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The Dynamics of Asteroidal Dust and Structure of the Zodiacal Cloud

Permanent Link: http://ufdc.ufl.edu/UFE0041050/00001

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Title: The Dynamics of Asteroidal Dust and Structure of the Zodiacal Cloud
Physical Description: 1 online resource (186 p.)
Language: english
Creator: Espy, Ashley
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: 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: The zodiacal cloud, the debris disk of our solar system, has been studied for many years, yet we still do not know the origin of the background cloud particles. We know the cloud has asteroidal and cometary components, but in what proportions? The zodiacal dust bands, discovered by the Infrared Astronomical Satellite (IRAS; Low et al., 1984), are known to be asteroidal and thus hold the key to determining the asteroidal contribution of dust to the cloud. When an asteroid is disrupted, a wave of dust is injected into the zodiacal cloud. Through an investigation of the dynamical evolution of this dust from its source region to the resonant inner edge of the main belt, dynamical models and line-of-sight thermal emission profiles of the dust are created and compared directly with observations. The comparison of the models to the dust band observations constrains the parameters of the dust in the bands, including the cross-sectional area, and the particle-size, orbital-element, and heliocentric distributions of the dust. Using these constraints on the dust, we estimate the magnitude of the asteroidal component of the zodiacal cloud. Then, through a method of coadding the IRAS data, we reveal an additional, very young dust band. An analytical model of the dynamical evolution of the dust of this young still-forming band is created. The comparison of the thermal emission dust torus of the model dust distribution with that of the coadded observations of this young structure constrains the node and age, in addition to the inclination, and allows us, for the first time, to determine a unique source for a dust band. Because the dust in this band is so young, it has not yet been altered by collisions, thus modeling of this band allows us a first ever look at the original size-distribution and magnitude of dust produced in the catastrophic disruption of an asteroid. This knowledge of the dust produced immediately following a disruption then allows us to estimate the magnitude of dust produced in the original disruptions that created the other dust bands. Understanding how much dust is produced in a disruption further allows us to constrain how the magnitude of the zodiacal cloud may vary with time. Finally, we investigate how the dust produced in the asteroidal disruptions is perturbed by Mars as it migrates into the inner solar system. We find a potential bias in the size and orbital-element distributions of the dust that evolve into near-Earth space unperturbed which may explain the compositional diversity of the IDPs (Interplanetary Dust Particles) collected at the Earth.
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 Ashley Espy.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Dermott, Stanley F.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-10-31

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041050:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041050/00001

Material Information

Title: The Dynamics of Asteroidal Dust and Structure of the Zodiacal Cloud
Physical Description: 1 online resource (186 p.)
Language: english
Creator: Espy, Ashley
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: 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: The zodiacal cloud, the debris disk of our solar system, has been studied for many years, yet we still do not know the origin of the background cloud particles. We know the cloud has asteroidal and cometary components, but in what proportions? The zodiacal dust bands, discovered by the Infrared Astronomical Satellite (IRAS; Low et al., 1984), are known to be asteroidal and thus hold the key to determining the asteroidal contribution of dust to the cloud. When an asteroid is disrupted, a wave of dust is injected into the zodiacal cloud. Through an investigation of the dynamical evolution of this dust from its source region to the resonant inner edge of the main belt, dynamical models and line-of-sight thermal emission profiles of the dust are created and compared directly with observations. The comparison of the models to the dust band observations constrains the parameters of the dust in the bands, including the cross-sectional area, and the particle-size, orbital-element, and heliocentric distributions of the dust. Using these constraints on the dust, we estimate the magnitude of the asteroidal component of the zodiacal cloud. Then, through a method of coadding the IRAS data, we reveal an additional, very young dust band. An analytical model of the dynamical evolution of the dust of this young still-forming band is created. The comparison of the thermal emission dust torus of the model dust distribution with that of the coadded observations of this young structure constrains the node and age, in addition to the inclination, and allows us, for the first time, to determine a unique source for a dust band. Because the dust in this band is so young, it has not yet been altered by collisions, thus modeling of this band allows us a first ever look at the original size-distribution and magnitude of dust produced in the catastrophic disruption of an asteroid. This knowledge of the dust produced immediately following a disruption then allows us to estimate the magnitude of dust produced in the original disruptions that created the other dust bands. Understanding how much dust is produced in a disruption further allows us to constrain how the magnitude of the zodiacal cloud may vary with time. Finally, we investigate how the dust produced in the asteroidal disruptions is perturbed by Mars as it migrates into the inner solar system. We find a potential bias in the size and orbital-element distributions of the dust that evolve into near-Earth space unperturbed which may explain the compositional diversity of the IDPs (Interplanetary Dust Particles) collected at the Earth.
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 Ashley Espy.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Dermott, Stanley F.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-10-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041050:00001


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THEDYNAMICSOFASTEROIDALDUSTANDSTRUCTUREOFTHEZODIACAL CLOUD By ASHLEYJEANNEESPY ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2010 1

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c 2010AshleyJeanneEspy 2

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Tomyparentsforalloftheirloveandsupportinhelpingmeach ievemydreams 3

