Averagedelectrondensityoftheopticaljetgas whereiscat=90,Landnearetheinclinationangle,characteristiclength,andelectrondensityofthescatteringregion,andT=6.651025cm2istheThomsoncross-section.istheinclinationofthejetstowardtheobserveratprecwhichisgivenbythedynamicalmodelofHmovinglines(seeEquation 6 ).AmoreaccuratemodeloftheobservedpolarizationisexplainedinSection 3.2.2 butthesimpleEquation 6 illustrateshowthepolarimetryvarieswiththeinclinationangleofthejetsandthus,withtheprecessionalphaseprec.Therefore,thestudyofthepolarizationwithrespecttogivesthevalueofLnebyttingthefunctionf()=Asin22+Btothepolarization, 190

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6-3 )butthetofthef()functionhaslargeuncertaintiesbecausewehaveonlyafewdatapoints,allwithlargeerrorbars. Ontheotherhand,Equation 6 givesthevalueofLneusingthepolarizationofthejetemissionlinesataparticularprecessionalphase.Forinstance,weuseddatasetD2tocalculatetheelectrondensityresponsibleofthepolarizationofthejets.Theinclinationangleofthejetatprec=0.24is=77,resultinginLne51023cm2.Thecharacteristiclengthofthescatteringregionisobtainedfromtheradiusofthebeamatthedistanceoftheopticaljet. Borisov&Fabrika ( 1987 )derivedtheopeninganglej=11.4oftheSS433'sjetsandtherangeofdistancesoftheopticaljetfromthecentralcored=[21014cm,31015cm],wherethemaximumintensityofthegasoccursatd0=41014cm.Asareference,thecharacteristiclengthL=d0tanjetisabout71012cm.Theresultingdensityofelectron-likeparticles,whichareresponsiblefortheobservedpolarizationfromThomsonscatteringintheopticaljet,isne7109cm31011cm3,assuminganhomogeneousdistributionoftheparticlesinthescatteringregion.WenotethatthesevaluesaregreaterthantheelectrondensityobtainedfromextrapolationofthethermalelectrondensityoftheX-raymovinglines. Osterbrock&Ferland 1995 )forHrecombinationandnegligiblecollisionalexcitation.Theemissivityandtheatomdensityarerelatedas, TheenergyofthetransitioncorrespondstotheHemissionh32=1.9eV.Therecombinationcoefcientis(3)(Te)=4.55e14cm3forlevelsn3atthetemperatureofthegasT104K.Therecombinationcoefcienttoaspeciedlevelvaries 191

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Panferovetal. 1997 ). Wemustdifferentiatetwoelectronpopulations:thescatteringelectronsresponsibleforthepolarization,andtheelectronsparticipatingintherecombination.Therearethreescenariosfortherecombinationinvolvingtheseelectronpopulationsandtheprotonsofthegas: 1. thereisepchargebalance(i.e.np=ne)andalltheelectronsparticipateintherecombination 2. thereisnotepchargebalance(i.e.np<
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6.2.1 ).Inscenario 3 ,theresultingprotondensityisevensmallerthanthevalueofscenario 2 becausenp<
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6-4 illustratesthecontextinwhichthescatteringhappens.IfascatteringregionofcharacteristicsizelissituatedatadistancedfromthesourceofintensityI0,theintensityofscatteredradiationwouldbeI1=I0l2 Thus,theobservedpolarizationPobsissmallerthanthepolarizationPscatofthelightwhichisreallyscattered.Ontheotherhand,wecalculatetheelectrondensityasne,measure=Pobs Inaddition,theseparationofparticlesisphysicallyunlikely.Nevertheless,ifthescatteringandemittingregionsareseparatedwithintheconeofthejet,themaximumseparationoftheelectronandprotonbeamsis1angle,thereforetheseparationbetweenthetworegionswouldbeintheorderof1013cmatthedistanced0oftheopticaljetsfromthesource.Inthecaseofascatteringregionofsize1012cm,Equation 6 resultinascatteringpolarizationof11%whichisanorderofmagnitudegreaterthantheobservepolarization,resultinginanelectrondensitytentimeshigherthantheoneweestimated.Inaddition,weexplainedinSection 3.1.2.1 thatpolarizationfromparticlesofmassmisaffectedbyafactor1=m2.Thus,thecontributiontothepolarizationoftheprotons,whosedensityinthejetis108cm3,wouldbeintheorderof3107timesthecontributionoftheelectrons.Therefore,theeffectsoftheprotonscatteringonourresultsarenegligeble.Consequently,weconsiderbulletsofgaswhicharesurroundedbyscatteringelectrons. First,westudytheeffectsofthegeometryontheestimatedelectrondensity.Protonsandelectronsaredistributedaroundthecentralpropagationdirectionofthe 194

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Borisov&Fabrika 1987 ).Theouterradiusisdenedbythejetopeningangle(1)andthedistanceofthebulletfromthecentralsource.Becausetheinnerradiusdependsonunknownjetgeometry,westudiedsolutionsoverarangeofvaluesfrom1010cmto71012cmandwefoundvaluesofshape-factorintherange0.41-0.49.Equation 3 showsthattheelectrondensityisaffectedasj13j1thus,theresultingelectrondensityincreasesafactoroftwotofour(i.e.ne2.42.91010cm3)duetotheinuenceofthegeometry. Thenextquestionweareconcernedaboutiswhatistheinuenceofthedistributionofthegasintheelectronandprotondensities.Asexplainedabove,thegasofthejetsisclumpyanditllsthejetinformofbullets.Theeffectofavolumellingfactorofthegasinthejetsistoincreasetheprotondensityas1=2inferedfromrecombination.Butitalsoaffectstheopticalpathofthescatteringregionincreasingtheelectrondensitybyafactor1=3inferedfrompolarization.Inordertoobtainthesamedensityforbothtypesofparticles,thellingfactorshouldbe1012,implyingahighparticledensityofnp1014cm3.Suchalargedensityisinconsistentwiththeobservedelectrondensityne104cm3inradiojets( Seaquistetal. 1980 ).AsmentionedinSection 6.2.1 ,anadiabaticexpansionofthedensityofgasparticlesresultsinadilutionofthedensityproportionalto1=d2wheredisthedistanceofthegastothecentralsource,meaningthatthedensitydecreasesatmostbyafactor106fromtheopticaljetstotheradiojets.Thus,expansionofthegascannotexplainthedilutionofopticaljetdensitynp1014cm3byafactor1010.Becauseofthisandoftheextremevalueofthellingfactorneededtomatchthenumberofprotonsandelectrons,webelievethatvariation 195

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Previousauthors( Panferov&Fabrika 1997b ; Davidson&McCray 1980 )calculatedallingfactorof=106whichgivesinourcaseaprotondensitynp=1011cm3.However,inthatcase,theelectrondensityne=1012cm3isstillhigherthantheprotondensitybyanorderofmagnitude.Allingfactorof0.11agreeswiththeexpectedprotondensityofanadiabaticallyexpandinggas.Inthatcase,theprotonandelectrondensityareaffectedbyafactor3and2respectively,meaningthattheproportionbetweenthetwoparticlepopulationsareonlyslightlyaffected. 196

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Margon&Anderson 1989 ; Eikenberryetal. 2001 )andthenutational( Katzetal. 1982 )models.Thejetsarelongstructuresandeachpartofthejethasslightlydifferentradialvelocities.Forthepurposeofourcomputationalmodels,weconsiderarticialsectionsofthejetsofsamelengthdsegthatwecalljetsegments.Theproleofthemovinglinesresultsfromthecontributiontotheemissionfromeachjetsegment.WeusedDESPEJO(seeChapter 4 )inordertoanalyzethecontributionofeachjetsegment.ThetheoryofthemethodthatweimplementedinDESPEJOisexplainedbelow. Westudiedthecontributiontotheradiationalongtheopticaljetsbydividingthelineproleintowavelengthrangesthatwecallspectralsegments.Eachspectralsegmentinthelineprolecorrespondstoajetsegment.TheDopplershiftoftheemissionfromthejetsegmentshasacomplexrelationtotheprecessionalphasewhichisdescribedbythedynamicalmodelofthejets(seeEquation 6 ).Therefore,thesizeofthespectralsegmentschangeswiththeprecessionalphase.InordertocalculatethelengthofeachspectralsegmentandthetotalnumberofsegmentsNseginthejets,wedenedthelifetimeoftheopticaljetsandthetimeintervalofejectionbetweenjetsegments.Thepropertiesthatareimportanttodenetheparametersofthesegmentation(lifetimeandsegmentationtime)areexplainedinSection 2.3 Borisov&Fabrika ( 1987 )foundthatthetypicallifetimesofthebulletsis3days,theopticaljetsextendfromdmin=1.51014cmtodmax=31015cm,andthegasisejectedatafrequencyof2-3bulletsperday.Wedividedthejetinto14jetsegmentsoflengthdseg=21014cm. Therearetwomainissuesthatcomplicatecalculationsoftheabsolutewavelengthpositionofeachspectralsegment.Firstly,themodelofthemovingHlinedynamics 197

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Margon&Anderson ( 1989 )and Eikenberryetal. ( 2001 ).Wedonotknowthephysicaloriginofthevelocityshiftresidualsandthereforeitisnotpossibletopredictthematanygiventime.InSection 6.4.2 ,wewilltalkinmoredetailabouttheseresiduals,butnowitisimportanttonotethatthetimescaleofvariationsoftheseresidualsareontheorderofweeksormonthsandthereforeonlyaffecttheabsolutepositionofthemovinglineatagivenprecessionalphase,butnottherelativepositionbetweenspectralsegmentsbecausethetimescaleoftheopticaljetisof2-3days.Secondly,thephysicalpropertiesofthejetsareuncertainandthelifetimeandtheabsolutedistancesdsegofthesegmentsfromthecorearenotaccuratelyknown.Tosolvetheseproblems,wecalculatedtherelativecontributionstotheradiationofthejetsegmentswithrespecttoaparticularjetsegmentthatwecallS0j-thereferencesegment.WedenedS0jasthejetsegmentthatemitsatthewavelengthresultingfromtheaveragedwavelengthpositionofthelineprole. Anotherproblemindeningthespectralsegmentscomesfromthefactthattwojetsegments(thatwelabel1and2)mayemitatthesamewavelength12becauseofthedynamicsofthejet.Weusetheluminosityproleofthegasalongthejet,modeledfromthelightcurvesofindividualclumpsofgas( Borisov&Fabrika 1987 ),toestimaterelativecontributionsofthetwojetsegments.Theradiationdecaysexponentiallywithdistanceofthejetsegment'fromthecentralcoreasF(d)=F0edsegdmax ddecaywiththedistancescaleddecay=6.70.51014cmandthedistanceofignitionfromtheaccretiondiskdmax=41014cm.TherelativecontributiontothelineproleofI,Q,and 198

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(6) (6) whereSseg1andSseg2aretheStokesvectoroftheradiationfromeachjetsegmentandS(12)istheobservedStokesvectoratthewavelength12.WeshowinFigure 6-5 thecontributionstoI,Q,andUalongthejetinthedatasetD2. Consequently,wearenowabletocalculatethegeometry,emissionintensityandpolarizationofjetsegmentsalongthejetandwewillusethesetocalculatethedensityofparticlesalongthejetsusingthesamemethodforeachspecicjetsegmentastheoneinSection 6.2.3 .Below,wewillcalculatetheelectronandprotondensitiesofjetsegmentsfromtheiremissivityandpolarizations.WeassumejetsegmentstobecylindersofheightdsegandradiusRseg.WewillseethatS0jplaysanimportantroleinthestudyoftheseparticledensitiesalongthejets. 6 forarstestimationofprotondensityalongthejets.Theemissivityj32ofHfromjetsegmentsisrelatedtotheluminosityoftheradiationandthevolumeofthejetsegment.TheluminosityisproportionaltotheintensityoftheradiationasL32/10AV Lockmanetal. 2007 ).TheextinctionintheVlterisAV7.80.5magnitudes( Wagner 1986 ).ErrorsoftheextinctionAVchangetheluminositybyL32=10AV ThevolumeofthegasineachjetsegmentisVseg=R2segdseg.Thedeterminationofthevolumeisdifcultmainlybecausewedonotknowtheexact 199

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2(seeEquation 6 ).Ontheotherhand,thevolumeofthejetsegmentdependsonthedistancedsegofthesegmenttothecentralcore.Infact,theradiusRsegofthecylinderisproportionaltodsegandthevolumeofthejetsegmentisVseg=R2segdseg.Eventhoughwedonotknowtheexactvaluedseg, Borisov&Fabrika ( 1987 )estimatedarangeofdistancesoftheopticaljetgivingarangeofvalues21014cm
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FromthestudyoftherelativedensitiesofjetsegmentswithrespecttotheS0jwenotethattheprotonandelectrondensitiesshowstructuresalongthejetconsistentwithbulletsofgas(seeFigure 6-6 ).However,inordertocomparetheamplitudeofelectronandprotondensitystructures,itisimportanttoanalyzewhataretheabsoluteprotonandelectrondensities.Thus,werequiremeasurementoftheexactprotonandelectronpopulationsofoneofthejetsegments,forinstanceS0j.ThesecondpartoftheanalysisconsistedofcalculatingtheabsoluteprotondensityofS0jforthewholerangeofpossiblevalues21014cm
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First,wecalculatetherelativeelectrondensityofajetsegmentwithrespecttoS0jusing, Figure 6-6 showstherelativeelectrondensityalongthejet.Wenotethattheuctuationsalongthejetoftherelativeelectrondensityaresmallercomparedtotheuctuationsoftherelativeprotondensity.Therelativeelectronandprotondensityprolesarenothighlycorrelatedsuggestingdifferentpropertiesoftheowofelectronsandprotons.Thesevariationsareinconsistentwithapurenormalplasmacontainingonlyprotonsandelectrons,sincetheirnumbershouldvarysimultaneously. TheabsoluteelectrondensityiscalculatedforS0jassumingthatitcanbeinthewholerangeofdistancesoftheopticaljet(seeFigure 6-7 ).TheabsoluteelectrondensityiscalculatedusingthemodelsdescribedinSection 3.2.2 whichwereimplementedinDESPEJO.TheelectrondensityofS0jis24109cm3ifthisjetsegmentissituatedatthebaseoftheopticaljetand0.71.5109cm3iftheemissionofS0jhappensfromtheendoftheopticaljet.AtanygivendistanceofS0jintheopticaljet,theabsolutedensityofelectronsisaboutahundredtimeshigherthanprotonsassuggestedbyourpreliminaryanalysisabove. TheinuenceofthellingfactorandthegeometryintheparticledensityarethesameasexplainedinSection 6.2.3.3 .Thefactorcanincreasetheelectrondensityuptothreetimesoverthecalculationabove-i.e.28109cm3.Condensationofjetgasintheformofbulletsincreasesboththecalculatedprotonandelectrondensities,butdecreasesthedensitydifferencebetweenthesetwoparticlepopulations.However,theelectrondensityisstill10timeshigherinthecaseof=1e6.UncertaintiesintheextinctiontowardSS433orinthedistancefromSS433totheEarthdonotaffect 202

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2.1.2 ,themainmechanismsofjetformationinvolveeitheranelectron-protonplasma(alsocallednormalplasmaore+pplasma)whichislaunchedbyamagneticeldintheaccretiondisk;oranelectron-positronplasma(alsocalledeplasma)whichispropelledbythemagneticeldattheergosphereofthecompactobject.PreviousobservationsofthejetsofSS433arguedfortheexistenceofane+pjetbecauseoftheobservedHemissionfromtheopticaljets.However,hereweshowedthattheopticaljetsofSS433alsocontainpositronparticles.ThiscurrentpictureraisesnewquestionsabouttheformationofSS433jetsandtherefore,aboutthegeneraltheoriesofjetformationwhichinvolveonlyoneoftheplasmaows:either 203

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Wecanthinkofthreepossiblescenariosexplainingtheexistenceoftwoplasmasinthejet: 1. Thee+pplasmaisattheoriginofthejetformationanddragstheeplasma. 2. Theeplasmaisattheoriginofthejetformationanddragsthee+pplasma. 3. Bothplasmasarelaunchedindependentlyfromeachother. Ifthespeeddifferenceofthesetwoplasmaisverylarge,theremustbecollisioninteractionwhichwoulddestroythebulletofgasandannihilatetheepairs.Therefore,Scenario 3 requirestwodistinctmechanismsinvolvingtwodifferentplasmathatcreatetwoparallelowswiththesamespeed.Webelievethatthisisveryunlikelyandwedonotconsiderthiscase.Ontheotherhand,itisinterestingtoexplorehowhypotheses 1 and 2 mayexplainourresults. 1 ismorelikely.Obviously,thenormalplasmaowcandragtheeplasmaonlyiftheepairsareproducedinthephysicalpathoftheow.Modelsofaccelerationofepairsbyradiation( Ghisellinietal. 1992 )andelectromagneticenergy( Levinson&Blandford 1996 )suggestthatepairsarecreatedwithinafewSchwarzschildradii(RS=2GMc McKinney 2006 )farawayfromtheregionepaircreation.Thismakesscenario 2 asthemostprobable 204

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2 6.3.3.1Interactionbetweentheejetandtheaccretiondisk 2 isaowofepairplasmadraggingae+pplasmaviaaninteractionwiththeaccretiondisk.InChapter 5 ,weconcludedthatwindsfromtheaccretiondiskextendtodistancesupto1011cm,increasingthethicknessoftheaccretiondiskandthereforetheprobabilityofinteractionwiththeejet.Inaddition, Begelmanetal. ( 2006 )explainedthattheprecessionalandnutationalmotions,whichhappenattheouterdisk,canpropagatethroughtheaccretiondiskviabendingwavesbutitisveryunlikelythatitreachesthecenterofthediskneartheregionofjetformation.Therefore,theinteractionofthejetwiththeaccretiondiskmaybeattheoriginoftheprecessionalandnutationalmodulationofSS344'sjetswhichotherwisewouldfollowadirectionthatisxedbythepropertiesofthecompactobject(e.g.thespinaxisinthecaseofaBH).Inthiscase,thejetcollideswiththewindandsomeofthejetmomentumuxistransmittedtothegasthatdeviatesthejet. Theresultofthisinteractionisthattheoriginaljetwoulddecreaseitsspeedandchangethedirectionofitsow.Thelossofthekineticenergyofthejetistransmittedtothegasoftheaccretiondiskwhich,weassumeis,eitherdeviatedparalleltotheaccretiondisk,orisdraggedalongthejet.Weknowwithcertaintysomeoftheparametersofthenaljet(afterinteraction)andtheaccretiondisk.Forinstance,thenalspeedofthejet=0.26wasderivedfromthekinematicalmodel.InChapter 5 ,wecalculatedthespeedofthewind(vw=1700km=s)andtheextensionoftheaccretiondiskwinds(1011cm).WedonotexactlyknowthetotalnumberofprotonsNp,interandpairsNe,interwhichparticipateintheinteraction.However,wearefamiliarwithsomeof 205