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ACKNOWLEDGMENTS FirstandforemostIwouldliketothankDr.ThomasKehoeforall hishelpand guidance(ontheclockando)andforbeingawonderfulteamm ateinscienceandinlife. Iwouldliketothankformyadviser,Dr.StanleyDermott,oneo ftheworld's greatestdynamicists,forinspiration,helpingmetoseethebigp icture,andforwritingthe textbookthatmakesthissubjectunderstandable. Iwouldliketoacknowledgemycommittee:Dr.JamesChannell ,Dr.EricFord,Dr. BoGustafson,andDr.CharlesTelescoforthoroughlyreviewing thisworkandasking insightful,thought-provokingquestions. Icouldn'thavecompletedthisworkwithoutthecontributio nofallofthemembers oftheDermott/UFsolarsystemdynamicsgroupthathavepreceded mehereandarenow leadersintheeld(Dan,Renu,Keith,Sumita,Steve,J.C.,Ma rk,Beth),IhopeIcan carryonthetradition! Iwouldliketoacknowledgeallmyfellowgradstudentsandpost docs,thosewho camebeforeandafterandmadethisjourneyallthebetter;Mi chelle(forabsolutely everything),Dave(forcomingtomyrescueintheU-haulincide nt),Margaret(forUT relief),Paola(forthejeep/remanincident),Dimitri(for llingthe3rdoorwithcookies anddynamics),andDan(forhis\contributions"totheoce)just tonameafew. Thanksgoouttomyrunningteam(Lane1)andcoachDaveforall thesteam-venting andmilesoftrialsandtrialsofmiles.Tomymanytrainingpar tnersthroughoutthis adventure;JoeandMary(formakingmyIRONMANdreamcometrue) ,Sheryl(for perfectpace),myRoad-Thrillteam,SanFelasco,andallthef olkswhohavepoundedout themilesalongsideme. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................4 LISTOFTABLES .....................................7 LISTOFFIGURES ....................................8 ABSTRACT ........................................11 CHAPTER 1INTRODUCTION ..................................13 1.1Summary ....................................13 1.2WhatisKnownAbouttheZodiacalCloud? .................14 1.3InfraredObservationsoftheZodiacalCloud .................15 1.4GlobalStructureoftheZodiacalCloud ....................17 1.5TheZodiacalDustBands ...........................18 1.6EarlyModelingoftheZodiacalDustBands .................20 1.7ContributionsofthisWork ...........................23 1.8LayoutofChapters ...............................25 2THEZODIACALDUSTBANDS ..........................37 2.1Introduction ...................................37 2.2WhatisKnownAbouttheZodiacalDustBands ...............38 2.3DustBandModeling ..............................43 2.3.1Forces ..................................43 2.3.1.1Radiationpressure ......................44 2.3.1.2Poynting-Robertsondrag ...................45 2.3.1.3Solarwind ...........................46 2.3.2DynamicalEvolution ..........................47 2.3.3CreationofModels ...........................50 2.4Models ......................................51 2.4.1Parameters ................................51 2.4.1.1Size-frequencydistribution ..................52 2.4.1.2Heliocentricdistribution ...................52 2.4.1.3Cross-sectionalarea ......................54 2.4.2ComparisontoIRASdata .......................54 2.5Discussion ...................................58 2.5.1Results ..................................58 2.5.2TheAsteroidalContributiontoCloud .................62 2.5.3FutureWork ...............................64 5

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3AVERYYOUNG,STILLFORMINGDUSTBAND ...............86 3.1Introduction ...................................86 3.2CoaddingtheIRASData ............................88 3.2.1Solarelongationvariations .......................88 3.2.2Longitudevariations ..........................89 3.3ANewDustBandat17 ............................90 3.3.1ANewBandAppears ..........................90 3.3.2EvidenceforaPartialBand ......................92 3.3.3PossibleSources .............................96 3.4TheRoleofCollisionsinDustBandFormation ...............97 3.5DynamicalModel ................................101 3.5.1CreationoftheModel ..........................101 3.5.2DynamicalEvolution ..........................102 3.5.3SingleParticleSizeModel .......................104 3.5.4FullModel ................................106 3.6Discussion ....................................108 3.6.1ComparisonofModelsWithObservations ...............108 3.6.2LargerParticleSizeModels .......................110 3.6.3Anupdatedage .............................112 3.6.4Cross-sectionalareacontribution ....................113 3.6.5ErrorAnalysis ..............................115 3.7TheImportanceofPartialDustBands ....................117 3.8TheFuturewithWISE .............................120 4INTERACTIONSWITHMARS ..........................150 4.1Introduction ...................................150 4.2Method .....................................152 4.3Results ......................................154 4.3.1Inclination ................................154 4.3.2Size ....................................155 4.3.3Eccentricity ...............................156 4.3.4NumericalSimulations .........................156 4.3.5QuantifyingthePerturbation ......................157 4.4SummaryandFutureWork ..........................158 5CONCLUSION ....................................172 5.1SummaryofResults ..............................172 5.2ContributionstotheField ...........................175 5.3ImportanceofThisWork ............................176 5.4FutureDirections ................................178 REFERENCES .......................................180 BIOGRAPHICALSKETCH ................................186 6

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LISTOFTABLES Table page 2-1Propertiesofselectedasteroidfamilies .......................67 2-2Observationalfeatures ................................70 3-1Emilkowalskiclusterdata ..............................134 7

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LISTOFFIGURES Figure page 1-1TheorbitofIRAS ..................................27 1-2Inclinationoftheglobalcloud ............................28 1-3Warpoftheglobalcloud ...............................29 1-4Osetoftheglobalcloud. ..............................30 1-5Schematicofosetoftheglobalcloud. .......................31 1-6IRASintensityprole ................................32 1-7Asteroidfamilies ...................................33 1-8Temporalvariationofamodelzodiacalcloud ...................34 1-9Eectofinclinationdispersionondustbandstructure ..............35 1-10Possiblesourcesofthe\10degree"band ......................36 2-1Datingthefamilies ..................................66 2-2Theformationofadustband ............................68 2-3Inclinationofthedustbandmidplane ........................69 2-4Schematicofinclinationofthedustbandmidplane ................70 2-5Forcedandproperelements. .............................71 2-6Particle-on-a-circle. ..................................72 2-7Properandforcedinclination. ............................73 2-8Semimajoraxisvariationofthedustbandsstructurefor20 micronparticles. ..74 2-9Semimajoraxisvariationofthedustbandsstructurefor10 0micronparticles. .75 2-10Semimajoraxisvariationofthedustbandsstructurefor5 00micronparticles. .76 2-11Sizedistribution-q. ..................................77 2-12Heliocentricdistribution .............................78 2-13Modelwithasizedistributionq=1.83for =25 m. ................79 2-14Modelwithasizedistributionq=1.6for =25 m. ................80 2-15Modelwithasizedistributionq=1.5for =25 m. ................81 8

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2-16Modelwithasizedistributionq=1.4for =25 m. ................82 2-17Modelwithasizedistributionq=1.4for =12,60 m. ..............83 2-18Modelforaheliocentricdistributionof =2at =25 m. ............84 2-19Asteroidalcontributiontothezodiacalcloud. ...................85 3-1Schematicofsolarelongationobservinggeometry .................123 3-2Solar-elongation-induceddustbandseparationvariatio n .............124 3-3Linearvariationofthelatitudeofthebandswithelonga tionangle ........125 3-4Schematicofaninclineddusttorus .........................126 3-5Inclination-inducedlatitudeshiftofdustbandmidplane .............127 3-6ThenewdustbandasseeninthecoaddedIRASdata ...............128 3-7Coaddedleadinglunes ................................129 3-8Coaddedtrailinglunes ................................130 3-9Thetimestepsofformationofthe17 dustband ..................131 3-10Longitudinalvariationofthepartialband .....................132 3-11Longitudinalvariationcomparisonwiththe10 band ...............133 3-12Collisiontimescales ..................................135 3-13Singleparticlesizemodel ...............................136 3-14Heliocentricdistributionofparticlesizesresultingfro mEmilkowalski ......137 3-15Main-beltnodalprecessionrates ...........................138 3-16Fullmodelthermalemissiontorus ..........................139 3-17Nodaldispersionofparticlesizes ..........................140 3-18Nodalphasemismatchwith 1mmdiameterparticles ..............141 3-19Nodallocationofparticlesrelativetosource ....................142 3-20Incrementalareadistributionintoparticlesizes ..................143 3-21Thermalemissionuxasafunctionofparticlesizeanddistan ce .........144 3-22Longitudinalvariationofthelarge-particle,q=1.7m odel .............145 3-23Longitudinalvariationofthelarge-particle,q=1.8m odel .............146 9

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3-24Longitudinalvariationofthelarge-particle,q=1.8m odelatanageof236kyrs .147 3-25P-Rdragdecayofareawithtime ..........................148 3-26Variationofdustbandswithwavelength ......................149 4-1Schematicofpenetrationdepths ...........................160 4-2LikelihoodofpassagethroughtheHillsphereasafunctionof inclination ....161 4-3Likelihoodofpassagewithin50%oftheHillsphereasafuncti onofinclination .162 4-4Likelihoodofpassagewithin10%oftheHillsphereasafuncti onofinclination .163 4-5LikelihoodofpassagethroughtheHillsphereasafunctionof size ........164 4-6Likelihoodofpassagewithin50%oftheHillsphereasafuncti onofsize .....165 4-7Likelihoodofpassagewithin10%oftheHillsphereasafuncti onofsize .....166 4-8LikelihoodofpassagethroughtheHillsphereasafunctionof eccentricity ....167 4-9Likelihoodofpassagewithin50%oftheHillsphereasafuncti onofeccentricity 168 4-10Likelihoodofpassagewithin10%oftheHillsphereasafunct ionofeccentricity 169 4-11Survivalfractionversusinclinationascomparedwithn umericalsimulations ...170 4-12Survivalfractionversussizeascomparedwithnumerical simulations ......171 10

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy THEDYNAMICSOFASTEROIDALDUSTANDSTRUCTUREOFTHEZODIACAL CLOUD By AshleyJeanneEspy May2010 Chair:StanleyF.DermottMajor:Astronomy Thezodiacalcloud,thedebrisdiskofoursolarsystem,hasbeenst udiedformany years,yetwestilldonotknowtheoriginofthebackgroundclou dparticles.Weknow thecloudhasasteroidalandcometarycomponents,butinwhatp roportions?The zodiacaldustbands,discoveredbytheInfraredAstronomicalSat ellite(IRAS;Lowetal., 1984),areknowntobeasteroidalandthusholdthekeytodeter miningtheasteroidal contributionofdusttothecloud.Whenanasteroidisdisrupted ,awaveofdustis injectedintothezodiacalcloud.Throughaninvestigationo fthedynamicalevolutionof thisdustfromitssourceregiontotheresonantinneredgeofthe mainbelt,dynamical modelsandline-of-sightthermalemissionprolesofthedustare createdandcompared directlywithobservations.Thecomparisonofthemodelstothe dustbandobservations constrainstheparametersofthedustinthebands,includingth ecross-sectionalarea, andtheparticle-size,orbital-element,andheliocentricd istributionsofthedust.Using theseconstraintsonthedust,weestimatethemagnitudeoftheast eroidalcomponent ofthezodiacalcloud.Then,throughamethodofcoaddingthe IRASdata,wereveal anadditional,veryyoungdustband.Ananalyticalmodelofthe dynamicalevolution ofthedustofthisyoungstill-formingbandiscreated.Thecom parisonofthethermal emissiondusttorusofthemodeldustdistributionwiththatofthe coaddedobservations ofthisyoungstructureconstrainsthenodeandage,inadditio ntotheinclination,and allowsus,forthersttime,todetermineauniquesourceforadust band.Becausethe 11