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Figure 6-8 describesthescenarioinwhichtheinteractionbetweentheinitialjetandtheaccretiondiskhappens.Inthisframework,theinitialjetiscomposedexclusivelyofNe,interepairsandowswitharelativisticspeed~vj,0.Thus,thekineticenergyandmomentumuxoftheplasmaoftheinitialjetareEk,j0=Ne(2me)(01)c2and~pj,0=Ne(2me)0vj,0(sindec~Xinter+cosdec~Yinter)wheremeistheelectronmass,and0istheinitialLorentzfactorofthejet.Afterinteractionwiththeaccretiondiskplasma,theeplasmafollowsthedirection~Xinterwithaspeedc.ThekineticenergyandmomentumuxoftheeplasmaaftertheinteractionbecomesEk,j=Ne(2me)(1)c2and~pj=Ne(2me)c~XinterwhereistheLorentzfactorofthenaljet. Ontheotherhand,weassumedthatthejetdragsafractionfofthetotalnumberNp,interofhydrogenatomsduringtheinteraction.Thisgashasarelativisticspeedc~Xinter,thusakineticenergyEk,fp=(1)fNp,inter(mp+me)c2andamomentumux~pk,fp=fNp,inter(mp+me)c~Xinterwherempistheprotonmass.Theremaininggas,whichendsupmovingalong~Yinterwithaspeedv,acquiresallthemomentumalong~Yinterlostbythejetgas.Thefraction1foftheNp,interprotonsremainingintheaccretiondiskhasakineticenergyEk,=1 2(1f)Np,inter(mp+me)v2andamomentumux 206

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2Np,inter(mp+me)v2wand~pk,w=Np,inter(mp+me)vw~Xinter. Finally,wecanwritetheequationofconservationofthekineticenergybeforeandafterinteractionofthetwoplasmaasEbefore=Eafter(Equation 6 ).Assumingthatthetwoplasma(ep+andeplasma)participatingintheinteractionareisolatedfromtherestofthesystem,thetotalkineticenergybeforeinteractionisEbefore=Ek,j0+Ek,wandthenalkineticenergyisEafter=Ek,j+Ek,fp+Ek,.Similarly,theequationofconservationofmomentumuxis~pk,j0+~pk,w=~pk,j+~pk,fp+~pk,whichcanbeprojectedalong~Xinter(Equation 6 )and~Yinter(Equation 6 ).IfwedeneKpe=Np,inter(mp+me) (01)c2+1 2Kpev2w=(1)1+fKpec2+1 2Kpev2 Inarstorderapproximation(vw c<<1),Equation 6 givestheinitialLorentzfactorofthejetas, Inthischapter,weestimatedthedensityofepairsinthejetwithrespecttotheprotondensitytobefNp,inter 207

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Mirabel&Rodrguez 1994 )andGROJ1655-50( Tingayetal. 1995 ; Hjellming&Rupen 1995 ). Accordingtoourmodel,theresultingmotionvofthegasandfractionfofprotonsowinginthejetdependonthenumberofparticlesparticipatingontheinteraction,theefciencyofthedrag,andtheinclinationangledevoftheinitialjetwithrespecttothedirectionoftheaccretiondiskaxis.Thelast,islikelyclosetotheprecessionalangleofthejetprec=20.92butitisnotnecessarilyequalsincethespinaxisofthecompactobjectmaybemisalignedwithrespecttotheorbitalaxis.Therefore,wecannotformallysolvetheproblembasedonthesethreeequation,althoughwewilldosomeestimationsofthevaluesoftheseparameters. Borisov&Fabrika 1987 ),wecancalculatethesizeoftheinteractionregionwhichisproportionaltothedistancebetweenthecompactsourceandtheaccretiondiskwinds.ThegasofthewindisexpelledfromaringoftheaccretiondiskdenedbytheminimumradiusatwhichtheKeplerianorbitofthegasisequaltothespeedofthewind,thatisRwind=2GM v2w=c2 Begelmanetal. 2006 ).Forinstance,atensolarmassesBH(RS10=3106cm)resultsinRwind=9.31010cm.Assumingthatdevprec,thejethitstheaccretiondiskatadistancefromthecentralcoreofdinterRwind=cosprec1011cmandadistancefromtheaccretiondiskofHwjRwindtanprec3.51010cm.TheinteractioncanphysicallyoccurbecausetheheightoftheaccretiondiskwindregionemittingthecomponentsH2andH3isaboutHw=5101010cm. 208

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6-4 209

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( 1982 )calculatedthenumberofpairannihilationsneperunitvolumeforacoolepairbeamofpairdensityneas, ne=n2ecpa(6) whereistheLorentzfactoroftheepairsintheobservingframeandpaistheparticleannihilationcross-sectionintheco-movingframe.Theannihilationcross-sectionatmoderatelyrelativisticspeedsispa=r2e=2.51025cm2wherere=e2 6.2.4.3 ),meaningthatthemaximumannihilationrateis3104cm3=s. WeassumethatbulletsarecylindersofradiusL=d0tanjet=71012cmandheighth1012cm(seeSection 6.2.3 ).Thus,thetotalannihilationrateisgivenbythepairannihilationhappeninginthisvolumewhichisNpa=41041pairspersecond.Ifweassumeisotropicemission,thetotalphotonuxattheEarthisNEarth=Npa Teegarden&Watanabe ( 2006 )wereabletodetectGalactic511keVemissionsourceswithsensitivitiesintheorderof104photons=s=cm2.WecalculatedtheexposuretimeneededtoobservetheemissionofthefeaturesfromtheejetsusingtheSPectrometeronINTEGRAL(SPI).Wecalculate40minutesofobservationswiththeexposuretimecalculatorprovidedbyEuropeanSpaceAgency(ESA)inordertoobserveafeaturewithin3oflineenergy511keV,width10keV,andux104photons=s=cm2.Therefore,the511keVemissionduetotheannihilationofepairsintheopticaljetsofSS433shouldbedetectable.Forinstance, Teegarden&Watanabe ( 2006 )observedfromSS433anupperlimitofuxof511keVphotonsof<1.6104s1cm2.Thisisconsistentwithourresultsbecausewewouldnotbeabletoobservetheexpected511keVemissionresultingfromannihilationofepairswhichwecalculatedforourmodelstobe104photons=s=cm2. 210

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ne(t)=nene(t)dt d2(t)2cpa(6) Theannihilationratedecreasesthelifetimeoftheepairsandthesolutiontotheequationgivesaquantitativevalueoftheevolutionalthough,wedonotintendtosolvethisequationwhichrequiresabetterunderstandingofthepropertiesofthejet.Aqualitativeanswertoourquestion(Doesthelifetimeoftheematchthelifetimeofthebullets?)isgivenbyaveragingthelifetimeoftheepairsalongtheopticaljet.Infact,theaveragedlifetimeis3.2dayswhichisconsistentwiththeobservedlifetimeofthebulletsintheopticaljets. 6.4.1 ,themassexchangemechanismbetweenjetsandaccretiondiskwindsisprobablyverycomplexandthenumberofprotonsandepairsparticipatingintheprocessaresubjecttotheconditionsoftheregionwhichmaybemodiedbyshocks,densitywaves,andcompressionofthegas.Forinstance,thefractionfofaccretiondiskgasthatisexchangeddependsonthephysicalmechanismoftheinteraction.Becausewecanmeasuretheproportionofprotonstoepairsinthe 211

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2.3.5.2 ). Forinstance,letusassumethatalayerofgas(thatwecallY)movingalongtheejetcapturesalltheprotonswhichweobserveintheopticaljets.Theexchangeprocessisrelatedtothephysicalpropertiesofthejetanddiskgas(seeSection 6.4.1.1 )buthere,weroughlyestimatethenumberofprotonsthataredraggedbythejetassumingthatitisproportionaltothevolumeofthenormalplasmagasthatintersectsbytheeplasma.ThetotalnumberofexchangedprotonsisNp,out=np,accLinterA,whereAisthesurfaceareaofthesectionofthejetandLinteristhelengthoftheinteraction(seeTable 6-4 ).InSection 5.3 ,wecalculatedthedensityoftheaccretiondiskwindsnp,acc=5101010cm3fromtheH2andH3polarization.Forsimplicityweassumethatthesurfaceareaalongtheinteractionregionisconstantandequaltothesectionofthejetbeforecollidingwiththeaccretiondiskwind.Therefore,ifweassumethatthethicknessofYisl,theprotondensityintheYlayeraftertheinteractionisnp,out=Np,out Borisov&Fabrika 1987 )isthedistanceoftheopticaljetfromthecompactobject.Whendev=precthedilutionfactorisgdilut=1.5107.Thisresultsinalayersizescaleof4.8106cm
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2(dinter+Hw DuringthistimeintervalthejetcoversadistanceL=vjtinterwherec
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Margon&Anderson 1989 ; Eikenberryetal. 2001 ). Itisinterestingtonotetwoapparentlydifferentphenomenawhichmaybecorrelated.First,theobservedwavelengthpositionsofthejetlinesdeviatefromthedynamicalmodelwithvelocityshiftresidualstothemodelthatarestatisticallysignicant( Margon&Anderson 1989 ; Eikenberryetal. 2001 ).Second,inourmodel,theexpecteddeviationandspeedofthejetduringtheinteractionwoulddependonthepropertiesoftheaccretiondiskwindwhichmayvaryconsiderablywithtime. Inthissection,westudythepossiblecorrelationbetweenthesetwofactswiththegoalofbetterunderstandingtheinteractionmechanismbetweenthepairandthenormalplasma.Westartthediscussionbydescribingthephysicalmechanismswhichleadtothenaltwoplasmajet.Duringthedescription,weanalyzehowthephysicalpropertiesoftheaccretiondiskcouldaffecttheorientationandthespeedoftheresultingjet.Then,weexplorethebehavioroftheDopplershiftresidualsandwenallyintroduceourmodelttingtheresidualvelocityshiftwhichwecorrelatewiththephysicalpropertiespropertiesofthejet. 6.4.1.1Interactionmechanismsbetweennormalandpairplasma Kahn 1980 ).Therefore,entrainmentofaccretiondiskgasbySS433ejetsmayhappenviaturbulentdiffusionbetweenthejetoutowandthewindoftheaccretiondisk.Forinstance, Canto&Raga ( 1991 )presentedamodeldescribingthetransportanddissipationofmaterialofanoutowmovingintoamediumwhichisassumedtobeatrest.Accordingtotheirmodel,obliqueshocksmayformduringtheinteractionofthe 214

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Computationalsimulationsofshockproperties( Landau&Lifshitz 1959 )showthatanobliqueshockundergoessmallkineticenergydissipations(1%).Inthisscenario,thepost-shockvelocityissupersonicandthedensityofthepost-shockedgasisfourtimesgreaterthanthedensityofthepre-shock.Thedensityofthepre-shockcanbecomesmallerthanthedensityoftheaccretiondiskandtherebythejetentrainssomeoftheaccretiondisk'smass.Thematerialwhichisreceivedfromtheaccretiondiskslowsdownanddeectstheregionofthejetparticipatinginthemassexchange.Theresultofthisprocessisthatthewholejetisdeectedandsomewhatmayberecollimated.Therefore,itisinterestingtostudytheamountofgasthatcanbecollectedfromthisprocessandhowitrelatestothedeectionanddecelerationoftheinitialejetduringthismassexchange. 6.3.3.5 )aslabofjetgaswiththicknessl107cmcrossingthroughtheinteractionregion.Theinteractionbetweenthejetandtheaccretiondiskproducesamixinglayerinwhichtheexchangehappens( Canto&Raga 1991 ).Atanypositionoftheslabintheinteractionregion,themaximummassuxthatcanbeentrainedfromtheaccretiondiskinthemixinglayerism0<0c0iftheexchangegasvelocitiesarelowerthanthespeedofthesound.Here,c0and0arethesoundspeedandmassdensityofthegas-donormedium.Asareference,themassdensity0=2dintertanjlis=5107g=cmfora10MsunBH.Thesoundspeedc0q mdependsonthegastemperatureT0,andthemassoftheparticlesmp.TheBoltzmann'sconstantisk=1.381023m2kgs2K1.FortemperaturesT0=104KandT0=106,the 215

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Wenotethatthesevaluesaremuchhigherthantheobservedmassrateofthejetswhichis5107Msunyr1( Fabrika&Borisov 1987 ).However,theentrainmentratem0=0c0isalsosubjecttotheefciencyoftheentrainmentwhichdependsonthestructureoftheturbulentmixinglayer.Numericalandcomputationalcalculationsofthisthermodynamicalsystemarequitecomplexrequiringanextensivework.Butwecancalculatethemforsomeparticularcases.Forexample, Canto&Raga ( 1991 )denedtheupperlimit=0.5c0 Becausealargeamountofgasfromtheaccretiondiskisentrained,aslowerbutdenserjetformswhiletheejetcrossthroughtheinteractionregion.Thegasfromtheaccretiondiskandjetalsoexchangesvelocitymomentuminthemixinglayer,attheoutskirtofthejet,whichmodiesthedirectionoftheinitialjet.Realistically,thisprocesshappensthroughaseriesofsmalldeectionsalongtheinteractionregionwhichresultintheglobaldirectionoftheknownjet.Therefore,thedissipationoftheenergyhappensthroughaseriesofobliqueshocksandthustheenergydissipatedindeectingthejetisnotsignicantcomparedwiththeoverallenergyofthesystem.Themostimportantcontributiontoslowingthejetcomesfromthedragofheavygas.Thus,variationsofjetspeedanddirection,aswellasthegasexchangeefciency,dependonthegastemperatureanddensityoftheaccretiondisk.Equation 6 showsthatthedeviationangleforthedifferentinteractionsdependon1f,whichisproportionaltop 216

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6 whichshowsthatthedependenceofthespeedwiththepropertiesoftheaccretiondiskgasisrathercomplex.Furtherworkintheeldofcomputationalsimulationsisrequiredinordertounderstandhowtheseparametersarerelated.However,inourthesis,wequalitativelyexplorethetimescaleandamplitudeofaccretiondiskinstabilitiesaffectingthevaluesoff,dev,and. Pringle ( 1981 )explaintherelationbetweentheviscosityandthesurfacedensityofthedisktobe, @Rp @Rp Findingthesolutiontothisequationisnotobviousanditcanbedoneanalyticallyonlyinsomeparticularcases.Forexample,iftheviscosityprolealongthediskisapowerlaw=Rn,wherenisanarbitraryinteger,thesolutiontoEquation 6 involvesaBesselfunctionJkwithk>0( Pringle 1981 ). Inthegeneralcase,Equation 6 isnon-linearanditisdifculttondasolutiontothediffusionequation.Nevertheless,wecanstatethreecharacteristictimesoftheinstabilitiesoftheaccretiondisk.TheshortesttimescaleisrelatedtothetimethataparticlesituatedataradiusRtakestorotatearoundthecompactobjectanditisgivenbyt1.ThetimescaleatthedistanceRwind1011cmfromthecenterofthe 217

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c0which,consideringthevaluesthatweusedontheprevioussectionbecomestz26260days.Finally,thetimescaleinvolvingtheviscosityofthediskwoulddenethecharacteristictimeofchangesoccurringinthelocalsurfacedensityast=R2=.Thisisthelargesttimescaleandbecauset>>t,weshouldnotbeconcernedaboutthesevariationsforthepurposeofourstudy.Themostimportanteffectscomefromthehydrostaticequilibriumoscillationsinthedirectionperpendiculartothediskbecausetheinteractionhappensfarawayinthisdirection. WenotethatthetimescaleofthesevariationsforagasatT0=104Kislargerthantheprecessionalperiod.Inourmodel,thespeedanddirectionofthenaljetdependonthepropertiesoftheaccretiondiskthus,thevelocityshiftoftheemissionfromthejetshouldbemodulatedonthetimescaleoftz.Aswewillseebelow,changesoftheseparameterswouldmodulatetheresidualsofthevelocityshiftwiththeprecessionalphaseaswell.Becausethetimescaletzislargerthantheprecessionalperiod,thevelocityshiftresidualsareexpectedtooscillatewiththeprecessionalphaseandtheamplitudeoftheseoscillationsmustchangefromoneprecessionalperiodtothenextone. 6.4.2.1Noisemodelsforresiduals Margon&Anderson ( 1989 )and Eikenberryetal. ( 2001 )explainedthattherearestatisticallysignicantvelocityshiftresiduals.Thesedonotmerelycomefromuncertaintiesintheshiftmeasurementwhichshouldbeintheorderofz=0.003.Theseresidual 218

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Margon&Anderson ( 1989 )whichincludedFourieranalysisandauto-correlationoftheresidualshiftpatternwithtime.Theseauthorsshowtimescalesofthevariationsofafewhoursorweeks.Inaddition, Eikenberryetal. ( 2001 )foundcorrelationsoftheresidualsontimescalesofweekstomonths.However,eventhoughthecorrelationofthevelocityresidualsonsuchalargerangeoftimescales,thereisnotanyapparentcorrelationontheevolutionofthevelocityresidualstotheprecessionalororbitalphases. However,ourmodelpredictsvariationsofandprecwhichmaybeattheoriginoftheseshiftresiduals.Thesevariationswouldbeintimatelyrelatedtothedensityoftheaccretiondiskatthetimeofinteractionoftheejetwiththewind.Therefore,thestudyofthecorrelationbetweentheerrorsonandprecandtheintensityoftheaccretiondiskemissioncanelucidatetheoriginoftheresiduals.WecallanerrorontheparameterX(e.g.X=orX=prec)thesmallvalueXthatisrequiredtoaddtoXinordertomatchthevelocityshiftpredictedbythemodelandtheobservedvelocityshiftofthemovingHlines.Forinstance,wecanwritethedynamicalmodelwithparameters,iorb,prec,precwhichmayslightlychangeof,orb,prec,andprecalongthetimeas, (6) (6) Wenotethatvariationonanyofthesefourparameterswouldmodulatethevelocityshiftwiththeprecessionalphase. Eikenberryetal. ( 2001 )foundnoapparentcorrelationoftheresidualswithanysingleparameter. Panferovetal. ( 1997 )(seeTable 6-4 )inordertostudythecorrelationofthevelocityshiftresidualsandthedensityoftheaccretiondiskwind.Because,previouslytoourwork,theemissionfromtheaccretiondiskwind(whichisthe 219

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6 becomes, wheresorb=siniorb,sprec=sinorb,corb=cosiorb,andcprec=cosorb.Consequently,therstorderapproximationofEquation 6 isdescribedbythefollowingequation: (6) (6) (6) (6) Foranygivenprecessionalphase,wecalculatedseparatelyerrorsofsingleparametersassumingthattheothererrorsarenull.WestudiederrorsforeachoftheparameterswithrespecttothemotionoftheSS433systems(precessionandorbit)andweconrmedtheconclusionsofpreviousauthors.Wedidnotndanyclearcorrelationoftheseparametersandtheprecessionalororbitalphases.Inaddition,weanalyzedpossiblecorrelationsbetweentheresidualsandtheintensityoftheline.Figure 6-9 showtheequivalentwidthofthelineswithrespecttothevelocityshiftresiduals.Wealso 220

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6-10 6-11 ,and 6-12 ).Becausetheequivalentwidthwouldberelatedtothedensityoftheaccretiondiskbyamonotonicallyincreasingfunction,thereisnoclearrelationbetweenthedensityoftheaccretiondiskandtheobservedvelocityshiftortheerrorparametersofthedynamicalmodel. Previousconclusionsseemtoruleoutanydirectcorrelationoftheresidualsandthepropertiesoftheaccretiondisk,indisagreementwithourpredictions.Furthermore,westudiedthecorrelationusinganderrorssimultaneouslyandtheconclusionsarestillverydiscouraging.Forinstance,weassumedthreedifferenthypothesesforourstudywithand: 1. Theenergygiventotheaccretiondiskgaswilldeterminethenalspeed)/v Thenalspeeddependonotherparametersaswellbutthevariationonthekineticenergyoftheenergychangesthekineticenergyofthejet)/d(v) Changesinthevelocityofthejetandthedirectionaredirectlyrelated)/cos(+) Noneofthesethreemodelswereabletocorrelatetheanderrorsandthevelocityshiftresiduals.Moreover,theseerrorsarestillnotdirectlycorrelatedtotheequivalentwidthofthemovinglinesandtherefore,tothedensityoftheaccretiondisk. Consequently,thecurrentresultsofthestudyofthevelocityshiftresidualsdisagreewiththemodelthatwesetupinSection 6.3 .Webelievethatthecomplexityofinteractionbetweentheejetandtheaccretiondiskdoesnotallowalinearcorrelationbetweentheparametersofthesystem.Infact,thethermodynamicalequationsofaturbulentandlaminarlayerofsuchexplosivescenarioinvolvesnon-linearequations.Inaddition,theshiftresidualmayinvolvethecombinationoftwomechanisms.Below,wewilldescribeourstudysuggestingtheexistenceofthesetwodifferentmechanismsandwewillexplorethephysicscausingtheobservedeffectsontheshiftresiduals. 221