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dustinthisbandissoyoung,ithasnotyetbeenalteredbycolli sions,thusmodeling ofthisbandallowsusarsteverlookattheoriginalsize-distri butionandmagnitude ofdustproducedinthecatastrophicdisruptionofanasteroid.T hisknowledgeof thedustproducedimmediatelyfollowingadisruptionthenall owsustoestimatethe magnitudeofdustproducedintheoriginaldisruptionsthatcr eatedtheotherdustbands. Understandinghowmuchdustisproducedinadisruptionfurthera llowsustoconstrain howthemagnitudeofthezodiacalcloudmayvarywithtime.Fi nally,weinvestigate howthedustproducedintheasteroidaldisruptionsisperturbe dbyMarsasitmigrates intotheinnersolarsystem.Wendapotentialbiasinthesizeando rbital-element distributionsofthedustthatevolveintonear-Earthspaceunp erturbedwhichmayexplain thecompositionaldiversityoftheIDPs(InterplanetaryDustP articles)collectedatthe Earth. 12

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CHAPTER1 INTRODUCTION 1.1Summary Thedebrisdiskofthesolarsystem,thezodiacalcloud,isatenuo usdiskofdust particlesorbitingtheinnersolarsystem.Thecloudanditscon stituentdustparticles havebeenstudiedforcenturiesand,whilemuchhasbeenlearn ed,thereremainseveral important,unansweredquestionsthatarethesubjectofongoin gdebate.Themain questionscurrentlyattheforefrontofthestudyofthezodiac alcloudandtheinterplanetary dustcomplexare:`Whatarethedominantsourcesofthedustandi nwhatrelative proportionsdothesesourcescontribute?',`Howdoesthezodia calcloudbrightnessvary withtime?',and`WhatarethesourcesoftheIDP's(Interplan etaryDustParticles) collectedattheEarth?'. Inthisthesiswewillcontributetothediscussionbyexaminingt heasteroidal componentofthezodiacalcloudandhowasteroidscontribute dusttothecloud.Through ourexaminationofthistopicweaimtoanswerseveralquestions thataredirectlyrelevant tothemaintopicsanddebatesthatcurrentlydenetheeld.How muchdustisreleased inthedisruptionofanasteroid?Whatpercentageofthecloudi sduetoasteroidal sources?Aretheknownasteroidaldustbandsduetocollisionalero sionofoldasteroids orrecentcatastrophicdisruptions?Howdoesthedustevolveasit reachestheinnersolar system?AretheIDP'scollectedattheEarthpartofthesamepopul ationofdustaswe seeinthedustbands? Ourstudyoftheasteroidalcomponentofthecloudwillfocuson theknownasteroidal featuresofthecloud|thezodiacaldustbands.Adustbandisane structurefeature ofthecloudcomposedofdustfromthecatastrophicdisruptionof anasteroid.Webegin bymodelingtheknowndustbandsandusethesemodelstodetermin ethemagnitudeof theasteroidalcontributiontothecloud.Then,throughamet hodofcoaddingthedatato increasethesignal-to-noise,werevealafaint,newdustbandwh ichturnsouttobevery 13

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young.Thisyoungdustbandallowsus,forthersttime,todeterm ineauniquesolution forthesourceofadustband.Thesubsequentstudyofthisyoungban dalsoallowsusa never-before-seenlookatthedustoriginallyproducedinthe catastrophicdisruptionofan asteroid|beforethedustisalteredbytime.Thisuniquelooka ttheunalteredproducts ofadisruptionallowsustoestimatetheamountofdustproduced inadisruptionand, therefore,tobetterunderstandhowasteroidscontributedust tothecloud.Usingthis constraintonthedustproducedinadisruption,wecanthenbett erdeterminehowmuch dustmayhaveinitiallybeeninjectedintothecloudfollowin gthedisruptionsthatcreated thethreepreviouslyknown,olderbands.This,then,allowsust oputsomeconstraints onthetemporalvariationofthecloud.Finally,inordertod etermineiftheasteroid disruptionsthatproducethebandsarealsothesourceoftheIDP 'scollectedattheEarth, welookathowtheorbitsofthedustparticlescreatedinthesed isruptionsareperturbed byMarsastheyevolveintotheinnersolarsystem. 1.2WhatisKnownAbouttheZodiacalCloud? Thezodiacallight,sunlightscatteredfromthezodiacalclou ddustparticles,gavethe rstindicationofthepresenceofthedust.Thephenomenonwasrst investigatedbythe astronomerGiovanniDomenicoCassiniin1683andrstexplaineda ssunlightscattering odustparticlesbyNicolasFatiodeDuillierin1684(e.g.Dom son,1972).Despitethese earlyadvances,forcenturiesfollowing,thenatureofthedu stthatmakesupthezodiacal cloudremainedpoorlyunderstood.Evenuntiltheearly1980s, thecloudwasthoughtto beasmoothlenticulardistributionofcometarydebris,center edontheSun,andlyingin theplaneoftheecliptic(e.g.Gieseetal.,1986).Thelaunch oftheInfraredAstronomical Satellite(IRAS;Lowetal.,1984)gaveusourrstcomprehensive lookatthecloudin infraredwavelengthsandrevolutionizedourunderstanding ofthecloud. FollowingIRAS,therehavesincebeenmanyotherobservationsm adeofthezodiacal cloud.Inadditiontootherinfraredobservationsofthether malemissionofthecloud (Section 1.3 ),theparticlesarealsodetectedthroughopticalscattering ,radarechoes, 14

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meteorsintheEarth'satmosphereandinsitudetectorsinspace (ofwhichtheLong DurationExposureFacilityLDEF(LoveandBrownleee,1993)g aveusourrstlookat thesizedistributionanddominantparticlesize).TheInterpl anetaryDustParticles(IDPs) thatmakeupthecloudareevencollectedattheEarth|frommi crometeoritesonthe surfacetoextractionfromtheseaoorsedimentsandupperatmosp here.Theanalysisof thesecollectedparticlesgivesusinformationontheirchem icalcompositions.Through thiswealthofdataonthecloud,wenowknowthatthezodiacal cloudiscomposedof dustfromasteroidsandcomets,withasmallercontributionfrom Kuiperbeltobjects, crateringevents,andeveninterstellardustsweepingthrought hesolarsystem.Weknow asteroidsandcometsarethedominantcontributors,butthere lativeproportionsofthese twosourcesisstillthesubjectofmuchdebate.Weknowthatthez odiacalcloudhasan opticaldepthnormaltotheeclipticof O (10 ¡ 7 )(Backmanetal.,1997)andthatthetotal cross-sectionalareaofmaterialinthecloudis O (10 10 )km 2 (Dermottetal.,2001)andits totalmassis O (10 19 )grams(whichcorrespondstoasphereofabout20kmindiameter assumingasteroid-typedensitiesof2{3g/cm 3 (Hiltonetal.,2002)). 1.3InfraredObservationsoftheZodiacalCloud AnextensivereviewofallinfraredskysurveysisgivenbyPrice( 2009),butherewe focusonjustafew.Therehavebeenseveralinfraredsatellites ownsinceIRASthathave alsoprovidedextensivedataonthezodiacalcloud.TheCosmicM icrowaveBackground Explorer's(COBE)DiuseInfraredBackgroundExperiment(DI RBE;Boggessetal., 1992)providedscansatawiderangeofsolarelongationangles (theanglebetweenthe Sun-Earthlineandtheviewingdirectionoftheobservation) from60{124 .COBE dataalsoprovidedalargerangeofwavebandcoverage(1.25{2 40 m),atanincreased sensitivity,butatareducedresolutionascomparedtoIRAS.The MidcourseSpace eXperiment(MSX;Priceetal.,2006),whichwasaBallisticMissil eDefenseOrganization project,providedaviewofthecloudatveryhighsolarelonga tionangles(160{330 ) andlledinsomeofthegapsintheskycoverageoftheIRASdata.Th eInfraredSpace 15

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Observatory(e.g.Reach,1996)andthemostrecent,theSpitze rSpaceTelescope(e.g. Meadowsetal.,2004,forzodiacalclouddata)bothprovided increasedsensitivity,but onlyoversmallregionsofthesky.Althoughalltheseinstruments haveprovidedvaluable informationonthecloudanddetailedviewsofthedustbands( COBE|Reachetal., 1997;MSX|e.g.GroganandPrice,2003;Spitzer|Nesvornyeta l.,2008),thebest datasetforourpurposes,basedonitsresolution,skycoverageand observingstrategy,is stilltherst|IRAS. TheviewinggeometryofIRASwasidealforthestudyofthezodia calcloud.The spacecraftwasonapolarorbit,asshowninFigure 1-1 .Asaresultofthisorbit,IRAS tookpole-to-poleintensityscansinboththeleadingandtrai lingdirectionsoftheEarth's motioninitsorbitaroundtheSun.ThefulldetailsoftheIRAS orbitanditsdata acquisitionschemearediscussedinSection 2.4.2 ,butitissucientheretounderstand thattheobservingpatternfacilitatedtheprocessofcoaddin gthedata(whichwillbe discussedinSection 3.2 ).IRAStookdatainfourwavebands:12,25,60,and100 m.The 100 mdatasetwascontaminatedbyGalacticnoise,andtherewassome contamination fromGalacticnoiseinallthewavebandsintheregionswheret heGalacticplaneisclose totheecliptic.TheMediumResolutionZodiacalObservationHi storyFile(ZOHF),the datasetusedforthisproject,hasanin-scanresolutionof2arcm inandasensitivityof order0.5Jyinthe12,25,and60 mwavebands(Beichman,1987).Thisdatasetconsists ofhundredsofpole-to-poleintensityscans,coveringalmost30 0 ofeclipticlongitudewith viewingdirectionsinboththeleadingandtrailingdirecti onsoftheEarth'smotion.This comprehensivedataset,alongwiththatobtainedfromCOBE,yi eldedadetailedviewof thecloudwhichrevealedseveralglobalfeatures|atiltwith respecttotheecliptic,a warp,andanosetfromtheSun.Thesefeaturesallhavedynamica lexplanationsandare discussedinthenextsection. 16