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( 1989 )foundfromthehistogramofvelocityresidualsthatthereisnotaGaussiandistributionoftheresiduals,buttwodifferentproleswhichwethinkindicatethepresenceoftwodifferentmechanismscreatingtheobservedshiftvariations(seeFigure 6-13 ).Thesharpcoreoftheprolehasawidthof1500km/s,muchsmallerthanthewingsatthebasewhosewidthis5000km/s.Measurementuncertaintiescouldexplainthecentralcoreoftheprolebutnotthewidthofthewings.Itisinterestingtotrytoseparatetheeffectsofthetwomechanismscreatingthesetwoproleswhicheffectsarelikelyindependent. Previousworksshowalinearcorrelation(seeFigure 6-14 )betweenthevelocityshiftresidualsofthetwojetsofSS433( Margon&Anderson 1989 ; Eikenberryetal. 2001 ). Eikenberryetal. ( 2001 )calculatedthelinearfunctionofthecorrelationtobe, Aninteractionoftheejetwiththeaccretiondiskcanexplaintheobservedvelocityshiftwiththesamesenseofshiftoftheapproachingandrecedingjets.ThejetsofSS433aresymmetricandiftheconditionsoftheaccretiondiskareaxi-symmetricaswell,weexpecttohavethesameexchangebetweenbothjetsandaccretiondiskwind. WedecomposedtheresidualshiftintwocomponentsbasedonthelinearcorrelationofEquation 6 .Therstcomponents,whichwecally1,2,aretheprojectionsoftheresidualsontothelinedenedbytheEquation 6 .Forinstance,y1,2arerelatedasy2=0.69y1.Therefore,theEquationsgivingthesecomponentsare, Thesecondcomponents,whichwecallx1,2,correspondtotheoscillationaroundthislineartrend.Therefore,theyaregivenbythedistanceofthevelocityshiftresidualsto 222

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6 .Inotherwords,weobtainthesecondcomponentsas, Figure 6-15 showsthevariationsofthesetwocomponentswithrespecttotheprecessionalphase.Thesevariationssuggestaperiodicpatternwithoscillationamplitudesof0.2fory1,2and0.05forx1,2.Thecomponentsx1,2havethesamephasebuty1,2areinphaseopposition.AccordingtoEquation 6 ,parameterserrorsofthedynamicalmodelshiftthetwojetsinoppositedirections.Therefore,theseerrorscouldnotexplaintheshiftresidualsx1,2.Ontheotherhand,theyareconsistentwiththeoscillationsofy1,2.Thus,thephysicaloriginofthesetworesidualsmaybedifferent.Itwouldbeinterestingtoaskwherethesecomponentscomefromandwhatarethephysicalmechanismsinthejetoraccretiondiskresponsibleforx1,2andy1,2. 6 andassumingthatthevelocityshiftsy1,2aresolelyduetoasingleparameter,wecalculatedthecorrespondingvaluesoftheerrorsthatagreewiththeamplitudeoftheoscillations.Onlytheresults=0.55andprec=46arephysicallypossiblealthoughtheydonotseemveryreasonabletous.Thesevaluesresultinaveragedvaluesof 6-15 andthus,oscillationsofy1,2canonlybeduetoprecerrors.Unfortunately,aphysicalmodelexplainingsuchvariationsrequiresamoreextensiveanalysisoftheoscillationsandtheircorrelationwiththeparametererrorsandtheaccretiondiskdensityvariations.Furthermore,theanalysismayconsidercombinationofvariousoftheseerrorparameters.Atpresent,wecansaythaty1,2oscillationsmaybeexplainedby 223

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Concerningx1,2,itsoriginisnotrelatedtotheoscillationsofpropertiesorgeometryoftheaccretiondisk,whichwouldaffectsymmetricallyandinoppositedirectionsthevelocityshiftresidualsofthetwojets.Infact,weobservethatx1andx2havethesamephase,implyingthatthesecomponentscomefromaprocessthatisnotrelatedwiththeaccretiondiskwindsortheinitialejet.However,theshiftresidualsx1,2aremodulatedwiththeprecessionalmotionandtherefore,mustberelatedtotheprecessionofthedisk.Thisisveryhardtoexplainfromvariationsofdirectionorspeedofthejetassumingthatthetwoplasmaowatthesamespeed.Ontheotherhand,twoplasmawithdifferentspeedsintheorderof0.05ccouldexplaintheobservedoscillations.Conrmingthishypothesisisofgreatinterestbecausetheshearbetweentheepairplasmaandnormalplasmamaybeattheoriginoftheheatofthebullets.TheoriginoftheheathasbeenamainpointofdebateabouttheopticaljetsofSS433.Withourstudy,weproposeanotherclueforfuturestudiesoftheheatmechanismsexcitingthemovingHlines. 224

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ThissuggeststhatthejetsofSS433containepairsowinginparallelwiththenormalplasmajet.Weproposedamodeltoexplainhowthesetwoowsco-existwitheachother.Ourmodelisbasedontheinteractionofaninitialepairjetwiththeaccretiondiskwhichresultonanexchangeofmatterbetweentheaccretiondiskandthejet,andonthemodulationofthedirectionofthejetandthedecelerationoftheinitialplasmaow.Intheframeworkofourmodel,weveriedthattheresidualsoftheDopplershiftobservedinspectroscopyareconsistentwiththeexpectedvariationsoftheparametersofthedynamicalmodelduetoinstabilitiesofthedisk.Wefoundthattheresidualshavetwocomponentswhichoscillationsareconsistentwithourmodel. However,severalquestionsarestillontheairincludingwhatarethegeometryandtherelativeconnectionofthetwoplasmaintheopticaljets,andhowtheaccretiondiskwindandearlyjetinteract.Furtherstudiesofthepolarimetryfromthejetsandaccretiondiskwillbeabletoelucidatethesequestionsandtheobservedvariationsoftheresidualswhichrequireamoreaccurateunderstandingofparametersofourmodel.Thesewillrequirealargeamountofspectropolarimetryfromtheopticaljets.WeworkedinthedesignandfabricationofTheCanariasInfraRedCameraExperiment(CIRCE)whichwillbeuseina10metertelescope.CIRCEallowslowresolutionspectropolarimetryintheinfraredanditwillbeauniqueopportunityforfurtherstudiesofthejetsofSS433. 225

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ParameterofDynamicalModelsofSS433Jetsderivedfromtheopticaljets( Eikenberryetal. 2001 )[model1]andfromtheradiojets( Stirlingetal. 2002 )[model2] Model1Model2 Velocity=v=c0.26470.00080.2602AxisAngleprec20.920.0819.81InclinationAngleiorb78.000.0578.83PrecessionalPeriodPprec(days)162.3750.011162.5PrecessionalAmplitude11Precessionalt0(MJD)3563.230.11(atT1)8615.5(atT3)NoddingPeriodPnut(days)6.29NoddingAmplitude0.00655Noddingt0(MJD)35888.0(atT3)SynodicPeriod(days)5.838SynodicAmplitude0.00382Synodict0(MJD)3587.4(atT3) Table6-2. Blue-JettoRed-JetIntensitiesRatio.RatioarecalculatedfromHorHlines.Itiscalculatedformainandsecondarycomponentsofjetlineprolesindependently main0.2372902230.280794970.1985023590.3595712130.25419164main0.1728156742.5052204380.0616064741.4766251160.036312041secondary0.2354609550.5186595030.8831138290.6479137061.10319304secondary0.1746449432.5769639790.0879550921.41978070.04845894 Distancescales(inunitsofcentimeter)oftheinteractionregionoftheeJetwiththeaccretiondisk.Weshowforvariousmassesofthecompactobjecttheradiusofexpelletionoftheaccretiondiskwind(Rwind),thedistancefromthecompactobjectoftheinteractionregion(dinter),thedistancefromtheaccretiondiskoftheinteractionregion(Hwj),andtheminimum(Linter(min))andmaximum(Linter(max))lengthoftheinteractionpath. MassRwinddinterHwjLinter(min)Linter(max) 5Msun4.61010510101.710108.310102.3101110Msun9.3101010113.510106.410101.7101120Msun1.910112101171010310108.41010

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MovinglinesfromJet1andJet2( Panferovetal. 1997 ).Thetableshowsthepositionjet1andjet2ofthejetlinesatagivendateandtheequivalentwidthWoftheJet1 4437.427108670376jj4832.3260394438.3970916709104jj4825.459764441.467122648156jj4825.460384442.487152645758jj4825.460824442.4871004.7jj4826.3859474443.447210641553jj4826.3860324443.447154645517jj4826.3860824764.467180644242.8jj4827.3159824765.467153646798.8jj4827.3159494766.4571456455110.8jj4827.3160134767.447244641556jj4876.286510700027.24767.447147647023jj4876.2870424768.467276638971.6jj4876.2870714768.467145636016.3jj4876.2871004769.457292633060jj4884.2870204769.45714663882.8jj4886.276404714138.84770.477298631062.3jj4886.2764587077114777.377452614092.3jj4886.2770394778.377447616290.3jj4887.346389720137.84779.377446618480.3jj4887.34643571617.54780.377529613278.7jj4887.3471154780.376195jj4888.36392703311.14781.427549609752.2jj4888.3643170921.24782.425989jj5227.23644551.94782.426025jj5227.23640541.44782.426054jj5248.3170826225299.44807.377755582627.7jj5250.37018661692.54807.37757357983.2jj5250.3713218.44807.375854jj5251.286981661036.64807.375912jj5251.2870096627224808.437817575923.3jj5251.287032124808.435795jj5251.28705018.94808.435822jj5251.28710724.84808.435850jj5252.187145651885.94808.435918jj5253.27149649948.54809.367721580028.1jj5254.27173646234.94809.36781058556.4jj5256.2364064809.365764jj5256.2364374809.365913jj5256.2363854809.365828jj6583.560094810.36773959388.4jj6583.559634810.36764759095.5jj6583.559214810.365856jj6584.360234810.365827jj6585.4359344810.365802jj6585.4359844810.365762jj6585.4360264811.32762059377.5jj6587.458334811.32774058055.6jj6587.459774812.32767359459jj6615.4861934812.325925jj6616.5161944812.325833jj6617.5161094812.325812jj6617.5161494813.225815jj6620.5162204813.225942jj6620.5161564813.225916jj6620.5161134813.225845jj6624.5162564814.335810jj6626.5264094814.335941jj6626.5262614814.335910jj6935.4259954814.335852jj6939.5159644815.297757585119.6jj6945.4160934815.297716581312.6jj6946.461854816.355923jj6946.461064816.355847jj6949.4762854816.355814jj6950.1662404817.35949jj6952.4662304817.35850jj6953.462414817.35812jj6953.463024820.365911jj7668.56674875.94820.365914jj7669.5467701664822.37557606827.7jj7670.5467511074822.37580603912.2jj7673.5269154822.36005jj7675.4469004823.32753947jj7837.426597689622.24825.4757034.2jj7838.416914659764.24826.38766519jj7839.3869316596764827.31754435.2jj8032.57582697433.94832.326088jj8035.487551602356.74832.326006jj8036.487545604087.14832.325957jj8037.487546603738.8

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Bluetoredjethydrogenratiobehaviorversusprecessionalphase.Main(triangle)andSecondary(square)ComponentsfromdatasetD2,D3,andD6areplotted. Asadullaev&Cherepashchuk ( 1986 )data(asterisk)andtheiraverageoverprec=0.1areshownasareference. 228

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BluetoredjetratioofdatasetD2,D3,D6anddatafrom Asadullaev&Cherepashchuk ( 1986 )areshownwithrespecttotheorbitalphase.Dataarerepresentedaccordingtoprecessionalgroups:[0,0.1](diamond),[0.1,0.5](triangle),[0.5,0.8](square),[0.8,1](asterisk)]. 229

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PolarizationofapproachingandrecedingjetsindatasetD1,D2,D3andD6withrespecttosin2iscatwhereiscatistheinclinationangleofthejetswithrespecttotheobserver.AccordingtoEquation 6 thepolarizationofthejetsarerelatedtosin2iscatbyalinearfunction.Thelinearequationisnotclearforthesedatasetsalthoughthenumberofdatapointsisinsufcientwithlargeerrors,speciallyondatasetsD6

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Polarizationandelectrondensitymeasurementsofascatteringregionawayfromtheemissionregion.Wesketchthescenarioofscatteringofaregionwhichisseparatedfromtheemittingsource.Thesource(bluedot)radiateswithuxI0.Theradiationisrepresentedwithyellowarrows.Theuxarrivingtothescatteringregion(redcloud)isscattered.TheresultingI0,I1andI2uxesareobservedandthemeasuredpolarizationislowerthanpurepolarizationresultingonlyfromthescattering.Therefore,themeasuredelectrondensityislowerthantheelectrondensityresponsibleofthescattering. 231

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6.2.4.1 .Thepositioniscalculatedwithrespecttothereferencesegment(S0j).Weshowthatthecontributionfromeachjetsegmentisnothomogeneousbutitvariesalongthejet. 232

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ModeledprotonandelectrondensitiesalongjetswithrespecttoSj0referencesegment.Fromtoptobottom,plots1and2showtheevolutionalongthejetofthemodeledprotondensityofdatasetsD1andD2respectively.Plots3and4showtheevolutionalongthejetofthemodeledelectrondensityofdatasetsD1andD2respectively.Approachingandrecedingjetsarerepresentedwithsolidanddashedlinesrespectively.ThemodeledparticlepopulationsareshownversusthedistancewithrespecttoSj0indaysofgasowingat0.26c.Weobservefeaturesintheprotonandelectrondensitiesalongthejetalthoughtheyareweaklycorrelated.Thesefeaturesaredeepfortheprotondensityprole. 233

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ModeledprotonandelectrondensitiesalongjetsoftheSj0referencesegment.Fromtoptobottom,plots1and2showtheevolutionalongthejetofthemodeledprotondensityofdatasetsD1andD2respectively.Plots3and4showtheevolutionalongthejetofthemodeledelectrondensityofdatasetsD1andD2respectively.Approachingandrecedingjetsarerepresentedwithsolidanddashedlinesrespectively.Inourmodel,particlepopulationsvariesaccordingtothedistanceofSj0tothecentralcore.Weseethatforanyassumeddistancetheprotondensityis100timeslowerthantheelectrondensity.Theendoftheopticaljetisat0inthex-axis.Thedistancefromthispositionisexpressedindaysoftravelofthegasathespeed0.26c. 234

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Geometryoftheregionofinteractionbetweentheejetandtheaccretiondisk.Thetopshowsthecongurationofthegasbeforeinteraction.Thebottomshowsthecongurationofthegasafterinteractionbutitalsoindicatesthegeometryofthegasinpreviouscongurationwithdashedlines.Thesetwodiagramsareintendedtoshowthegeneralpictureoftheinteraction:particlesparticipatingintheinteractionandtheirmotion.Theregionswithelectron-protonparticlesareredandtheregionswithelectron-positronspairsareblue.Thecompactobject(blackbigdot)andtheaccretiondisk(longblackstructure)arealsodrawn.Thenumberofparticlesineachregionaswellastheirvelocityareindicatednexttotheregion.Theaccretiondiskwindissketchwithwavyarrows.Theinitialdirectionofthejetisshownwithdashedlines.Thenaldirectionofthejet,whichispredictedbythekinematicmodeloftheHmovinglines,isalongXinter. 235

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EquivalentWidthofthemovingHlineswithrespecttotheresidualstothedynamicalmodel.TheresidualsarecalculatedbysubtractingtheobservedwavelengthpositiontothewavelengthpositionpredictedbythekinematicalmodeloftheHmovinglines.Weseethatthereisnotobviouscorrelationbetweentheresidualsandtheequivalentwidthofthelines. EquivalentWidthofthemovingHlineswithrespecttoresiduals.TheresidualsarecalculatedbysubtractingtheneedtomatchtheobservedwavelengthpositiontotheofthekinematicalmodeloftheHmovinglines.Weseethatthereisnotobviouscorrelationbetweentheresidualsandtheequivalentwidthofthelines. 236

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EquivalentWidthofthemovingHlineswithrespecttoresiduals.TheresidualsarecalculatedbysubtractingtheneedtomatchtheobservedwavelengthpositiontotheofthekinematicalmodeloftheHmovinglines.Weseethatthereisnotobviouscorrelationbetweentheresidualsandtheequivalentwidthofthelines. EquivalentWidthofthemovingHlineswithrespecttotheprecessionalphaseresidual.TheresidualsarecalculatedbysubtractingtheneedtomatchtheobservedwavelengthpositiontotheofthekinematicalmodeloftheHmovinglines.Weseethatthereisnotobviouscorrelationbetweentheresidualsandtheequivalentwidthofthelines. 237

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ResidualsoftheDopplershiftofthemovingHlines.Credit:Figure4 Margon&Anderson ( 1989 ) 238

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CorrelationofresidualsoftheDopplershiftofthemovingHlinesofthetwojets.Credit:Figure5 Eikenberryetal. ( 2001 ) 239

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DecompositionofresidualsoftheDopplershiftofthemovingHlinesofthetwojets.Velocityshiftresidualsareseparatedintwocomponentsx1,2andy1,2withrespecttothelinearcorrelationoftheshiftresidualsofthetwojets(redandbluepointsintheplot)foundby Eikenberryetal. ( 2001 ):z2=0.69z1.Componentsx1,2aretheoscillationsaroundthelineartrend.y1,2aretheoscillationswithinthelineartrend.Thegureshowsperiodictrendsofthesefourcomponents.Oscillationsofy1andy2areinoppositephaseindicatingthattheoscillationsareduetochangesoftheaccretiondiskproperties.Oscillationsofx1andx2areinsamephaseindicatingthattheoscillationsareduetochangesofthepropertiesoftheplasma. 240

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Inthischapter,wepresenttheinfraredimage/cameraspectrographthatwewilluseinthenearfuturetocomplementtheresultsofthisthesis.TheCanariasInfraRedCameraExperiment(CIRCE)isaninfraredcameraandspectrographforthe10.4mGranTelescopiodeCanarias(GTC)telescope.OurworkincludesthedesignofthepolarimetrysystemforCIRCEthatisrequiredtoinvestigatethejetsofmicroquasars,especiallytheSS433optical/IRjets.OurdesignofthemechanicalcomponentsofCIRCEandtheeffectonthenalperformanceofthepolarimetrymeasurementsarealsoexplainedhere.Wepresentaswellthethermo-mechanicalstudyprecedingtheComputer-AidedDesign(CAD)modelsoftheinstrument.Thethermo-mechanicaldimensioningwasperformedafterdevelopingasoftwarethatwillbehandyforfutureproposalsofotherinstruments.Weintroduceourapplicationandthetestswemadetoestimateitsreliability.ThischapteralsoincludesananalysisofourCADmodelsandtheconceptsfortheassemblyofthemechanicalparts.Thepolarimetryanditsperformanceareexplainedattheendofthechapter.WestartthechapterintroducingtheinterestofIRobservationsforthestudyofjetsofSS433. Thompsonetal. 1979 ; Allen 1979 ).Thevariationsofthemagnitudemeasurementsbetweenthedifferentauthorsareontheorderofthephotometricvariationsduetothemotionsofthesystem.WhileextendedstudiesintheopticalandradiowavelengthrangeshavebeencarriedoutinthehistoryofSS433,veryfewpublishedobservationsexistintheinfrared(IR).ThecurrentIRobservationsconrmthedynamicalmodelobtainedfromtheopticalrange(seeSection 6.1.1 )buttheoverallresultsfromIRrangearefew.WepresenthereasummaryofallpublishedresultsfromSS433derivedfromIRobservations. 241