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1.4GlobalStructureoftheZodiacalCloud Tilt .Oneofthemainasymmetriesoftheglobalcloudisaninclinat ionofthe planeofsymmetryofthecloudwithrespecttotheeclipticplan e(Dermottetal.,1996). Figure 1-2 showsthevariationofthelatitudeofpeakuxofthezodiacalc loudwith eclipticlongitudeoftheEarthasobservedbyCOBEinthe25 mwaveband.Theopen circlesrepresentdatatakenintheleadingdirectionoftheE arth'sorbitat90 solar elongationangle,andthesolidcirclesarefordatatakenint hetrailingdirectionat90 solarelongationangle.Iftheplaneofthesymmetryoftheclou dwastheecliptic,we wouldexpectnovariationofthelatitudeofpeakuxastheEar thmovesarounditsorbit. Thesinusoidalvariationofthislatitudeofpeakuxindicates theinclinationoftheplane ofsymmetryofthecloudwithrespecttotheecliptic.Theeclip ticlongitudesatwhich thelatitudesofpeakuxareequalandopposite,fortheleadin gandtrailingdata,lie alongtheintersectionofthetwoplanesandcorrespondtothel ongitudesoftheascending anddescendingnodesoftheplaneofsymmetryofthezodiacalcl oudwithrespecttothe ecliptic.Thelatitudeofthepeakuxatthenodesgivesthein clinationoftheplaneof symmetrywithrespecttotheecliptic.Theinclinationisfoun dtobe1.49 § 0.07 andthe longitudeoftheascendingnodeis58.4 § 2.3 (Dermottetal.,1996). Warp .Theinclinationandnodeofthecloudwithrespecttotheecli pticvarywith distancefromtheSun,creatingawarptothecloud(Dermottet al.,1999).Figure 1-3 showstheCOBEobservationsofthevariationofthepolarbrigh tnessfortheNorth(open circles)andSouth(lledcircles)poles.TheNorthandSouthpola rbrightnessesareequal atthenodesoftheplaneofsymmetryofthecloudwithrespectto theecliptic.The longitudeoftheascendingnodeisfoundtobe70.7 § 0.4 (Dermottetal.,1999).These measurementsofthepolarbrightness,whichareshowninFigure 1-3 ,samplethecloudat theEarth'sorbit(1AU),butthemeasurementsshowninFigure 1-2 areforobservations madefrom1AUlookingradiallyoutwardfromtheSunandthussa mplingthecloudat > 1AU.Sincethesetwoobservationsnddierentnodesoftheplaneo fsymmetryofthe 17

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cloudwithrespecttotheecliptic,thentheorientationofth eplaneofsymmetrywith respecttotheeclipticischangingwithheliocentricdistanc e.Thismeansthattheplaneof symmetryofthecloudisnotonlytiltedwithrespecttotheecli ptic,butisalsowarped. Oset .ThecenterofsymmetryofthecloudisosetfromtheSun(Dermot tet al.,1999).Figure 1-4 showsCOBEobservationsoftheaveragedNorthandSouthpole brightnesses.AveragingtheNorthandSouthpoledataremovesany variationsthat wouldbeexpectedtocomefromtheinclinationoftheplaneof symmetryofthecloud withrespecttotheecliptic.Ifthecloudwererotationallysy mmetricwiththeSunatthe center,itisreasonabletoexpectthattheminimumoftheaver agedpolarbrightnesses wouldbeatanextremeoftheEarth'sorbit,eitherapheliono rperihelion(dependingon howthematerialisdistributedheliocentrically).However, asisshowninFigure 1-4 ,the minimumintensityisosetfromtheaphelionlocation,whichis expectedonlyiftheSun isnotatthecenterofsymmetryofthecloud.Theosethasbeensug gested(Dermottet al.,1999)tobeduetoseculargravitationalperturbations,w hichcausethedistribution ofzodiacalcloudparticlestobebiasedtowardsthesamedirec tion,asisrepresented schematicallyinFigure 1-5 1.5TheZodiacalDustBands Inadditiontotheglobalstructuralfeaturesoftheclouddesc ribedpreviously, therearealsone-structurecomponentsofthecloud|comettra ilsandasteroidaldust bands.Thesene-structurefeaturesareanindicationthatboth asteroidsandcometsare contributingdusttothecloud,buttherelativeproportions ofthecontributionsremains anoutstandingquestion.Comettrailsaretrailsofdustknownt obedistributedalong theorbitsofshort-periodcomets(e.g.SykesandWalker,199 2).Thesestructuresare interestingandoeradynamicsapplicationalltheirown,but arebeyondthescopeofthis work.Asdiscussedpreviously,theasteroidaldustbandsoeralinkt odeterminingthe magnitudeofthecloudthatisduetoasteroidalsourcesand,as such,thesebandswillbe thesubjectofmuchofthisthesis. 18

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TheasteroidaldustbandswererstobservedwhenIRASshowedthatth emid-IR emissionproleofthezodiacalcloud(Figure 1-6 )wasnotjustasmoothdistribution, butinsteadappearedtohavesomelocalizedfeatures.Theprole seemedtohavea\hat andshoulders"(apairat 10 latitudeaboveandbelowtheeclipticandacapnear theeclipticplane)superimposedonthebroadbackgroundemissi onneartheecliptic.In ordertoseethisne-structuremoreclearly,theproleswerepr ocessedthroughaFourier lterwhichhastheeectofseparatingthehighfrequencycompo nent(inthiscasethe ne-spatial-structuredustbands)fromthelowfrequencycompon ent(inthiscasethe broadbackgroundemission).Thisprocessrevealedtheshapeand structureofthezodiacal dustbands(thoughitshouldbenoted,aswillbediscussedinSecti on 2.2 ,theshapeand magnitudeofthebandsisdependentonthelteringprocess).Th edustbandsappear inpairs,asparallelbandsofmaterialatalmostconstantgeoce ntriclatitudes,aboveand belowtheeclipticaroundthewholesky.Ofcourse,physicalban dsofmaterialoating aboveandbelowtheeclipticwouldbegravitationallyunstab le,butthedustbands actuallyrepresentanapparentoverdensityofmaterialatthe edgesofatorusofdust,each formedofdustparticlesfromacommonasteroidsource.Thiswil lbeexplainedinmore detailinChapter2. Anasteroidfamilyisagroupofasteroidsthatshareacommonance storandwere createdinthedisruptionofthatlargerbody(Section 2.2 containsamorecomplete explanation).ThethreelargestasteroidfamiliesaretheHira yamafamilies(Hirayama, 1918)|Eos(at10.2 inclination),Koronis(at2.1 inclination),andThemis(at1.4 inclination).Becausethelatitudeofthedustbands(apairat 10 inclinationandsome structureneartheecliptic)matchedtheinclinationofthese threelargestasteroidfamilies, thedustbandswerequicklyattributedtoasteroidfamilysourc es(Dermottetal.,1984). Tofurthersupporttheasteroidalnatureofthedustbands,thebr ightnesstemperatureof thebandsputstheirheliocentricdistancelocationsinthea steroidbelt(Lowetal.,1984). 19