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Gilesetal. 1980 )andsmallerthananhour( Kodaira&Lenzen 1983 ).ThedynamicssuggeststhattheIRemissionisrelatedtothebinarysystembecausetherearetimecorrelationsintheorderoftheorbitalperiod.Otherstudies( Catchpoleetal. 1981 )showthattheIRphotometryisalsocorrelatedtotheprecessionalmotion. HighresolutionspectroscopyinJbandshowsthatthestationaryPaschenandHlineshavesimilarprolesatprec=0( Vermeulenetal. 1993 )andprec=0.5( Filippenkoetal. 1988 )whentheabsorptionbythewindisstronglyblue-shifted.Theradialvelocity(185km=s)ofthestationarycentralcomponentofthePaschenlinefollowsthedynamicalmodelthatwasobtainedfromspectroscopyintheopticalrange.Forinstance,thevelocityofCaII8927isabout100km=satprec=0.5.Asfortheopticalstationarylines,thestationaryPaschenlinealsoshowsadouble-peakedstructurewithtypicalseparationofabout290km=s,closertoKeplerianvelocitiesthanthoseofthedouble-peakstructuresofH,He6678,andHe7065. Thelinearpolarizationat2.2mis0.3%( Thompsonetal. 1979 ).TheobservedlinearpolarizationisonthesameorderastheISPindicatingnointrinsicpolarizationfromSS433.However,observationsinLandKbandsshowanexcessoftheIRuxcomparedwiththeopticalemission( Gilesetal. 1980 ; Kodairaetal. 1985 )suggestingfree-freeradiationfromthegasinthejets.Theexistanceoffreeelectronswouldcreatesynchrotronradiationasobservedintheradiojets,whichwouldbevisibleintheIRjetsaswell.Forinstance,polarimetryofotherXRBs( Shahbazetal. 2008 )showssynchrotronradiationinopticallythinNIRjets. Theopticaldepthchangesastheparticledensityinthejetsdilutes,thusachangeoftheindexofthespectrumisexpectedtooccuratsomewavelengthintheNIRrange.Atthiswavelength,correspondingtothetransitionpointbetweenopticallythinandthickregionsnearthebrightnesszoneofSS433,weexpecttoseevariationsofthelinearpolarization.Furtherobservationsofthepolarizationinthisrangearenecessaryin 242

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CIRCEhaspolarimetriccapabilitiesandahighspeedimageacquisitionmode.Itisanoff-axisreectivesystemexceptfortheentrancewindow,thelters,thegrisms,andthepolarimetryoptics.Itisdesignedtobeachromaticandtoencircle80%oftheincidentenergywithin2pixels.Figure 7-1 showstheopticallayoutofCIRCEincludingtheentrancewindowbeforethefocalplane,thecollimator,thecameraandthepupilwithalterandtheWedgedDouble-WollastonPrism(WeDoWo)(FormoreinformationabouttheWeDoWo,seeSection 7.4 ).ThecollimatoriscomposedoftwomirrorslabeledC1andC2.Twoatmirrors(F1andF2)aresituatedbeforethecollimator.F1andF2servetofoldtheinstrumentandkeepitwithintheGTCenvelopespecications.ThecameramirrorsM1,M2,M3,andM4aresituatedafterthelterbox.Thelterboxisatthepupiloftheinstrumentanditcontainsthewheelswiththelters,thegrismsandtheWeDoWo.Anyofthosecomponentscanbeinsertedinorremovedfromthelightbeamduringtheobservation. ThemaininterestforusingCIRCEinourfutureworkonjetsfrommicroquasarsisthatitcombinesspectropolarimetryusingaWeDoWo(seeSection 7.4 )withthehighspeedimageacquisitionmodeandthehighphotoncollectingareaoftheGTC.Therefore,wewillbeabletomeasurevariabilityofpolarizationfeaturesfromSS433onveryshorttimescales.Moreover,additionalpolarimetryofthejetsandthejet-diskregionisessentialtocompletethestudyofthepolarizationandthebehavioroftheemissionlinesfromSS433whicharepresentedinthiswork(seeChapters 5 and 6 ).Intherestofthechapter,weintroduceCIRCEandweshowthatthisinstrumentveries 243

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Edwardsetal. ( 2008 ).CIRCEhasa3.4'3.4'eldofview(FOV),25timelargerthanNIRC/KECKand3timeslargerthanNIRI/Gemini.OpticalqualityanalysisshowsthatCIRCEmeetsthescienticrequirementsspeciedfortheimageandspectroscopymodes.Theenclosedenergydiagrams(seeFigure 7-2 )indicatethatmorethan80%oftheenergyiscontainedintwopixelsinJ-bandthroughoutmostoftheFOV.Thepixelsattheedgeoftheimagecontain70%ofpointsourceenergy. AuniquesolutionforthefabricationofthislayouthasbeendevelopedwithJanosTechnology.Itconsistsoftestingandadjustingthewholeopticalsystemasaunitafterallthemirrorsaremountedonthebench.Thenaldiamondturnedcuttingensurestheopticalqualityoftheglobalopticalsystemeventhoughthespecicationsofeachmirrormaynotbemet.Thisnoveltechniquerequiresnishingthedesignofalltheopto-mechanicalcomponentsandthemechanicalpartsthatinuencethenalpolishedsystem.Therefore,itencompassesthedesignandthemanufactureofthebench,thebracket,andthemirrors.Thistechniquedelaysthenalphasebutitavoidsalignmentproblemswiththeopticsaftertheassemblystage. Thus,weneedacarefulandcompletestudyoftherequirementsandbehaviorofmechanicalsystems,inparticularoftheexuresandthermalpropertiesoftheopticalbench.Here,wepresentthefeasibilitystudyofthebenchandthethermalshields. 244

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Thetoleranceanalysisoftheopticaldesignestimatesthatthealloweddeectionofthebenchis25mRMSinordertomaintaintheopticalqualityofthesystem.Theexureofametallicstructureisproportionalto1 Furthermore,thetotalweightoftheinstrumentalsodependsonitsdimensionswithtwomajorconsequences.Firstly,thetotalweightoftheinstrumentmustfollowthetelescopespecications(themaximummassis1000kg).Secondly,theinstrumenttiltswithrespecttothetelescopecoordinatesystem.ItissupportedbyaG10-bercylindricalstructurethatreducestheheatconductionfromthetelescopeandambientair 245

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Thetemperatureinsidethedewar(77K)mustbemaintainedatleast24hwithoutrellingtheLN2tanks.TheLN2boilsbecausethebenchisheatedbyradiationfromthevacuumjacketmitigatedbyradiationshields,andconductionthroughtheG10andwiresforelectronics.Theshieldsincludetheactiveshieldatcryogenictemperature,andthepassiveshieldthatreducestheradiationfromthevacuumjacketwhichisatroomtemperature(300K).DetailsaboutthemechanicalandgeometricalpropertiesofthevacuumjacketandtheshieldsareexplainedinSection 7.3.1 Theequilibriumtemperatureofthepassiveshielddependsonitstotalsurfaceareaandtheactiveshieldsurfacearea.Therefore,theradiativeheatloaddependsontheradiioftheactiveandpassiveshields.Weassumethattheshieldsaregraybodieswithemissivity0.1tocalculatetheradiationheat.TheconductiveheatcomesfromthetelescopethroughtheG10ring.TheheatdependsonthethicknessandthelengthoftheG10ring.Aswenotedearlier,ashortandthickringwillbeverystiffdecreasingthetiltoftheinstrument.However,theheattransferisproportionaltothecrosssectionsurfaceareaoftheringAG10andinverselyproportionaltoLG10.Converselytothethestiffness,thethermalheatloadduetoconductionisreducedbydecreasingthethicknessoftheG10orincreasingthelength. ThetimethattheinstrumentremainscooldependsonthetotalheattransferandthevolumeofLN2inthetanksthatparticipatesinthecooling.IfthetotalvolumeofLN2wereraisedtheinstrumentwouldremaincoollonger.However,increasingthevolumeofLN2alsoincreasesthedistributedloadthatcontributestotheexureofthe 246

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7-3 ).WhilethemainpurposeofthistoolisthedimensioningofthebenchandtheshieldsofCIRCE,ithasbeencreatedforamoreextendedcontext.Theultimategoalofthissoftwareistoprovideatoolforinstrumentbuilders.Theusersintroducethegeometryoftheinstrumentandothercharacteristicofthestructure.Inresponse,thesoftwarereturnsthepropertiesfortheinputcongurationthatarenecessaryduringarstanalysisofthefeasibilityoftheinstrumentincludingthethermalbalance,thebending,thecoolingtime,thetilt,andthetotalweight. 247

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Concerningthegeometry,wemadeanalyticalcalculationsofmechanicalparameterssuchasthevolume,areas,andmomentsofinertia.Weveriedthatthevaluesobtainedfromthesoftwareagreewithouranalyticalresults.Wealsotestedthesevaluesusingtheonlinecalculator(http://www.mecatools.free.fr/generale/mtorsion.html).ThevaluesfromthecalculatoralsomatchtheITMASresults. Similarly,wetestedthedeectionusingouranalyticalcalculationsandanonlinecalculator(http://www.efunda.com/formulae/solid mechanics/beams/casestudy bc cantilever.cfm).Wecomparedtheresultsofthethreemethods(ITMAS,analytical,andonlinecalculator)usingsimplescenarios:homogeneousdistributedloadsorsingleconcentratedloadsatvariouspositions.Thedeection,shear,andmomentsofforcearethesameforallthreemethods. 1.jsp.Wecalculated 248

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7-3 )andweusedthesuperpositiontheorem( Fosdick&Shield 1963 )tocalculatethetotalexureateachposition.Weusedlinearinterpolationtodenethepositionsoftheopticalandmechanicalelements(seeTables 7-1 and 7-2 ).Thealuminumandnitrogendensitiesweusedarerespectively2.7106kg=mm3and8.08107kg=mm3. Thecalculationsfromtheanalyticalmethodandtheonlinewebpageareofthesameorderbuttheresultingcontributionsfromthebracketsisunderestimatedintheanalyticalsolutionattheendofthebeam(seeFigure 7-4 ).Ouranalyticalcalculationsassumethatthebracketsareatthesamepositionasthemirrorstheysupport.Thecontributiontothedeectionofaconcentratedloaddependsonthepositionoftheweight.Theassumptionofouranalyticalcalculationsunderestimatetheeffectofthebracketbecauseitconsidersthebrackettobeclosertothebulkheadthanitisinreality.TheresultsfromITMAScoincidewiththeonlinecalculator. Therearethreeotherfactorsthataffectthethermo-mechanicalqualityofthesystem:thelighteningofmaterialinthebench,thedifferentialpressurebetweentheinsideandtheoutside,andthetorsionofthebrackets.Lighteningofthebenchconsistsofremovingmaterialthatcontributesonlyslightlytothestiffnessofthestructureinordertoreducethedistributedweightofthesystem.WeuseITMAStocomparethevariationsoftheexurewithandwithoutlighteningofthebench.Theestimatedimprovementofthedeectionis3mfor30%ofremovedmaterialalongthebeam. Thesecondfactorcomesfromthedifferenceofpressurebetweentheinsideoftheinstrumentthatisundervacuumconditionsandtheoutsidethatisunderoneatmosphericpressure.Thepressuredifferencebendstheentrancewindow.Thecurvatureoftheentrancewindowcreatesopticalpoweroftheglassthatmaydistorttheopticalquality.Thisphenomenonhastobeconsideredwhencalculatingthethicknessoftheentrancewindowinfutureanalysis. 249

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OurstudywithITMASshowsthata5mmthickbenchwithtwounderneathcylindricalbeamstructures(containingtheLN2)ofinnerradius25.4mmandthickness2.5mmwouldcreatelessthan25mshiftbetweenmirrors.Thetotalheat,includingradiationandconvection,islessthan60W.FortheLN2tanksexplainedinSection 7.3.3 thetimethattheLN2takestoboilisabout48hours.Then,thiscongurationsfollowthespecicationsdenedbythetoleranceanalysisoftheopticaldesign( Edwardsetal. 2006 ).ThenextsectionexplainsthemainissuesoftheCADdesignoftheinstrumentthatisbasedonthecurrentthermo-mechanicalanalysisoftheinstrument. 250

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Thedesignprocessrequiresmultipleiterationsbecauseitissubjecttotheaccuracyofthefabricationofeachpieceandtheassemblyofthemechanicalsystem.ManyCIRCEpiecesarebigandtheyoftenexceedthecapabilitiesofourmachineshoprequiringmodicationstothedesignofsomemechanicalparts.Forinstance,thebenchdimensions(1543.5mm893.0mm)aretoobigtobemachinedwithourCNC.Wedecidedtodividethebenchintothreeatpiecesthatwillbeassembledlater,resultinginasolidatstructurethatholdsthemirrorsonthetop.Shiftsbetweenmirrorswithinthecameraorthecollimatorduetoafabricationormanufacturingerrorsresultinopticalaberrationsofthenalimage.WedecidedtohaveallthemirrorsM1,M2,M3,andM4ofthecameraonthesamebenchpieceandthemirrorsofthecollimatorC1andC2togetheronanotherpiece.Therefore,theeffectintheimageoftheshiftbetweenthesetwopieceswouldjustbevignettingwithnoadditionalopticalaberrations.Thethirdpiecedoesnotsupportanyimportantopticalcomponentbyitselfbutitisrequiredtoconservethesymmetryofthebenchandthusthesamestiffnessinalldirections.Thethreepiecesareassembledusinganunderlyingbeamstructurekeepingthebenchat.Weusepinholesinordertoassurethesamerelativepositioniftheyaredisassembled. 251

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D .Inthenextsection,weexplainthemainissuesofthefabricationandassemblythatwereconsideredduringthedesignstage. 7.3.1DesignandFabricationAnalysisoftheRadiationShields 7-5 ).ThebulkheadseparatestheinstrumentintotwopartsattheF1mirrorposition:thefrontpartcontainingtheentrancewindow;andthebackpartthatcontainsmostoftheoptics.Therearetwogroupofshields,eachwithanactiveandapassiveshield,whichareattachedineachsideofthebulkheadinordertoisolatethefrontandthebackpartoftheinstrumentfromexternalradiation(seeFigure 7-5 ).Thesizeoftheshieldsdependsontheremainingspacebetweenthebenchandtheinstrumentenvelope.Itwillalsobeconditionedbythestudyoftheheattransfer.Wechoseastandardthicknessfortheshields(3mm). Thedifferentialpressurebetweentheinsideandtheoutsideoftheinstrumentcreatesstressesonthematerialofthevacuumjacket.Forthepurposeofcalculationsweassumedthevacuumjacketasathin-walledcylinderofdiameterDc=1092.2mm 252

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7-4 )isgivenbyWc=KEtc 7-6 ). AnotherconstraintinthedimensioningoftheshieldsandvacuumjacketisimposedbytheO-rings.O-ringsblockairowsealingtheinterioroftheinstrumentthatisundervacuumconditions.WeuserubberO-ringsbecauseoftheirlowpermeabilityandtheirprice.O-ringsaretoroidsthatarecharacterizedbytheirinternal(ID)andoverall(OD)diameters.TheODistheradiusofthecircularchordmakingthetorus.ThethicknessoftheO-ringdependsontheODanditischaracterizedbythediameterofthecross-sectionofthetube,alsocalledID.AnO-ringthatcoversanextendedsurfacerequiresabigIDbecauseitishighlystretched.TheO-ringisseatedinagrooveanditiscompressedduetopressuredifferencescreatingapredictabledeformation.TheIDisgivenbytheParkercatalogforagivenOD.ThesizeofthegrooveanditsdistancetotheedgeofthepiecedependontheID.ThebiggertheO-ringthemorespaceisrequiredbetweenthegrooveandtheedge.Consequently,O-ringsreducetheminimumpossiblesizeofthevacuumjacket,decreasingthemaximumsizeoftheshields. 7.2 ,thebenchisnotperfectlyrigidandtheweightsofthematerialandtheLN2bendtheatsurfacewheretheopticalcomponentsrest.Fortunately,ourstudyshowsthat 253

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7.2.3 ,andttingthemtogetherwithprecisiongroundsurfacesandpinnedinterconnects.Ourmachinesareabletomakesurfacesatnesswithinthetolerancesoftheopticalsystem(25m)maintainingtheopticalquality.IntheframeworkofoursolutionfortheopticallayoutfabricationwithJanosCotheopticsaremeasuredandcorrectedonthebenchitself.Therefore,theerrorsonthefabricationwillbecorrectedduringthediamond-turningprocess.However,themanufacturingerrorswillcreatemisalignmentbetweenthepieces,mostimportantlyvariationsoftheorientationbetweenthepiecesthatcontainthecollimatorandthecamera.Wecanmeasuretheangleofthetabswithinathousandthofitslength.Theaccuracyoftheanglebetweenthetwopiecesis<0.5arsecondsandthemaximumshiftattheendofthecamerawouldbe0.6m.Theerrorcomingfromtheassemblytstheopticalspecications. 254

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Ozel&Altan 2000 ).Forinstance,theJohnson-Cook(JC)modelrepresentsthebehavioroftheworkmaterialsubjectedtoowstressasfollow, TheparametersA,B,C,nandmofthemodelareobtainedfromtestsofmaterialsatdifferentconstraintratesE.TheparameterAcorrespondstotheinitialyieldstrengthofthematerialatroomtemperature.Tmisthemeltingtemperatureofthematerial.ThestrainrateE0andthetemperatureT0arenormalizationparameters.Ofcourse,characterizingtheworkmaterialowstressatthedeformationzonesisoutofthegoalsofthisworkbecauseitrequiresextendedsimulationsandtestswithdifferentmaterials.However,itisimportanttobeawareoftheeffectsofthesestressesontheopticalbenchthatbendsundertheactionofthemachiningtool. Equation 7 indicatesthattheresidualstrainsdisturbthespatialpositionandtheshapeofthesurfacedependingonthepatternofthecut.Thetemperaturegradientdependsonthespeedofthetoolandthepattern,whichareimportantparametersdeningthedeformation.Wemachinedthecameraplatefromamilledaluminumplateandwemeasuredthesurfacedeformation.Thecameraplatesisatononesidebutithasalighteningpatternontheothersidecreatingadifferentialstressbetweenthetwosides.Thedifferenceofthestressbendsthepiecebyaboutonecentimeter.Thegeneralmethodtogrindaplatewithholesatconsistsofthermallycyclingitbetweeneachmachiningandcuttingpass.Thecryo-cyclingrelaxesthethermalandstructuralexpansionsthatarelocallyintroducedbythetoolinthebench.Weperformedthreethermalcyclesafterallthemachiningwasnished.Therstcoolingreducedconsiderablythecurvature(5mm).Afterthesecondcoolingthecurvatureisreducedto1.7mmanditremainsstable.Wedecidedtocutmaterialfromtheatsideinorder 255

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7.2 )includestheactionofthetanks.Infact,thetanksarecylinder-likestructuresthathaveamuchbiggersecondmomentofinertia(I)thanaatbeam,creatingthemajoritypartofthestiffness. Thedimensions,shape,andmaterialofthetanksdependsontheglobalmechanicalsystem.Thetankssupportthebench,whichshrinkswhenthetemperaturedrops.Thebench,mirrors,andbracketsareallmadeof6061-T651aluminuminordertohavethesamecontractionastheopticalelements.Theopticalpropertiesareconservedwhenthewholeopticallayoutisscaledbythesamefactor-apropertyknownashomologouscontraction.Thetankisalsomadeof6061-T651aluminumbecausethecontractiondifferencesbetweenthetankandthebenchwouldcreatemechanicalstresses,deformingtheopticalbenchanddegradingtheopticalqualityofthesystem. 256

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7.3.3.2 )becauseatplatesbendinthenormaldirectionduetolateralloads.Thebendofaatpiecemayforcethebenchtomovelocally,perturbingtheatnesswheretheopticalelementsrest.Weconsideredtwoshapesofthetanks:aportionofacylinderwithaatplatewhichmatchtheopticalbench,namelyhalf-cylinder;andacylinder.Inthecaseofthecylinderwestudiedthethermo-mechanicalperformancesofone,twoorthreecylinders. 7-7 ).Wecalculatedtheoptimumthicknessresistingoneatmosphericpressureandminimizingtheexureofthebench.Thetankbeamgivesmostofthestiffnessofthebench.Theexurecalculations(seeFigure 7-9 )estimatethatastructurewithonecentimeterwallbendlessthan10m.Ontheotherside,wefoundthata3mmcylindricalwallresists1.03atmospheresbyusingthesameequationsweappliedtocalculatethethicknessofthevacuumjacket(seeSection 7.3.1 ). Contrarytothecylindricalpart,theatsidehaslittleresistancetotheexureoftheopticalbenchanditsignicantlybendsduetothepressure.A50mmthickplatebends0.5mm,deformingthebenchwayoutofourrequirements.Toavoiddeformationofthebench,wecreateaclearancebetweenthebenchandthetankof2mmalongtheplate.However,theplateisverythickandheavy(250kg),increasingthetotalweightoftheinstrumentoutofthespecications. Thehalf-cylinderexhibitsotherdisadvantageswhichconcernthethermaltransfertothebench,andthedistributionoftheLN2inthetank.Denitely,thetimethattheLN2

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Inaddition,whentheinstrumentisside-up,theLN2issituatedinthelowerpartofthetankawayfromtheopticalbench.TheheatofthebenchistransferedtotheLN2alongtheexternalcylindricalwalls.Theradiusofthecylindricalwallisbigandthetemperaturedifferenceisgreaterthan10Kforthespecicdimensions.Weinvestigatedsomesolutionsthatincludedcoppercylindricaloratstructuresinsidethetank(seeFigure 7-7 ).Thesestructuresmaybeusedasbafesaswell,preventingtheoscillationsoftheLN2.TheyalsoallowmorehomogeneousdistributionoftheLN2inthetank.Infact,theLN2tendstogotothebottomofthetank.Forinstance,iftheinstrumentisvertical,thetemperatureofthefrontoftheinstrumentwouldriseconsiderably(morethan20K)comparedwiththeLN2temperature. However,asmentionedearlier,thissolutionisdifculttomanufactureanditincreasesthetotalweightoftheinstrument.Thecurrentstudysuggeststhatthehalf-cylindertanksolutionisnotfeasible.Weinvestigatedotherpossibilitiesbasedonthesameshape.Thesesolutionspresentedalsofabricationorassemblydifcultiesanddidnotsatisedourexpectations.Adifferentconceptwasnecessary.Next,wepresentanothersolutionbasedoncylindricalbeams,amoreadaptedsolutionforCIRCE.

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Weassumedthatthewallisametallicbarwithathermalconductivityk(T),across-sectionsurfaceareaA,andalengthL.Thewallissubjectedtoathermalconductiveandradiativeheatqinthesidenexttothebench.ThetemperatureTbenchoftheheatedsideishigherthanthetemperatureTLN2ofthecooledsideasestimatedbythefollowingequation, k(T)A(7) ThesurfaceareaA=LtubetwalldependsonthelengthLtubeofthecylinderandthicknesstwallofthewall.ThelengthL=2 Themainissueforthissolutionisthefabricationofthesetanks,whichmustbedonecarefully. 259

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Eachtankconsistsofacylindricalpipewithtwocapsthatarehermeticallyweldedateachend.TheroughfabricationwillbeperformedbyPrecisionCryogenicsbutwewilldotheaccuratealignmentandmachiningofthesetwotanks.Ourstrategyconsistsofmachiningthefrontcapofthebeamsperpendiculartotheats.Weusethefrontlipofthebenchasareferencetopreciselycutthefrontcaps.Werstmeasuretheorientationofthebenchfrontlipwithrespecttothebenchmountingholestohighaccuracy.Aftertheatsaremachinedinordertobeco-planarthetrickconsistsofcuttingthefrontcapsperpendiculartothem.Inreality,wecanonlymeasurethefrontcapangletoabout25moveritsdiameterwithanuncertaintyof104radians.Thiserrorisgreaterthanonemillimeterattheendofthebenchcreatinglargestressesinthestructureanddeformingthebenchwhenthetankbeamsareattachedtothebulkhead.Therefore,themachiningrequiresasecondstepthatalignsthefrontcapsandthebulkhead.Weattachthebenchtothetwotankbeams.Thebeamsarenolongerperfectlyparallel,butwecanusethefrontlipasareferenceforre-deningthesurfaceofthefrontcapthatmatchesthebulkhead. 260

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Thecriticalelementsofthelterboxdesignarethemotorsmovingthewheelsandtheswitchesactingarotationreference.WeinitiallyusedtheFLAMINGOS-2(F2)designsforthewheels,shafts,ballbearings,andotherelementsnecessarytomaintainthemechanismsturningthewheels;andtheexperiencefromF2fortheuseofsteppermotorsatcryogenictemperatures.Concerningtheswitches,wedesignedanewmechanicalcomponentwhichcontainsalltheswitchesandcanberemovedinordertoperformsmallmodicationstothesystem.Thedetailsofthemotorsandswitchesareexplainedbelow. Normally,IRinstrumentsusecryogenicsteppermotorswhichworkatLN2temperatures.Thesemotorsareveryexpensiveandwedecidedtoadaptstandardsteppermotorstothecryogenicenvironment.Standardsteppermotorsarecheaper($300)buttheydonotworkwhentheyarecoldbecausethelubricantsfreeze.However,weturnedthemintocryogenicsteppermotorsbycleaningthemotorandremovingthelubricant.ThistaskwasperformedwiththecollaborationofJavierCenarro 261

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Thetestsconsistedofmeasuringthemaximumspeedatwhichthemotorsturnedwhentheyarecold.Themotorvelocityincreasesprogressivelybeforereachingmaximumspeed.Wesuspectedthatthemaximumvelocitymaydependontheslopeofthevelocitywhenthemotorstarts.Heatmaybeanotherfactordegradingtheperformanceofthemotor.Themotorsheatwhiletheyturnandtheirtemperatureincreasesaftersometime.Wemeasuredthebehaviorofthemotorfordifferentmaximumandslopespeeds.Werecordedthetimeofmeasurementsandthetemperaturesofthemotorstoinvestigatehowthemotorschangetheirperformancewhiletheyareused.ThemeasurementsareshowninAppendix F .Thetestsindicatedthatthespeedintheaccelerationregimehassmalleffectsontheperformanceofthemotor.Sixofthemotorsworkproperlyuntil800stepspersecond(sps).Theirmaximumvelocityrangesbetween825spsand925sps.Twomotorshaveveryrandommaximumspeeds.Theirmaximumvelocityvaryupto50%withnoapparentrelationwithtemperature,slopevelocityoranyotherparameterofthespeedpattern.Onemotordidnotwork. Oncetheperformanceofthecryogenicmotorswascharacterizedinthesmalltestingdewar,wetestedmotorveusingthelterwheelFW1.Thistestalsoincludedthecalibrationoftheswitchmechanism.WeusedmicroswitcheswithJX-45actuators.Theswitchesareinstalledinaseparatemechanismthatisconnectedtothelterbox.Thissolutionallowsmountingthemicroswitchesseparatelybeforeinstallationinthelterboxwheretheycanbeneadjusted.ThewholesystemwascharacterizedrstunderroomtemperaturebeforedunkingitintheLN2.Themotorworkeduntil1200atroomtemperatureand450undercryogenicconditions. 262

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Clarkeetal. 1983 ; Simmons&Stewart 1985 )andnosignicantdegradationofopticalqualityinK,HandJbandswithrespecttoregularimagemodewithintheFOV.Werequirelessthan2.5pixels(0.25arcseconds)distortion.Inaddition,thesystemthroughputmustbegreaterthan75%alongthewholewavelengthrange.WebasedourdesignontheDouble-BeamSpectrograph(DBS)congurationthatallowstoincludepolarimetrywithoutmodicationoftheinitialopticaldesign(seeSection 3.1.3 ).Polarimetryandstandardmodescanbechangedduringobservationsbyselectingtheappropiatecongurationofthelterboxandfocalplanemechanisms.However,thesplitterinthepupiloftheinstrumentintroduceschromaticaberrations,inparticularatlongerwavelengths.Imagingpolarimetryrequiresspecialattentionbecausethechromaticaberrationsinspectropolarimetryappearjustasgeometricaldistortionsofspectrathatcanbesoftware-corrected.Wepresentinthissectionthefeasibilityanalysis,theoptimumsolutionandthenalopticaldesignwithpolarimetry. Edwardsetal. ( 2006 ).WefollowtheWeDoWosolution( Oliva 1997 )thatallowsmeasurementofalllinearStokesparameterswithasingleexposure.Itisparticularlyinterestingforhighspeedimageacquisitionsandobservationswithbadseeing.Inpractice,resultscomefromtwoexposuresat0and45HWPanglesusingEquation 3 263

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7-8 ).Theyareinsertedbytranslatingthemasksparalleltothefocalplane.Thefocalplanemaskcontainsthreelongslitsforregularspectroscopy,9slitsforspectropolarimetryand3slotsforimagepolarimetry.Thedeckermaskhidestheslotsandslitsthatarenotrequiredforthespecicmode.Spectroscopyandspectropolarimetrycanbeperformedwith0.4,0.7and1arcsecondsslits.Theslitsforspectroscopyarelong(3.4arcminutes).Thefocalplanemaskhasforeachofthoseslitwidths,threeshort(12arcseconds)slitsforspectropolarimetry.ThetotalFOVofthespectropolarimetrymodeis2arcminutes.Theslotsforimagepolarimetryare12arcseconds50arcsecondsbuttheglobalFOVofthismodeextendsto50arcseconds2arcminutes. Thecentralslitandslotforpolarimetryhaveaspecialinterest.TheHWPcoverscentralslotandslitallowingmoreaccuratepolarimetrymeasurementofthecentraleld.TheHWPisatthedeckermaskthatisinsertedclosetoP0wherethebeamsizeisminimal.ItcontainstheHWPthatcanberotatedatanyangleintheplaneofthedeckermask.Inaddition,thepolarimetrymeasurementfromthecentralslotmaybeacquiredathigh-speedreadout.High-acquisitionisperformedbyreadingonlythecentralpartofthedetector.Thefourimagesresultingfromthecentralslotareintheregionofhigh-speedreadout. 264

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Thereection,theelongation,theseparation,andtheopto-mechanicalpropertiesaremajorfactorsintheselectionoftheWeDoWomaterial.Oncethematerialischosen,theoptimizationofthepolarimetryconcernsthegeometryoftheWeDoWo(seeFigure 7-1 )andthesizesofslot/slit.TwoanglesoftheWeDoWoaffectthebeamseparation:theedgeangle()splittheraysbetweenbothWP;theprismangle()denestheseparationofe-oraysineachWP.TheWeDoWomaybecoupledwithFusedSilica(FSi)inordertodecreasechromatism.Thislayerdenesathirdangle()ofthegeometry.ThesystemgeometryforagivenFOViscalculatedinrstorderapproximationfromtheSnell'slaws.However,CIRCEisacomplexsystemwithasphericmirrorsandaccurateanalyticalresultsarecomplex.WeuseZEMAXcomputationtooptimizetheFOVandthechromaticaberrations(seeSection 7.4.3 ) ( 1994 )discusstheopticalbehaviorofmaterialsintheNIRrange.Theimportantconsiderationsofthesematerialsforthepolarizationsystemarethetransmission,thebeamseparation,thebirefringence,therefractiveindexandthewavelengthdependence.MgF2isthecheapestmaterialusedinthisrange.Itisthemostcommonbecauseithasagoodopticaltransmissionbelow<6m.Forinstance,itstypicalabsorptionis40103cm1at2.7m. Theindexesofrefractionat0.4moftheordinaryandextraordinaryraysofMgF2areno=1.3836andne=1.3957,respectively.Thelossoflightduetoreectionatthesurfacesoftheprismsfortheserefractionindexisabout5.2%at0.6m.Inaddition,it 265

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Thethermo-opticalpropertiesofMgF2adaptwelltocryogenicconditions.At0.4m,thevariationsoftheindexesofrefractionnoandnearedno Calciumuoride(CaF2)andinfrasilaregoodoptionsforthematerialoftheentrancewindowbecauseoftheirgoodtransmittanceintheinfrared.Bothmaterialshaveindexofrefractionabout1.4atambienttemperatureintheNIR.Therefore,thelossoflightattherefractingsurface,crossingperpendiculartothewindowis6%.ContrarytoCaF2,infrasil301isopticallyhomogeneousalongthethreespatialaxes(n<5106).Thisisanimportantpropertyforpolarizationmeasurements.Inaddition,infrasil301 266

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WeusedmulticongurationanalysiswithZemaxanddatatreatmentwithExceltooptimizethepolarization.TheprocessisillustratedwithdiagramsintheAppendix H .OptimizationconsistsofndingtheanglesoftheWeDoWo(,,and)thatresultinthemaximumFOVwithangoodopticalquality.TheclassicalconceptofZemaxdoesnotsupportdesignswithrayswithsimultaneousvaluesofthesamecharacteristic.Multi-congurationsareusedtodesignoroptimizeopticaldesignsatdifferentwavelengths,oratvariouscongurationsthataredenedinaspreadsheet.Thesoftwarereplacethevaluesoftheparameterswhenadenedcongurationiscalled.Acongurationconsistsofanarrayofvaluesforsomegivenparameters.Forexample,aWPprismwouldhavedifferentcongurationsfortheordinaryandextraordinaryraysthatseetheglassdifferently. ThecongurationsofoursystemincludethebirefringenceoftheWeDoWoforordinaryandextraordinaryrays;theorientationofthemainaxisoftheHWPalongtheX-axisandY-axis;thewavelengthatagivenIRlter;theinputanglesoftherays;thematerialoftheWeDoWo;andthegeometryoftheWeDoWo.Wetesteddifferent 267

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G .Wefoundthatacombinationofdeckerandfocalplanemasksisabettersolution. WecodedamacroinZemaxthatchangestheparametersfortherequiredconguration.ThismacroalsocalculatesthevaluesfromtheopticalanalysisofZemaxandprinttheminanoutputle.Theresultsofeachwavelength,congurationandeldincludeinformationabouttherayposition,thescattering,thevignettingandtheZernikes'coefcients.WeprogrammedamacroinExceltoextractthisinformationfromtheZemaxoutputle.Themacroalsocalculatesandplotsthepositionofeachrayandthechromaticaberrationsatanydenedeld. Theimagesareoverallcenteredintothedetector(seeFigure 7-10 ).Theoptimumgeometryisgivenbytheeo=0.8separationandthe=22.1wedgeangle.Theresultingseparation(1315)isbigenoughtoavoidoverlappingafterconsiderationofmanufacturingandalignmenterrors.Thechromaticaberrationsarelessthan1.6pixelsinJbandbuttheimagedegradationinKbandisimportant.TheopticalqualityinKbandareshownintheAppendix B .Whilsttheencircledenergyismoreconcentratedintheinitialopticaldesign(10m),theresultsofthepolarizationarestillacceptable.Theencircleenergyatthediffractionlimitshowthat80%oftheenergyiscontained 268

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(7) (7) (7) However,errorsinthemeasurementintroduceuncertaintiesinthecalculatedpolarization(seeSection 3.1.4 ).Thesourcesoferrorsaredividedintothreemaincategories:Instrumentalpolarization(IP)otherthanthepolarizationsystem,defectsofthepolarizationsystemandstatisticalerrorsofpolarization. Thelasthasbeenstudiedby Simmons&Stewart ( 1985 ).TheclassicalmedianvalueisonlythebestestimatorforSNR>0.7becausePiscalculatedfromaquadraturerelation.Atlowsignaltonoisetheseauthorsproposeanothermaximumlikelihoodthatremovesthebiasfromthepolarization. TheIPconcernspolarizationthatisintroducedbeforethebeamissplitbytheWeDoWo.Thepost-analyzer(PA)opticsincludethelters,thegrismsandthecamera.Asarstapproximation,theMuellermatricesdescribetransmissionofStokesvector.A 269

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where=cos(2(x,y)),p=p(x,y)=(x,y)and=(x,y).Thepolarizationtransfermatrixdependsonthe(x,y)positionoftherayintheimage.Therefore,weassumeamatrixforeachofthefourbeamsoftheWeDoWo.Contrarytothediagonalelements,theoff-diagonaltermsaccountforcross-talkbetweenpolarizationcomponents.ThestandardtechniqueforIPcalibrationdoesnotremovethird-ordereffectsthatarenon-negligibleforstronglytiltedsurfacesasasphericmirrors.ThecalibrationisaffectedbythepositionofthesubtractedpolarizationstandardbecausetheIPdependsstronglyonthepositionofthestar.ItisimportanttocharacterizetheIPMuellermatrixinordertoevaluatetheseeffects. ThePApolarizationismainlyduetothecamera.OtherPAuncertaintiesincludetheerrorsintroducedbytheHWPandtheWeDoWothemselves.Forinstance,thedefocusofamaterialwitharefractingindexnandathicknessdisd(11=n).TheerroroftheHWPorientationcreatesdefocusaswellthathasaradius, TheeffectsofthePAinstrumentationmayberemovedbytakingvariousmeasurementsatdifferentHWPangles.Weplantocharacterizethesystembytaking8measurementswithi=i=4andusingthefollowingfunctions:FiB1cos(21)+qcos(4i)andGiB2cos(22)+ucos(4i)whereBdescribesthepolarizationdegreeoftheoptics.FourieranalysisusingFiandGiateachpositioncanbeusedtocharacterizethepolarizationerrors.Thisanalysishasbeenusedpreviouslyforthestudyoftheclassical 270

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Patat&Romaniello 2006 ).Inourcase,thenormalizedlinearStokesparametersQ[orU]areobtainedbyaveraging(1)iFi[or(1)iGi]fori=[0,7]. ThetransmissionoftheWeDoWoforeachofthefourbeams(T01,Te1,To2andTe2)areasfollows, 8XF2iF2i+1 8XG2iG2i+1 ThedifferencesinWeDoWoraytransmissions,HWPretardancevariationsandpleochronismaffectsthevaluesofFiandGi.Forthegiventransmissionsk1andk2oftheordinaryandextraordinaryraysoftheWeDoWo,thecoefcientsoftheMuellermatrix(seeEquation 7 )oftheIParechanged, Ideally,k11andk20attherstprismandk10andk21atthesecondprism.Variationskoftransmissioncreatemeasurement2Fi=q(cos(4i2k)+cos(4i))and2Gi=u(cos(4i2k)+cos(4i)).Forinstance,smallerrorsoftheangleoftheHWP(<0.15rd)createmeasurementerrorslowerthan0.05%.TheerrorsoftheHWPretardanceretcreateacouplingoflinearandcircularpolarizationaddingsin(i)sin(ret)andcos(i)sin(ret)termsinQandUrespectively,asshownbythefollowingequations, 271