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1.6EarlyModelingoftheZodiacalDustBands Twodierentscenarioswerepresentedforthemechanismbywhich thedustbands werecreated.Thebandscouldstemfromeitheracontinualcom minutionofmaterial associatedwithlarge,olderfamiliesasinthe\equilibriumm odel"(Dermottetal., 1984)orfromrandomdisruptionsintheasteroidbeltofsmaller ,singleasteroidsasin the\catastrophicmodel"(SykesandGreenberg,1986).Thefo rmerwouldresultina continuousproductionofdustfromthesource,fromsmallercol lisionswithinanexisting family.Thelaterwouldresultinawaveofdustfromarecentdisr uptionbeinginjected intothecloudallatonce.Inadditiontothemechanismbywhic hthedustisproduced, thesetwoscenariosimplydierentdescriptionsofthetemporal variationofthebrightness ofthecloud.Theequilibriummodel,withitscontinuous,smal lerdisruptions,would resultinamoresteady-statetypezodiacalcloud,butthecatast rophicmodel,withits infrequent,butlarge,injectionsofdust,wouldimplyamore stochasticallyvaryingcloud. Figure 1-8 showsapossiblescenarioforthetemporalvariationofthecloud basedon thetotalcross-sectionalareaassociatedwiththemainbeltaster oidsanddescribedbythe stochasticbreakupofasteroidfragments(DurdaandDermott,1 997;Groganetal.,2001). Theheightofthespikesissomewhatarbitrary,comingfromana ssumedsize-distribution (Section 2.4.1.1 )ofq=1.9.Additionally,themodelisbasedonlyoncollisional breakup andremoval,andnotlossthroughPoynting-Robertson(P-R)dr ag.P-Rdragisadrag forceduetotheinteractionofthedustwithsolarradiationth atresultsinthedecayofthe semimajoraxisoftheparticle|seeSection 2.3.1.2 forafullexplanation.Regardlessof thesediscrepancies,themodelisstillinstructive|themagnitu deofthecross-sectional areaofthecloudisdecayingwithtime,butwitheachdisrupti onofanasteroid,awave ofdustisinjectedintothecloud,creatingaspike.Thisspiket hendecayswithtime duetocollisionalloss(andinreality,todecayoftheorbitsv iaP-Rdrag).Thequestion stillremains,though,whatarethemagnitudesofthespikes.Aret heylargeorsmall comparedtothebackgrounddustdistribution?Areweseeingaclo udwhichisdominated 20

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byarecentspikeofdust,orarethespikessmallincomparisontoth ebackgrounddust production?Iftheasteroidalcomponentofthecloudiscreat edviatheequilibriummodel, withsmall,frequentbreakups,thenwemightexpectfrequent, smallspikesofdusttobe injectedintothecloud.Thismightresultinacloudwherethe overallenvelopeofthedust production/injectionremainsinarelativelysteadystate,u ctuatingslightlydepending onthetimesinceadisruption.Ifthescenarioisinsteadthatoft hecatastrophicmodel, thenwemightexpectmorewidelyspaced,largerspikesofdustto beinjectedintothe cloud.Thismightresultinacloudthatwouldvarydrastically dependingonthetime since(andmagnitudeof)alargedisruption.Oneofthegoalsof thisthesisistodetermine howtheclouddoesvarywithtime.Arethespikeslarge,suchthat arecentspikewould greatlyaectthemagnitudeofthecloud?Arewecurrentlyinasp ikeofdustproduction orbetweenspikes?Isthemagnitudeofthecloudwecurrentlyme asurerepresentativeofa uctuationduetoaspike,orthebackgrounddustproduction.If weareinaspike,what wasthemagnitudeofthedustspikeimmediatelyfollowingthed isruptionthatproduced it?Thesequestionshaveremainedunresolved,butthroughthew orkofthisthesis,they willagainbeaddressed. Asthisearlyworkintheeldmovedforward,workbeganonmodel ingthedust bandsbasedonthethermalemissionthatwouldbeexpectedfromt heorbitsofthedust releasedfromthesourcelocationsandcomposingthebands.Them odelingwasdone assumingthemethodofdustproductionwastheequilibriummode l,aswouldbeexpected fortheold,largefamiliesthoughttobethesourcesatthisti me.Detailedmodelingwork byGroganetal.(1997)onthe10 bandshowedthatthestructureofthebandcould bematchedbydustparticlesfromtheEosfamilyonlyifadisper sionwasappliedtothe inclinationoftheparticleorbits,becausetheobservedlatit udeofthisband(about9.35 ) islessthanthemeaninclinationoftheEosfamily(about10.2 ).Addingadispersion totheinclinationdistributionofthelarger-bodyfamilyme mbersinordertodescribe theinclinationdistributionofthedust,though,wasreasonab lesincethedustparticles 21