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8PFicosi1 8PGicosi. 272

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ConcentratedloadsincludeMirrors(F1,F2,C1,C2,IM1,IM2,IM3andIM4),Filterstructures(Box,wheelsandFilters)andmirrorbrackets.PositionoftheircenterofgravityandtheirvolumeisobtainedfromCADdesign F117.535613140-15.64092.2976286.226572F2-89.995482190.000001016286.35032.789537.559625C1703.0348439-0.013157454283.3724.83671713.1075C2140.9170908-0.0184073893.410910.4367131.183491IM11062.68148-0.132106416-211.0912.8430167.704575IM2878.95552940.037731446-12.09420.1912660.518332IM31051.71924-0.01861515211.008910.1721810.46661IM4876.0236838-0.026206704326.89843.0657128.30808FiltWheels405.14608891.09913928-66.66491.1936363.234755FiltBox477.6064936-33.46281293-116.2891.5187624.115844Detector1175.882949-42.898490782.5391520.2752130.745828Bracket164.23266732-56.26286944-52.12461.0323582.79769Bracket2-128.4971514-49.37481489324.32090.9443012.559056Bracket3679.0453993-49.53429819291.71842.2343316.055038Bracket4118.1489204-84.5258200395.343270.6110581.655966Bracket51146.165147-56.88742801-210.8630.9817542.660553Bracket6854.6161028-88.1876156-6.044310.5380641.458153Bracket71071.206688-88.43974032-1.835250.4818061.305695Bracket8886.7877801-74.98995365319.31131.8379024.980715

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Physicalvaluesoftheinstrumentstructure.ThesevalueswereobtainedfromCADdesign L1246.52mmLengthoftheBeamd914.4mmWidthofthebeamatthetopofthebenchRnout476.9663mmOuterradiusofthecaneC188.9mmThicknessofthebenchandcaneat-surfaceC23mmThicknessofthecanearcH135.89mmDistancefromcenteroftanktotopofopticalbenchHhole25.4mmDistancefromtopoftheopticalbenchtotopofhole.Holeismadetoavoidbendingofbenchduetointernalpressurethole12.7mmThicknessoftheholeofthebenchdhole825.2892mmWidthofthehole Flat-beam(noincludingmaterialofthehole) Cylindricaltank Holeofatbeam GlobalSystem

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DeectionofOpticalElementsobtainedfromanalyticalcalculationsassumingopticalbenchasacantileverbeam OpticalComponenty(m) F10.00075F2BehindbulkheadC10.812C20.045IM11.36IM21.03IM31.34IM41.09FilterWheels0.33FilterBox0.44Detector1.41 Table7-4. Collapsingpressuresofwallssubjecttovacuum RD tKWc(atm) BackVacuumJacket1428.1546.112.72.6862527.1535BackVacuumCover02410.12.901657.3920.0003FrontVacuumJacket66.0518.210.20.13102250162.75 275

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CIRCEOpticalLayoutshowingFold1(F1),Fold2(F2),Collimator1(C1),Collimator2(C2),Imager1(Im1),Imager2(IM2),Imager3(IM3),Imager4(IM4).FocalPlane,entrancewindow,half-waveplateandWeDoWoarealsorepresented EncircledenergydiagramofthelayoutofCIRCEexplainedby Edwardsetal. ( 2008 ).ThedistanceatwhichwecalculatetheenergyiscalculatedfromthecentroidofthebeamaveragedforarangeofwavelengthintheJband.Theangularxandypositionwithrespectwiththebeamcenteredintheopticalaxisislabeledforeachcurve. 276

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TheIDLThermo-MechanicalAnalysisSoftwareInterface.Thepictureshowsthetabwherethepropertiesandsizesofthestructureareintroduced(leftside)andthediagramwiththeresultingstructureandtheopticalcomponentsonthetop(rightside) DeectionoftheBenchofCIRCEusingtheAUTOCADdesign.Thediagramshowsthetotalexurefromtheonlinecalculatorhttp://www.soft4structures.com/Beam/JSPageBeam 1.jsp(pink);thepartialexureconsideringonlythebrackets(blue);thepartialexureduetoloadsotherthanbrackets(yellow);theexurecalculateanalytically(yellowtriangles). 277

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CIRCEMechanicalLayout.Thediagramshowstheopticalbenchfromtop,sideandbackside.Thebracketsandthesurfacesofthemirrorsaregrey;andthelterboxisred.Theyaresituatedonthetopoftheopticalbench.Thebulkheadisbrownandseparatethebenchinfrontandbacksides.Theshieldsandvacuumjacketofthebacksidearesketchinblack,redandgreencolors.Weshowtheinstrumentange(yellow),theshields,andtheG10inthefrontpart.The3Dviewisshownasareference.Thecomponentsaresplitinordertoshowtheorderoftheassembly. 278

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Kcoefcientvaluesforpressurecollapsingpressureunderconditionsofradialexternalpressurewithsimplysupportededges SectionofthevariousLN2tankcongurations.WeseefromtoptoBottomthetheclassicalhalf-cylinderwiththermalconductions;thehalf-cylinderwiththermalconductionsseparatedintwotanks;thecylindricaltankcongurationswithtwobeams. 279

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FocalPlaneandDeckerMasks.Thebluelineshowsthelimitofthemask.SlitsandslotsoftheFocalPlaneMaskaredrawninorange.TheredlinesintheDeckerMaskshowtheapertures.ThepositionoftheHWPisindicatedwithagreenhexagon. Flexureofthebenchforthehalf-cylinderconguration.TheexuresareplottedwithrespecttothethicknessC1oftheatbench(left)andthethicknessC2ofthecylindricalshield(right) 280

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TheplotspresenttheseparationofthefourbeamsintheWeDoWocongurationofCIRCEforasingleslotinJ-band.Thefourcolors(Green,Yellow,Pink,andBlue)arethepositionsofthebeamsfor4anglesoftheprisms(eo).Thepositionsarerelativetoeachotherforeachcolor.Theabsolutepositionisshiftedinordertoclarifytheplotbuttheaveragedpositionofthefourbeamsiscenteronthedetector.Theorangerectanglesshowresultswithaberrationlessthan2pixels.Theredrectanglesshowresultsthatdonotoverlap. 281

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Wehavereviewedthecurrentunderstandingofjetformation,inparticularjetformationinmicroquasars.WepaidspecialattentiontothecaseofSS433whoseopticaljetsareatthecoreofthepresentwork.Thetwomainscenariosforrelativisticjetformationinvolveamagneticeldinteractingwithaplasma.Intherstcase,amagneticeldfromtheaccretiondiskinteractswithaproton-electronplasmawhilethesecondscenarioinvolvesanelectron-positronplasmawhichislaunchedbyamagneticeldfromtheergosphereofthecompactobject.Untilnow,SS433hasbeenconsideredthesoleproofoftherstscenariobecausethisastronomicalobjectexhibitshydrogenemissionlinesfromitsjets.However,ourresultssupporttheexistenceofanelectron-positronplasmawhichdragstheline-producingelectron-protonplasmawhileinteractingwiththewindsoftheaccretiondisk.WederivedthisscenariousingtherstobservationalapplicationofspectropolarimetrytoSS433,whichhelpedtostudythepropertiesoftheopticaljetsofSS433aswellastheinteractionregionintheaccretiondisk. Usingspectropolarimetry,wewereabletoseparatethecontributionofthreephysicalregionstotheproleofthestationaryHline.Fromthestudyofthesethreecomponents,wederivedtheorbitalspeedtobeVorb=280km=s100km=swhichresultsinaminimumcompactobjectmassof7Msun.Inaddition,wedeterminedthepropertiesofthewindfromtheaccretiondiskconrmingpreviousresultsfortheirvelocities,whichwefoundtobeVwind=1700km=s300km=s.Furthermore,weexploredthesizeoftheseregionsandwefoundthattheheightoftheseregionsisaboutH1011cmextendinguptoH1012cm,dependingonthegeometryandthedistributionoftheparticles.Ourresultagreeswith Begelmanetal. ( 2006 ),whostudiedtheinteractionofthejetswithanaccretiondiskofsizeH=31011cm.Thisinteractionresultsin 282

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Moreover,measurementsofthepolarizationofthemovingHlinesindicatestheexistenceofepairsintheopticaljets.OurstudyoftheoriginofthepolarizationsuggestsThomsonscatteringbyepairsthatwemeasuredtobe10-100timesmorenumerousthantheprotons.Webelievethattheobservedopticaljetformsasaepairplasmajetwhichdragsanormalplasmathroughamixinglayerthatformsbetweenthetwoplasmaattheinteractionregionoftheaccretiondisk.Ourmodelpredictsthattheexchangeofprotonshappensatdistances341010cmfromtheaccretiondisk.ThestudyofthekinematicsoftheinteractionbetweentheepairjetandtheaccretiondisksuggeststhattheLorentzfactoroftheinitialjetis=1.7,whichisconsistentwiththejetspeedofothermembersofthemicroquasarfamily. Inaddition,weanalyzedtheeffectsoftheinteractionondynamicalpropertiesoftheobservedjetsinthecontextofourmodel.Wefoundthatthedeviationandspeedofthenaljetduringtheinteractiondependsonthedensityandtemperatureoftheaccretiondiskwinds,whichcanvaryduetolocalunstabilities.Fromthestudyofthevelocityshiftresiduals,weconcludedthattherearetwomechanismsproducingthedeviationsoftheDopplershiftofthemovinglinesfromtheexpectedpositionofthedynamicalmodel( Margon&Anderson 1989 ; Eikenberryetal. 2001 ).Onemechanismisrelatedtothevariationsoftheaccretiondiskpropertiesandtheotherisrelatedtothepropertiesoftheresultingjet. AbetterunderstandingofhowthesetwocomponentsareaffectedbythepropertiesoftheaccretiondiskandjetrequiresamoreextensivestudyofthedynamicsoftheopticaljetsandmorespectropolarimetryfromSS433.WeplantofollowupthecurrentstudyandtoanswerthesequestionsusingtheCanariasInfraRedCameraExperiment(CIRCE)andoursoftwareapplicationDynamicalEvolutionofSpectropolarimetryEmissionofJetObjects(DESPEJO).CIRCEisaninfraredcameraandspectrograph 283

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Inthisthesis,wedevelopedandtestedourIDLThermo-MechanicalAnalysisSoftware(ITMAS)forpreliminarydimensioningofinstruments.Weuseditforouranalysisoftheopto-mechanicalfeasibilitywhichshowsthatthequalityofthepolarimetryinCIRCEmeetsthescienticrequirementsneededtopursuethecurrentstudyoftheopticaljetsofSS433.TheCIRCEpolarimetricdesignisbasedonaWedged-DoubleWollaston(WeDoWo)whichwillallowaccuratemeasurementsofthepolarizationfromthejetsusingthelargecollectingareaoftheGranTelescopiodeCanarias(GTC).WewillanalyzethespectropolarimetryofSS433obtainedwithCIRCEusingDESPEJO,whichwecoded,optimized,andtestedduringthecurrentthesis.DESPEJOhasbeenaverypowerfultoolforthecurrentanalysisbutourplansincludefurtheranalysisofSS433usingnewspectropolarimetryobtainedrecentlybyourcollaboratorsaswellasthedataobtainedlaterwithCIRCEatGTC. Morespecically,ourfutureplansincludethestudyoftheevolutionofthepolarimetryofthestationarycomponentswithrespecttotheorbitalandprecessionalphases.Weexpecttoobtainmoreaccuratevaluesofthegeometry,sizeandcompositionoftheinteractionregionwhichwewillcomparetothepropertiesoftheopticaljets.Wealsoplantostudythetwomechanismsproducingthevelocityshiftresidualcomponentsbycomparingthepropertiesoftheaccretiondiskwinds,derivedfromemissionandpolarimetryofH2andH3,withtheepairandprotondensities,directionandspeedofthegasinthejet.Webelievethatthecorrelationofthevelocityshiftresidualstothepropertiesoftheopticaljetwillgivethemechanismofinteractionoftheepairandprotonplasmawhichmaybeatthebaseofthegasheatintheopticaljets.This,combinedwiththestudyoftheevolutionofthepolarimetryfromthejets,willrevealaclearpictureofthegeometryandstructuresofthegasintheopticaljetswhich 284

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285

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Denitionofthecoordinatesystems(seeFigure 5-8 ): 1. Coordinatesysteminthenutationframework:Cnut=(Xnut,Ynut,Znut)isrotatedby\(Znut,Zprec)=nutaroundYprecand\(Ynut,Yprec)=2nutaroundZprec; 2. Coordinatesystemintheprecessionalframework:Cprec=(Xprec,Yprec,Zprec)isrotatedby\(Zprec,Zorb)=precaroundYorband\(Yprec,Yorb)=2precaroundZorb; 3. 4. Ifweconsideraowvow,nut=vow,XnutXnut+vow,YnutYnut+vow,ZnutZnutthatisexpressedintheCnutcoordinatesystem,wewrite: intheCobswith ThecoefcientsofAnut>obscanbeobtainedfromthefollowingrelationsoftheunitvectorofeachcoordinatesysteminothercoordinatesystems. 1.

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(A) Twocommoncasesarewhentheowisperpendiculartothediskorthemotionisintheplaneoftheorbit.Wedenethephase0orboforbitatthegivenprecessionalphase0,andthephase0nutofnutationatsamegivenprecessionalphase0.Thephaseorb=[0,1]isthephasewithrespectto0orbthatisnullwhenthediskiseclipsed.Weassumethattheshiftispositivewhenthelineisblueshifted.ThevelocitytothelineofsighttoorbitalmotionisstraightlyobtainedfromtheprojectionoftheorbitalplaneinCobsas, ThevelocitytothelineofsightofaowparalleltojetrequiresmultipleprojectionsinthecoordinatesystemsCprec,Corb,andCorboftheow~vow=vow~Znut.Thesolutionisas 287

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with (A) Thesecondorderapproximationshift=a2orb+borb+coftheshiftisobtainedfromtherelationsofcosandsinfunctionsforthesumoftwoparameterssin(a+b)=sinacosb+cosasinbandcos(a+b)=cosacosbsinasinb;andthesecondorderapproximationsinX=XandcosX=1X2 Theresultis, (A) (A) (A) 288

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Thisappendixshowthespotdiagramsoftheopticaldesigninspectropolarimetryandimagingpolarimetrymodes.ThediagramsareshownfortheJ-bandandK-bandrespectively.Theyshowtheopticalqualityofvariouseldsofeachmulticongurationmodes.ThemulticongurationmodescorrespondtotheraytraceoftheextraordinaryandordinaryraysofeachprismfortwodifferentpositionsoftheHWP. Wealsoshowthefootprintdiagramthatshowstheseparationbetweentheseeightcongurations.TheseparationbetweentheextraordinaryandordinaryraysindicatesthemaximumFieldofViewofthesystemwithpolarimetriccapabilities. 289

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Spotandfootprintdiagramsinspectropolarimetrymode(JBand) 290

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Spotdiagraminimagingpolarimetrymode(KBand) 291

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Footprintdiagraminimagingpolarimetrymode(KBand) 292

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LinearStokesParametersI,Q,andUofD1set.Thespectraarephotometricallycalibrated. 293

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LinearStokesParametersI,Q,andUofD1set.Thespectraarenotphotometricallycalibrated. 294

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LinearStokesParametersI,Q,andUofD3set.Thespectraarenotphotometricallycalibrated. 295

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LinearStokesParametersI,Q,andUofD4set.Thespectraarenotphotometricallycalibrated. 296

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LinearStokesParametersI,Q,andUofD5set.Thespectraarenotphotometricallycalibrated. 297

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LinearStokesParametersI,Q,andUofD6set.Thespectraarephotometricallycalibrated. 298

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LinearPolarizationofD1set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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LinearPolarizationofD2set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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LinearPolarizationofD3set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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LinearPolarizationofD4set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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LinearPolarizationofD5set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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LinearPolarizationofD6set.FromtoptobottomspectrarepresentintensityIoftheemission,polarizationlevelPandpolarizationangle

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CADdesignoftheinstrumentsviewfromthebackside.Itincludesthebrackets,themirrors,theopticalbench,theinstrumentange,thebulkhead,theunderneathLN2tanks,thelterbox 305

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CADdesignoftheinstrumentsviewfromthefrontside.Itincludesthebrackets,themirrors,theopticalbench,thefocalplanemechanism,thebulkhead,theunderneathLN2tanks,thelterbox 306

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CADdesignofthelterbox.Itincludesthemotors,thewheels,theswitches,themotorshafts,andthestructure 307

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ThisAppendixshowstheUniedModelingLanguage(UML)diagramsexplainedinSection 4.2.3 .Aclassisrepresentedbyarectanglethatisdividedinthreesections:Thetopcontainsthenameoftheclass;themiddlecontainsthevariables;andthebottomtheapplicationsthatapplytotheobjectsofthisclass.Someoftherelationsbetweenobjectsareshowninthesediagrams.Arelationisrepresentedwithalinewithadiamondattheendthatindicatesthatoneclasscontainsobjectsoftheotherclass. DiagramofthetreewiththedifferentpackagesofDESPEJOandthelistofactorsandactions 308

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Diagramofclasseswithsomeoftherelationsbetweentheseclasses 309

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ThisAppendixshowsthemeasurementsofthetestsofthemotorsofthelterboxofCIRCE(seeSection 7.3.4 ).Thetablesincludetwocolumnswiththetemperatures(Kelvindegrees)oftheplateofthedewarwherethemotorisattachedandthemotor.Thethirdandfourthrowsaretheinitialvelocityandtheslopevelocity(stepspersecond)duringtheaccelerationanddecelerationofthemotor.Themaximumspeed(stepspersecond)isinthenextcolumn.Thesixandseventhcolumnsshowifthemotorwork(OK)oritdoesnot(NO).ThecolumnlabeledasTimeindicatesthetimeatwhichwemadethemeasurement.Thestep+andstep-indicatesthenumberofstepsthatweturnedthemotorbeforethemeasurement.+or-indicatesthedirectionoftherotation. 320

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MOTOR1 78.3484.0425100/100300OKOK18:17100078.4184.225100/100400OKOK18:18100078.4484.4125100/100500OKOK18:19100078.4684.6125100/100600OKOK18:20100078.4984.8625100/100700OKOK18:211000200078.5685.3525100/100800OKOK18:221000200078.6385.9825100/100900OKOK18:231000200078.786.4925100/1001000NONO18:241000100078.7686.9125100/100950OKNO18:252000200078.8287.3925100/100925OKOK18:262000400078.6485.6825200/200600OKOK18:391000200078.7286.2725200/200800OKOK18:402000200078.8487.3525200/200900OKOK18:412000200078.9988.6225200/2001000NONO18:422000200079.1589.8725200/200950NOOK18:432000200079.3291.2125200/200925OKOK18:452000200078.8486.662550/50600OKOK19:05150078.8486.682550/50800OKOK19:06150078.8486.682550/50900OKOK19:072000200078.8686.842550/501000NONO19:081500150078.8987.042550/50950NONO19:092000200078.9287.312550/50925OKOK19:102000200078.7585.4525150/150600OKOK19:24200078.7785.6625150/150800OKOK19:252000200078.8586.2725150/150900OKOK19:264000200078.9987.5625150/1501000NONO19:271500150079.1388.5925150/150950OKOK19:282000200079.2789.6725150/150975NONO19:292000200078.9686.2525100/100800OKOK19:472000200079.0086.5325100/100900OKOK19:482000200079.0687.0125100/1001000NONO19:491500150079.1387.6525100/100950NOOK19:502000200079.2288.2925100/100925OKOK19:512000200079.0986.4225100/100900OKOK20:032000200079.1486.6825100/1001000NONO20:041500150079.1887.1325100/100950NOOK20:056000600079.3588.3725100/100925OKOK20:064000400079.2386.5225100/100900OKOK20:192000200079.2886.7725100/1001000NONO20:201500150079.3387.2225100/100950NOOK20:216000600079.4388.0225100/100925OKOK20:2240004000 289.71289.5625100/100900OKOK11:2920002000289.83290.2325100/1001000OKOK11:3020002000290.07292.4525100/1001100OKNO11:3120002000290.28293.9325100/1001050OKNO11:3220002000290.53295.2825100/1001025OKNO11:3340004000290.77296.1525100/1001000OKOK11:3440004000

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MOTOR2 79.0383.5325100/100400OKOK16:11100079.0283.5925100/100600OKOK16:12100079.0083.6525100/100800OKOK16:131500150079.0483.9225100/100900NONO16:141500150079.0784.1825100/1001000NONO16:151500150079.1284.5525100/100850OKOK16:162000200079.2185.0925100/100875OKOK16:172000200079.2685.3825100/100900NONO16:184000400079.2384.4625200/200900NONO16:394000200079.2384.7525200/200600OKOK16:41100079.2585.0525200/200800OKOK16:422000200079.3685.7325200/200850OKOK16:432000200079.5186.4625200/200875NONO16:443000300079.5985.792550/50600OKOK17:08150079.5985.752550/50800OKOK17:092000200079.5985.742550/50900NONO17:102000200079.6085.832550/50850OKOK17:112000200079.6286.012550/50875NOOK17:135000500078.7585.4525150/150600OKOK17:32100079.5785.0225150/150800OKOK17:332000200079.5885.3325150/150900NONO17:352000200079.6685.7625150/150850OKOK17:363000300079.7586.3525150/150875NONO17:384000400079.8085.2825100/100800OKOK18:022000200079.8085.3225100/100900NONO18:032000200079.8185.525100/100850OKOK18:042000200079.9186.0125100/100875NOOK18:066000600080.1185.1125100/100800OKOK18:332000200080.1385.2325100/100900NONO18:342000200080.1585.4225100/100850OKOK18:352000200080.1885.6825100/100875NONO18:365000500080.5385.4825100/100800OKOK18:572000200080.5485.5825100/100900NONO18:582000200080.5585.7125100/100850OKOK18:592000200080.5685.9625100/100875NONO19:0050005000 293.77293.1425100/100800OKOK15:1620002000293.79293.3125100/100900OKOK15:1720002000293.91294.3625100/1001000OKNO15:1820002000294.12295.9325100/100950OKNO15:1930003000294.35297.3925100/100925OKOK15:2030003000294.51298.2325100/100950OKOK15:2150005000294.69299.0425100/100975NONO15:2250005000

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MOTOR3(day1) 79.5285.6525100/100300OKOK15:5079.6184.9525100/100400OKOK15:5179.6385.0525100/100500OKOK15:5379.6985.3125100/100600NONO15:5579.8186.9525100/100550OKOK15:5779.9887.5525100/100575NONO16:0079.8985.8425200/200300OKOK16:2580.0186.2625200/200400OKOK16:2779.8986.3525200/200500NOOK16:2979.9386.2225200/200550NONO16:3179.9986.6725200/200450OKOK16:3280.2187.6825200/200475NONO16:3380.3887.262550/50300OKOK16:5580.4187.652550/50400OKOK16:5680.3987.572550/50500NOOK16:5780.4187.512550/50550NONO16:5880.4287.652550/50475OKOK16:5980.4686.8025150/150300OKOK17:1580.4786.9225150/150400OKOK17:1680.4586.7925150/150500OKNO17:1780.4786.8225150/150450OKOK17:1880.5287.0625150/150475OKOK17:1980.5987.5525150/150550NONO17:2181.2087.7525100/100300OKOK17:4681.2387.8625100/100400OKOK17:4781.2787.9525100/100500NONO17:4881.3788.2725100/100450OKOK17:5081.4688.5425100/100475OKOK17:5181.5788.8825100/100500OKOK17:5381.6689.1825100/100550NONO17:5481.7589.4925100/100525OKOK17:5581.9290.02500OKOK17:5782.0690.53550OKOK17:5882.1890.89575OKOK17:5982.2991.3600NONO18:0082.7192.78650OKOK18:0382.8893.31700OKOK18:0483.0593.8800OKOK18:0583.3694.06900NONO18:0783.4995.11850NONO18:0884.5497.90700OKOK18:1285.0099.00800NONO18:1586.41100.31800OKOK18:1788.43102.66700OKOK18:1989.70104.31550OKOK18:2190.66105.91850NONO18:2291.45106.34750OKOK18:2392.44106.56800NOOK18:2494.80109.91600OKOK18:26

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MOTOR3(day2) 296.01295.8425100/100500OKOK16:5720002000296.04296.1825100/100600OKOK16:5820002000296.21297.9725100/100700OKOK16:5920002000296.36299.4925100/100800OKOK17:0020002000296.53301.1325100/100900NONO17:0120002000296.73302.3625100/100850NONO17:0220002000296.87303.1525100/100875NONO17:0320002000297.05304.0425100/100850NONO17:0430003000297.25304.9725100/100825OKOK17:0530003000297.43305.4125100/100800OKOK17:0630003000 MOTOR4(day1) 294.32293.6625100/100500OKOK11:13294.33293.7725100/100600OKOK11:14294.37294.3125100/100700OKOK11:15294.51295.3525100/100800OKOK11:16294.65296.5725100/100900OKOK11:17294.85297.9925100/1001000NONO11:18295.02298.9925100/100950OKOK11:19295.12299.1525100/100975OKOK11:20295.21299.3625100/1001000OKNO11:21295.42300.5925100/1001050NONO11:22 324

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MOTOR4(day2) 79.5186.7225100/100300OKOK16:3079.5886.9825100/100400OKOK16:3179.687.0325100/100500OKOK16:3279.6787.4225100/100600OKOK16:3379.7387.825100/100700OKOK16:3479.7988.1225100/100800OKOK16:3479.8288.1925100/100900NONO16:3579.8588.3725100/100850OKOK16:3679.9188.6925100/100875NONO16:3779.8987.3525200/200500OKOK16:4879.9587.5625200/200600OKOK16:4980.0488.3725200/200700OKOK16:5080.2289.4425200/200800OKOK16:5180.4290.7225200/200900NONO16:5280.5291.3425200/200850OKOK16:5380.6792.1125200/200875NONO16:5480.5589.342550/50500OKOK17:1080.5689.262550/50600OKOK17:1180.5789.252550/50700OKNO17:1280.6189.322550/50800OKOK17:1380.6489.482550/50900NONO17:1480.6889.582550/50850OKOK17:1580.7289.632550/50875NONO17:1680.8188.2225150/150500OKOK17:2980.8688.3625150/150600OKOK17:3080.9188.6525150/150700OKOK17:3181.0689.4125150/150800OKOK17:3281.2690.3525150/150900NONO17:3381.3890.8825150/150850OKOK17:3481.591.3725150/150875NONO17:3581.9489.6225100/100500OKOK17:5081.9989.6825100/100600OKOK17:5182.0489.8325100/100700OKOK17:5282.1290.0825100/100800OKOK17:5382.2190.3525100/100900NONO17:5482.3190.6825100/100850OKOK17:5582.4791.1425100/100875NONO17:5682.7592.0825100/100500OKOK17:5882.8692.3825100/100600OKOK17:5982.9292.4925100/100700OKOK18:0083.0192.6525100/100800OKOK18:0183.1192.9925100/100900NONO18:0283.2393.4125100/100850OKOK18:0383.3893.6125100/100875NONO18:04

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MOTOR5 79.5184.0225100/100ANYNONO109.93111.9625100/100ANYNONO132.53134.0125100/100ANYNONONOTWORKINGUNDERANYCONDITION293.00293.0025100/100400OKOKFunnynoise293.00293.0025100/100500OKOKFunnynoise293.00293.0025100/100600OKOKFunnynoise293.00293.0025100/100700OKOKFunnynoise293.00293.0025100/100800OKOKFunnynoise293.00293.0025100/100850NONOFunnynoise293.00293.0025100/100825OKNOFunnynoise

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MOTOR7 79.8584.1525100/100400OK15:37200079.8684.325100/100600OK15:38400079.9784.8225100/100800OKOK15:3940001000080.0784.525100/100900NO15:40800080.1385.0225100/100850??15:4114000600080.2484.925100/100825OKOK15:435000600080.485.8525200/200400OK15:59200080.4986.2525200/200600OKOK16:00400080.5486.5325200/200800OKOK16:015000600080.6386.1125200/200900NONO16:023000500080.8586.9525200/200850??16:04500030008187.525200/200825OKOK16:065000500080.8386.22550/50600OK16:27400080.8286.512550/50800OKOK16:285000500080.81862550/50900NONO16:295000300080.7886.052550/50850??16:315000500080.7885.912550/50825OKOK16:335000500080.7185.3725150/150600OK16:44400080.7786.0125150/150800OKOK16:455000500080.986.3525150/150900NONO16:462000200080.9486.2225150/150850??16:475000500081.0486.7525150/150825OKOK16:485000400081.1786.2325100/100800OKOK17:065000500081.2386.4525100/100900NONO17:072000200081.2486.6325100/100850??17:085000500081.2986.5525100/100825OKOK17:095000500081.0985.8925100/100800OKOK17:225000500080.9386.2025100/100900NONO17:242000200080.8986.3025100/100850??17:252000400081.0086.6025100/100825OKOK17:265000500081.3086.4825100/100800OKOK17:345000500081.4686.7025100/100900NONO17:352000500081.5086.3025100/100850??17:362000200081.6087.0025100/100825OKOK17:3750005000 293.76293.1325100/100800OKOK12:5650005000293.79293.3725100/100900OKNO12:5750005000293.92294.5725100/100850OKOK12:5850005000294.09295.8825100/100875OKNO13:0050005000 327

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MOTOR8 79.7483.4225100/100400OK19:31200079.9584.5325100/100600OK19:32400080.0985.0125100/100800OKOK19:335000500080.2485.3525100/100900NO19:34200080.1785.1125100/100850??19:355000500080.2785.5525100/100825OKOK19:365000500080.2385.0625200/200600OK19:44400080.3485.7125200/200800OKOK19:455000500080.5486.9125200/200900NO19:46500080.5386.3125200/200850??19:475000500080.787.525200/200825OKOK19:485000500080.6286.352550/50600OK19:56400080.6686.852550/50800OKOK19:575000500080.7587.152550/50900NO19:58200080.6986.652550/50850??19:595000500080.7786.882550/50825OKOK20:005000500080.7186.5125150/150600OK20:09400080.7686.7425150/150800OKOK20:105000500080.9588.0125150/150900NO20:11200080.8886.7225150/150850??20:125000500081.0788.4325150/150825OKOK20:135000500080.9687.0325100/100800OKOK20:225000500081.1388.2625100/100900NO20:23200081.0987.6525100/100850??20:245000500081.1388.1625100/100825OKOK20:255000500080.9986.5225100/100800OKOK20:345000500081.2188.2225100/100900NO20:35200081.2287.7225100/100850??20:365000500081.2988.6425100/100825OKOK20:3750005000 290.63290.0125100/100800OKOK11:3750005000290.69290.4525100/100900OKOK11:3850005000290.81291.3725100/1001000NOOK11:3950005000290.92292.2925100/100950OKOK11:4050005000291.63292.2725100/100950OKOK11:5250005000291.69292.5525100/100975NOOK11:5350005000 328

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MOTOR9 78.6882.6525100/100400OK17:00200078.7683.2225100/100600OK17:01400078.8283.6625100/100800OKOK17:025000500078.8984.1425100/100900NO17:03500078.8984.1125100/100850??17:045000500078.9684.4325100/100825OKOK17:055000500078.9384.1425200/200600OK17:10400079.0584.8225200/200800OKOK17:115000500079.1785.3125200/200900NO17:13500079.1585.2525200/200850??17:145000500079.2385.8125200/200825OKOK17:165000500079.26862550/50600OK17:23400079.3286.232550/50800OKOK17:245000500079.3686.412550/50900NO17:25500079.3586.152550/50850??17:265000500079.3786.352550/50825OKOK17:275000500079.3185.8525150/150600OK17:36400079.4186.2525150/150800OKOK17:375000500079.5186.6925150/150900NO17:38200079.4886.6825150/150850??17:395000500079.5987.1525150/150825OKOK17:405000500079.4886.2725100/100800OKOK17:545000500079.5686.6225100/100900NO17:55500079.5786.7825100/100850??17:565000500079.6687.1525100/100825OKOK17:575000500079.5786.225100/100800OKOK18:105000500079.6986.6525100/100900NO18:11200079.6986.5425100/100850??18:125000500079.7586.8725100/100825OKOK18:1350005000 294.07293.4225100/100800OKOK16:2250005000294.1293.6925100/100900OKOK16:2350005000294.2294.6325100/1001000NONO16:2450005000294.33295.5925100/100950OKNO16:2550005000294.47296.5225100/100925OK?16:2650005000 329

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ThisappendixdescribesthefourcongurationsofthefocalplanemasksthatwestudiedatthebeginningofthedesignofthepolarimetrylayoutofCIRCE.Thedrawingsshowhowtheslitsandslotsofthemasksaredistributedintheeld.TheFOVislimitedbytheexternalsquare.Theslitsandslotsarerepresentedbyrectanglesinsidethebigsquare.Thehalf-waveplate(HWP)isrepresentedwithtwoconcentriccircles.Theinnercircleshowsthelimitofthecrystalwhiletheexternalcircleisthelimitoftheholder.ThefastaxisoftheHWPisdrawnwithadashedlineandlabeledwiththenameMainAxis.Thedrawingsofthecongurationstwo,three,andfourincludetwocongurationsofthemaskthatrotateswiththeHWPthathidetheslotswhendoingspectropolarimetry.Thecoveroftheslotsaredrawnusingtwocolors(greenandpink)inordertoclarifythedrawings.WeshowalsotheanalysisoftheopticalqualityinJ,H,andKbandsofthecongurationone,andinJ-bandofthecongurationtwo.TherstdiagramshowthepositionoftheraysasdenedinthemulticongurationmodeoftheopticalsysteminZEMAX. WedgedDouble-Wollaston(WeDoWo)prismwiththelabelsusedinZEMAXrepresentingthecongurationofeachray 330

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CongurationMask1:Patternofthefocalplanemask 331

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SpotdiagramoftheimagesinJ-bandofthecongurationmask1.EachmulticongurationmodeofZEMAXisrepresentedwithaspeciccolor.Thesquaresofthediagramshowa2pixelsquare. 332

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SpotdiagramoftheimagesinH-bandofthecongurationmask1.EachmulticongurationmodeofZEMAXisrepresentedwithaspeciccolor.Thesquaresofthediagramshowa2pixelsquare. 333

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SpotdiagramoftheimagesinK-bandofthecongurationmask1.EachmulticongurationmodeofZEMAXisrepresentedwithaspeciccolor.Thesquaresofthediagramshowa2pixelsquare. 334

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CongurationMask2:Patternofthefocalplanemask 335

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SpotdiagramoftheimagesinJ-bandofthecongurationmask2.EachmulticongurationmodeofZEMAXisrepresentedwithaspeciccolor.Thesquaresofthediagramshowa2pixelsquare. 336

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CongurationMask3:Patternofthefocalplanemask 337

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CongurationMask4:Patternofthefocalplanemask 338

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ThisappendixillustratesthedifferentstepsandshowstheparametersthatareusedforeachtreatmentduringtheoptimizationoftheWedgedDouble-Wollaston(WeDoWo)whichisusedforthepolarimetryofCIRCE.WeusedmulticongurationmodeinZEMAXandwechangetheparameterswithascript.WecodedamacroinExcelinordertoextractandplottheresultsfromtheZEMAXsimulations. 339

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DiagramoftheZEMAXscriptanddenitionoftheinitialparameters.Weshowthestepsofthealgorithmchangingtheparametersofthemulticongurationmodeoftheopticaldesign 340

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ZEMAXsimulationresultsofthepolarizationsystemofCIRCE.WeshowtheparametersresultingfromthesimulationwiththeopticaldesignwhichareextractedwiththeExcelmacro 341

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ExcelmacrofortheanalysisofthepolarizationsystemofCIRCE.WeillustratethedifferenttasksoftheExcelmacroandhowtheyareapplytotheprocessofextractionoftheresultsuntilthegraphicswiththedataareplotted. 342

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Abramowicz,M.A.,Igumenshchev,IgorV.andQuataert,E.,&Narayan,R.2002,ApJ,565,1101 Allen,D.A.1979,Nature,281,284 Aller,M.F.,Aller,H.D.,&Hughes,P.A.2003,ApJ,586,33 Asadullaev,S.S.&Cherepashchuk,A.M.1986,SOVIETASTR,30,57 Begelman,M.C.,Hatchett,S.P.,McKee,C.F.,Sarazin,C.L.,&Arons,J.1980,ApJ,238,722 Begelman,M.C.,King,A.R.,&Pringle,J.E.2006,MNRAS,370,399 Belloni,T.,Klein-Wolt,M.,Mndez,M.,vanderKlis,M.,&vanParadijs,J.2000,AstronomyandAstrophysics,355,271 Blandford,R.D.&Znajek,R.L.1977,MNRAS,179,433 Blundell,K.M.,Mioduszewski,A.J.,Muxlow,T.W.B.,Podsiadlowski,P.,&Rupen,M.P.2001,ApJ,562,L79 Borisov,N.V.&Fabrika,S.N.1987,SOVIETASTR,13,200 Bosch-Ramon,V.&Paredes,J.M.2004a,AstronomyandAstrophysics,425,1069 .2004b,AstronomyandAstrophysics,417,1075 Bosch-Ramon,V.,Paredes,J.M.,Romero,G.E.,&Torres,D.F.2005,ChineseJournalofAstronomyandAstrophysics,5,284 Bridle,A.H.&Perley,R.A.1984,Annualreviewofastronomyandastrophysics,22,319 Brinkmann,W.,Fink,H.H.,Massaglia,S.,Bodo,G.,&Ferrari,A.1988,AstronomyandAstrophysics,196,313 Brinkmann,W.,Kawai,N.,Matsuoka,M.,&Fink,H.H.1991,AstronomyandAstrophysics,241,112 Brocksopp,C.,Fender,R.P.,Larionov,V.,Lyuty,V.M.,Tarasov,A.E.,Pooley,G.G.,Paciesas,W.S.,&Roche,P.1999,MNRAS,309,1063 Brocksopp,C.,Groot,P.J.,&Wilms,J.2001,MNRAS,328,139 Brown,J.C.&Fletcher,L.1992,AstronomyandAstrophysics,259,L43 Brown,J.C.&McLean,I.S.1977,AstronomyandAstrophysics,57,141 Brown,JohnC.;Cassinelli,J.P.C.G.W.I.1991,AJ,378,307 343

PAGE 344

Casse,F.2008,PlasmaPhysicsandControlledFusion,50,124020 Catchpole,R.M.,Glass,I.S.,Carter,B.S.,&Roberts,G.1981,Nature,291,392 Celotti,A.&Blandford,R.D.2001,ESOASTROPHYSICSSYMPOSIA,206 Chattopadhyay,I.&Chakrabarti,S.K.2002,BulletinoftheAstronomicalSocietyofIndia,30,313 Cherepashchuk,A.M.1982,Journal,194,761 Chiueh,T.,Li,Z.-Y.,&Begelman,M.C.1991,RelativisticHadronsinCosmicCompactObjects,391,135 Clarke,D.,Stewart,B.G.,Schwarz,H.E.,&Brooks,A.1983,AstronomyandAstrophysics,126,260 Collins,G.W.&Scher,R.W.2002,MNRAS,336,1011 Corbel,S.,Fender,R.P.,Tzioumis,A.K.,Nowak,M.,McIntyre,V.,Durouchoux,P.,&Sood,R.2000,AstronomyandAstrophysics,359,251 Coyne,G.V.,Gehrels,T.,&Serkowski,K.1971,BulletinoftheAmericanAstronomicalSociety,3,390 Crampton,D.&Hutchings,J.B.1981a,VistainAstronomy,25,13 .1981b,ApJ,251,604 Davidson,K.&McCray,R.1980,ApJ,241,1082 Davis,Leverett,J.&Greenstein,J.L.1951,ApJ,114,206 deGouveiaDalPino,E.M.2005,BrazilianJournalofPhysics,35,1163 delToroIniesta,J.C.2003,IntroductiontoSpectropolarimetry(Cambridge:CambridgeUniversityPress) delToroIniesta,J.C.&LpezAriste,A.2003,AstronomyandAstrophysics,412,875 Dermer,C.D.&Bttcher,M.2006,ApJ,643,1081 D'Odorico,S.,Oosterloo,T.,Zwitter,T.,&Calvani,M.1991,Journal,353,329 Dolan,J.F.,Boyd,P.T.,Fabrika,S.,Tapia,S.,Bychkov,V.,Panferov,A.A.,Nelson,M.J.,Percival,J.W.,vanCitters,G.W.,Taylor,D.C.,&Taylor,M.J.1997,AstronomyandAstrophysics,327,648 Drake,S.A.&Ulrich,R.K.1980,ApJS,42,351 344

PAGE 345

Edwards,M.L.,Eikenberry,S.S.,Charcos-Llorens,M.,Marin-Franch,A.,Lasso,N.,Raines,S.N.,Julian,J.,Hanna,K.,Packham,C.,Rodgers,M.,&Bandyopadhyay,R.M.2008,SPIE,7014,70142L Edwards,M.L.,Eikenberry,S.S.,Marin-Franch,A.,Charcos-Llorens,M.,Rodgers,M.,Julian,J.,Raines,N.,&Packham,C.2006,SPIE,6269,62694Z Emov,I.S.,Shakhovskoi,N.M.,&Piirola,V.1984,AstronomyandAstrophysics,138,62 Eikenberry,S.S.,Cameron,P.B.,Fierce,B.W.,Kull,D.M.,Dror,D.H.,Houck,J.R.,&Margon,B.2001,Journal,561,1027 Eikenberry,S.S.,Matthews,K.,Morgan,E.H.,Remillard,R.A.,&Nelson,R.W.1998,ApJ,494,L61 Fabrika,S.N.&Borisov,N.V.1987,SovietAstronomicalLetter,13,279 Fabrika,S.N.&Bychkova,L.V.1990,AstronomyandAstrophysics,240,L5 Fabrika,S.N.,Panferov,A.A.,Bychkova,L.V.,&Rakhimov,V.Y.1997,ARI,43,95 Falcke,H.&Biermann,P.L.1996,AstronomyandAstrophysics,308,321 Falcke,H.,Krding,E.,&Markoff,S.2004,AstronomyandAstrophysics,414,895 Fender,R.2006,JetsfromX-raybinaries,CambridgeAstrophysicsSeries,No.39(Cambridge:CambridgeUniversityPress) Fender,R.&Belloni,T.2004,AnnualReviewofAstronomyandAstrophysics,42,317 Fender,R.,Belloni,T.,&Gallo,E.2005,AstrophysicsandSpaceScience,300,1 Fender,R.,Rayner,D.,Norris,R.,Sault,R.J.,&Pooley,G.2000,ApJ,530,L29 Fender,R.,Spencer,R.,Tzioumis,T.,Wu,K.,vanderKlis,M.,vanParadijs,J.,&Johnston,H.1998,ApJ,506,L121 Fender,R.P.,Belloni,T.M.,&Gallo,E.2004,MNRAS,355,1105 Fender,R.P.&Hendry,M.A.2000,MNRAS,317,1 Fender,R.P.,Hjellming,R.M.,Tilanus,R.P.J.,Pooley,G.G.,Deane,J.R.,Ogley,R.N.,&Spencer,R.E.2001,MNRAS,322,L23 Fender,R.P.&Kuulkers,E.2001,MNRAS,324,923 Fender,R.P.&Pooley,G.G.2000,MNRAS,318,L1 Filippenko,A.V.,Romani,R.W.,Sargent,W.L.W.,&Blandford,R.D.1988,AJ,96,242 345

PAGE 346

Gallo,E.,Fender,R.P.,&Pooley,G.G.2003,MNRAS,344,60 Geldzahler,B.J.,Johnston,K.J.,Spencer,J.H.,Klepczynski,W.J.,Josties,F.J.,Angerhofer,P.E.,Florkowski,D.R.,McCarthy,D.D.,Matsakis,D.N.,&Hjellming,R.M.1983,ApJ,273,L65 Ghisellini,G.,Celotti,A.,George,I.M.,&Fabian,A.C.1992,MNRAS,258,776 Gies,D.R.,Huang,W.,&McSwain,M.V.2002a,ApJ,578,L67 Gies,D.R.,McSwain,M.V.,Riddle,R.L.,Wang,Z.,Wiita,P.J.,&Wingert,D.W.2002b,ApJ,566,1069 Giles,A.B.,King,A.R.,Jameson,R.F.,Sherrington,M.R.,Hough,J.H.,Bailey,J.A.,&Cunningham,E.C.1980,Nature,286,689 Ginzburg,V.L.1979,Theoreticalphysicsandastrophysics,InternationalSeriesinNaturalPhilosophy(Oxford:Oxford:Pergamon) Gladyshev,S.V.,Goranskii,V.P.,&Cherepashchuk,A.M.1987,SOVIETASTR,31,541 Goosmann,R.W.,Gaskell,C.M.,&Shoji,M.2007,AstronomyandAstrophysics,465,129 Goranskii,V.P.,Esipov,V.F.,&Cherepashchuk,A.M.1998a,AIP,42,336 .1998b,AstronomyReports,42,209 Goranskii,V.P.,Fabrika,S.N.,Rakhimov,V.Y.,Panferov,A.A.,Belov,A.N.,&Bychkova,L.V.1997,AstronomyReport,41,656 Grandi,S.A.&Stone,R.P.S.1982,PASP,94,80 Grifn,R.F.1969,MNRAS,143,319 Grimm,H.-J.,Gilfanov,M.,&Sunyaev,R.2002,AstronomyandAstrophysics,391,923 Guessoum,N.,Jean,P.,&Prantzos,N.2006,AstronomyandAstrophysics,457,753 Heiles,C.2000,AJ,119,923 Heinz,S.,Aloy,M.A.,Fender,R.P.,&Russell,D.M.2006,ProceedingsoftheVIMicroquasarWorksho Heinz,S.&Sunyaev,R.2002,AstronomyandAstrophysics,390,751 Heinz,S.&Sunyaev,R.A.2003,MNRAS,343,L59 346

PAGE 347

Hjellming,R.M.&Han,X.1995,RadiopropertiesofX-raybinaries.(xrbi.nasa) Hjellming,R.M.&Johnston,K.J.1981,Nature,290,100 Hjellming,R.M.&Rupen,M.P.1995,Nature,375,464 Homan,D.C.,Kovalev,Y.Y.,Lister,M.L.,Ros,E.,Kellermann,K.I.,Cohen,M.H.,Vermeulen,R.C.,Zensus,J.A.,&Kadler,M.2006,ApJ,642,L115 Homan,J.,Fender,R.,Jonker,P.,Lewin,W.,Migliari,S.,&Russell,D.2008,SpitzerProposal,50767 Hough,J.H.,Chrysostomou,A.,&Bailey,J.A.1994,ExperimentalAstronomy,3,127 Jackson,J.D.1975,ClassicalElectrodynamics,2nded,NewYork(CA:JohnWiley&Sons) Johnson,W.N.,I.,Harnden,F.R.,J.,&Haymes,R.C.1972,ApJ,172,L1 Jorstad,S.G.,Marscher,A.P.,Lister,M.L.,Stirling,A.M.,Cawthorne,T.V.,Gear,W.K.,Gmez,J.L.,Stevens,J.A.,Smith,P.S.,Forster,J.R.,&Robson,E.I.2005,AJ,130,1418 Jorstad,S.G.,Marscher,A.P.,Mattox,J.R.,Wehrle,A.E.,Bloom,S.D.,&Yurchenko,A.V.2001,ApJ,134,181 Jowett,F.H.&Spencer,R.E.1995,TheXXVIIthYoungEuropeanRadioAstronomersConference Kahn,F.D.1980,AstronomyandAstrophysics,83,303 Katz,J.I.,Anderson,S.F.,Grandi,S.A.,&Margon,B.1982,ApJ,260,780 Kawai,N.,Matsuoka,M.,Pan,H.-C.,&Stewart,G.C.1989,AstronomicalSocietyofJapan,41,491 Kemp,J.C.,Henson,G.D.,Kraus,D.J.,Carroll,L.C.,Beardsley,I.S.,Takagishi,K.,Jugaku,J.,Matsuoka,M.,Leibowitz,E.M.,Mazeh,T.,&Mendelson,H.1986,ApJ,305,805 Kniffen,D.A.,Alberts,W.C.K.,Bertsch,D.L.,Dingus,B.L.,Esposito,J.A.,Fichtel,C.E.,Foster,R.S.,Hartman,R.C.,Hunter,S.D.,Kanbach,G.,Lin,Y.C.,Mattox,J.R.,Mayer-Hasselwander,H.A.,Michelson,P.F.,vonMontigny,C.,Mukherjee,R.,Nolan,P.L.,Paredes,J.M.,Ray,P.S.,Schneid,E.J.,Sreekumar,P.,Tavani,M.,&Thompson,D.J.1997,ApJ,486,126 Kodaira,K.&Lenzen,R.1983,SOVIETASTR.,126,440 Kodaira,K.,Nakada,Y.,&Backman,D.E.1985,ApJ,296,232 347

PAGE 348

Kopylov,I.M.,Bychkova,L.V.,Fabrika,S.N.andKumaigorodskaya,R.N.,&Somova,T.A.1989,SOVIETASTR.LETT,15,474 Kopylov,I.M.,Kumaigorodskaya,R.N.,Somov,N.N.,Somova,T.A.,&Fabrika,S.N.1986,SOVIETASTR.,30,408 .1987,SOVIETASTR,31,410 Kording,E.G.,Fender,R.P.,&Migliari,S.2006,MNRAS,369,1451 Kotani,T.,Kawai,N.,Matsuoka,M.,&Brinkmann,W.1996,PublicationoftheAstronomicalSocietyofJapan,41,619 Krautter,J.1980,AstronomyandAstrophysics,39,167 Landau,L.D.&Lifshitz,E.M.1959,Theoryofelasticity,PergamonPress(London:Addison-WesleyPub.Co) Levinson,A.&Blandford,R.1995,ApJ,449,86 .1996,AJ,456,L29 Liebert,J.,Angel,J.R.P.,Hege,E.K.,Martin,P.G.,&Blair,W.P.1979,Nature,279,384 Lister,M.L.&Homan,D.C.2005,AJ,130,1389 Liu,Q.Z.,vanParadijs,J.,&vandenHeuvel,E.P.J.2000a,AstronomyandAstrophysics,147,25 .2000b,AstronomyandAstrophysics,147,Acatalogueofhigh .2001a,AstronomyandAstrophysics,368,1021 .2001b,AstronomyandAstrophysics,368,1021 Lockman,F.J.,Blundell,K.M.,&Goss,W.M.2007,MNRAS,381,881 Lovelace,R.V.E.1976,Nature,262,649 Maccarone,T.J.2002,MNRAS,336,1371 Maccarone,T.J.,Gallo,E.,&Fender,R.2003,MNRAS,345,L19 Margon,B.1984,ARA&A,22,507 Margon,B.&Anderson,S.F.1989,ApJ,347,448 Margon,B.,Grandi,S.A.,Stone,R.P.S.,&Ford,H.C.1979,ApJ,233,L63 348

PAGE 349

Marscher,A.P.&Gear,W.K.1985,ApJ,298,114 Marshall,H.L.,Canizares,C.R.,&Schulz,N.S.2002,ApJ,564,941 McKinney,J.C.2006,MNRAS,368,1561 McLean&Tapia.1981,Journal,68,399 McLean,I.S.&Tapia,S.1980,Nature,287,703 Meier,D.L.,Koide,S.,&Uchida,Y.2000,Science,291,84 Merloni,A.,Heinz,S.,&diMatteo,T.2003,MNRAS,345,1057 Migliari,S.,Fender,R.,&Mndez,M.2002,Science,297,1673 Miller-Jones,J.C.A.,Fender,R.P.,&Nakar,E.2006,MNRAS,367,1432 Mirabel,I.F.1994,AstronomicalandAstrophysicalTransactions,5,147 Mirabel,I.F.&Rodrguez,L.F.1994,Nature,371,46 .1999,AnnualReviewofAstronomyandAstrophysics,37,409 Murdin,P.,Clark,D.H.,&Martin,P.G.1980,MNRAS,193,135 Oke,J.B.&Gunn,J.E.1982,PASP,94,586 Oliva,E.1997,AstronomyandAstrophysics,123,589 Osterbrock,D.E.&Ferland,G.J.1995,Astrophysicsofgaseousnebulaeandactivegalacticnuclei(CA:UniversityScienceBooks) Ozel,T.&Altan,T.2000,InternationalJournalofMachineToolsandManufacture,40 Panferov,A.A.&Fabrika,S.N.1997a,AIP,19,41 .1997b,AstronomyReport,41,506 Panferov,A.A.,Fabrika,S.N.,&Rakhimov,V.Y.1997,AIP,41,342 Paragi,Z.,Vermeulen,R.C.,Fejes,I.,Schilizzi,R.T.,Spencer,R.E.,&Stirling,A.M.1999,ApJ,348,910 Paredes,J.M.2005,ChineseJournalofAstronomyandAstrophysics,5,121 Paredes,J.M.,Mart,J.,Ribo,M.,&Massi,M.2000,Science,5475,2340 Patat,F.&Romaniello,M.2006,PASP,118,146 Pooley,G.G.&Fender,R.P.1997,MNRAS,292,925 349

PAGE 350

Pounds,K.A.,Done,C.,&Osborne,J.P.1995,MNRAS,277,L5 Pringle,J.E.1981,AnualReviewofastronomyandastrophysics,19 Proga,D.,Stone,J.M.,&Kallman,T.R.2000,ApJ,543,686 Readhead,A.C.S.1994,ApJ,426,51 Rodriguez,L.F.,Mirabel,I.F.,&Marti,J.1992,ApJ,401,L15 Romero,G.E.2005,ChineseJournalofAstronomyandAstrophysics,5,110 Romney,J.D.,Schilizzi,R.T.,Fejes,I.,&Spencer,R.E.1987,ApJ,321,822 Rybicki,G.B.&Lightman,A.P.1979,Radiativeprocessesinastrophysics(NewYork:NewYork,Wiley-Interscience) Sams,B.J.,Eckart,A.,&Sunyaev,R.1996,Nature,382,47 Seaquist,E.R.,Gilmore,W.,Nelson,G.J.,Payten,W.J.,&Slee,O.B.1980,Journal,241,L77 Shahbaz,T.,Fender,R.P.,Watson,C.A.,&O'Brien,K.2008,ApJ,672,510 Simmons,J.F.L.&Stewart,B.G.1985,AstronomyandAstrophysics,142,100 Smith,J.E.,Robinson,A.,Young,S.,Axon,D.J.,&Corbett,E.A.2005,MNRAS,359,846 Stephenson,C.B.&Sanduleak,N.1977,ApJ,33,459 Stewart,G.C.,Watson,M.G.,Matsuoka,M.,Brinkmann,W.,Jugaku,J.,Takagishi,K.,Omodaka,T.,Kemp,J.C.,Kenson,G.D.,Kraus,D.J.,Mazeh,T.,&Leibowitz,E.M.1987,MNRAS,228,293 Stewart,R.T.,Caswell,J.L.,Haynes,R.F.,&Nelson,G.J.1993,MNRAS,261,593 Stirling,A.M.,Jowett,F.H.,Spencer,R.E.,Paragi,Z.,Ogley,R.N.,&Cawthorne,T.V.2002,MNRAS,337,657 Stone,J.M.,Pringle,J.E.,&Begelman,M.C.1999,MNRAS,310,1002 Svensson,R.1982,ApJ,258,335 Tananbaum,H.,Gursky,H.,Kellogg,E.,Giacconi,R.,&Jones,C.1972,ApJ,177,L5 Teegarden,B.J.&Watanabe,K.2006,ApJ,646,965 Thompson,R.I.,Rieke,G.H.,Tokunaga,A.T.,&Lebofsky,M.J.1979,ApJ,234,L135 350

PAGE 351

Trushkin,S.A.,Bursov,N.N.,&Smirnova,Y.V.2001,Journal,45,804 Uchida,Y.&Shibata,K.1985,IAUS,107,287 Uttley,P.,McHardy,I.M.,&Vaughan,S.2005,MNRAS,359,345 vandenHeuvel,E.P.J.1981,VistasinAstronomy,25,95 vanderMarel,R.P.&Franx,M.1993,ApJ,407,525 vanParadijs,J.1995,1995xrbi.nasa..536V Vermeulen,R.C.,Icke,V.,Schilizzi,R.T.,Fejes,I.,&Spencer,R.E.1987,Nature,328,309 Vermeulen,R.C.,Schilizzi,R.T.,Spencer,R.E.,Romney,J.D.,&Fejes,I.1993,AstronomyandAstrophysics,270,177 Wagner,R.M.1986,ApJ,308,152 Watson,M.G.,Stewart,G.C.,King,A.R.,&Brinkmann,W.1986,MNRAS,222,261 Wiktorowicz,S.J.&Matthews,K.2008,PASP,120,1280 Wilking,B.A.,Lebofsky,M.J.,Kemp,J.C.,Martin,P.G.,&Rieke,G.H.1982,ApJ,235,905 351

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MiguelCharcosLlorenswasborninAlicante,SpainonMayof1977.HeattendedtheLyceeFrancaisd'Alicanteuntil1995,whenhemovedtoToulouse,France,forcollege.AtthecollegeLyceePierredeFermat,helearnedtheoreticalmathematicsandphysicsuntil1998.HepassedtheconcoursandgraduatedattheEcoleNationaleSuperieured'IngenieursenConstructionAeronautique(ENSICA)in2001.HissubsequentinternshipattheObservatoiredeMidi-Pyrenneewasthebeginningofhiscareerasaninstrumentaldesigner.HeworkedfortwoyearsattheInstitutodeAstrofsicadeCanarias(IAC)intwodifferentprojects.InAugust2004,hebeganhisgraduatestudiesinthedepartmentofAstronomyattheUniversityofFloridawithDr.StephenS.Eikenberrywherehespecializedininfraredinstrumentationandpolarization. 352