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evolvedierentlythantheirlargebodycounterpartsasshown intheresultsofnumerical simulations(Section 2.3.2 ).Addingthedispersiontotheinclinationresultedinadust bandmodelthatprovidedagoodttotheobservationsbecauseth edispersionhadthe eectofbothbroadeningthebandstructureandshiftingthelat itudeofpeakuxofthe bandstowardstheecliptic(Groganetal.,1997;Figure 1-9 ).However,thedustparticles releasedfromasourcewouldbeexpectedtodecayintotheinner solarsystemduetothe eectofP-Rdrag.Whentheseparticlesintheinnersolarsystemwe reincludedinthe models,however,thetswerenotasgood.Thedispersionthatwas neededtoshiftthe latitudeofpeakuxofthemodelthatnowincludedtheinnersol arsystemparticlesto thecorrectlocationalsoresultedinadustbandprolethatwast oobroadenedwhen comparedtotheobservationstoprovideaconvincingt.Insubse quentwork,Groganet al.(2001)wentontorenetheinclinationofthesourcethatwo uldbeneededtoprovide agoodmatchtotheobservations,asshowninFigure 1-10 .Theyfoundaninclinationof I 9 : 3 andwithadispersionof¢ I =1.5 wouldreproducetheobservations.(Groganet al.,2001). Thedetermination,aroundthesametime,ofayoungageforthe Veritasasteroid family(whichisataninclinationof9.35 )presentedanalternativesourceoftheband. FollowupmodelingbyNesvornyetal.(2006)thenshowed,infac t,thattheVeritasfamily couldprovideagoodmatchtothedustbandobservations.Incont rasttothe10 8 {10 9 yearoldHirayamafamilies,theVeritasfamilyhasbeendatedt ohaveanageofonly 8.3 § 0.5Myr(Nesvornyetal.,2003).Theagesofthefamiliesarede terminedthrough backwardintegrationofthefamilymemberorbitsandwillbe discussedinSection 2.2 ThepossibilitythatVeritaswasthesourceofthe 10 dustbandprovidedsupportfor thescenariothattheasteroidswerecontributingdusttothecl oudviathe\catastrophic model",ratherthanthe\equilibriummodel"aswouldbeimpl iedbytheHirayamafamily sources. 22

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ThesubsequentdiscoveryofrecentdisruptionswithintheKoron isandThemis families,theKarin(Nesvornyetal.,2003)andBeagle(Nesvorn yetal.,2008)subclusters, respectively,werealsofoundtoprovidegoodtstothecentral dustbandsat 1{2 (Nesvornyetal.,2006;2008).Theseclustersarequiteyoung|al soontheorderof10 6 yearsold(Nesvornyetal.,2006;2008).Withtheseresults,itmig htseemthatthescenario thatbestdescribesthedustproductionbyasteroidswouldbethe recent-disruption \catastrophicmodel",buttheproblemisstillnotfullysolved .Aquickexaminationof Figure 1-7 showsthattherearenumerousasteroidfamiliesthatliealong inclinations correspondingtothelatitudesofthedustbands(asmarkedbyh orizontallines).Sinceit ismainlyonlytheinclinationofthefamilythatdiscriminat esitasthesourceoftheband, followedupbydetailedmodelingtoconrm,theothersourcesa longthesameinclination cannotbeexcluded,andhavenotbeenruledout.Thus,theincl inationofthedustband providesanon-uniquesolutionofasource,evenwiththeaidof detailedmodeling. 1.7ContributionsofthisWork Inthiswork,throughamethodofcoaddingtheIRASdataset(whi chwillbe explainedindetailinSection 3.2 ),weidentifyanew,very-faint,dustbandthatisstill intheprocessofformation(Section 3.3.1 ).Becausethisdustbandisstillveryyoung, thebandstructuredoesnotextendallthewayaroundtheskyand theinformationon theoriginalnodeofthesourceisnotlosttothedierentialpre cessionoftheparticles resultinginacompletedispersionofthenode.Becauseadustband hastobeveryyoung toproducesuchastructure,wealsohaveaconstraintontheageof thefamilyproducing theband.Thus,thispartialdustbandgivesus,forthersttime,t heabilitytonda uniquesolutionforthesourceofadustbandbydeterminingthei nclination,nodeandage ofthedisruptionthatcouldproducetheband.Also,sinceweknow basedontheband structure(Section 3.3.2 ),thatitisveryyoung,wecancondentlysaythatfortherst timewearelookingataveryrecentdisruptionofanasteroidpa rentbodyandarecent injectionofdustintothecloud.Furthermore,sincethenewdu stbandissoyoungthat 23

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collisionshaven'tyetbeguntopayarole(Section 3.4 ),thedistributionoftheparticles composingthebandresultsin(aswillbefurtherexplainedinS ection 3.5.4 )aunique gradationofparticlediameterandnodewithdistancefromth eSun.Becausethisnew dustbandrepresentsauniquetypeofstructure,wedevelopanen tirelynewtechniqueto modelandunderstandthisnewdustband,includinganewmethod ofdeterminingthe sizedistributionofparticlespresent.Thenewmodelingmetho dthathasbeendeveloped herecanalsobeappliedtoanynewpartialdustbandsthatarere vealedintheupcoming infraredsurveys.Thecomparisonofthemodelscreatedinthisn ewwaycanbecompared heretothecoaddedobservationstoplaceconstraintsonthepa rametersthatdescribethe dustparticledistributions(e.g.size,area,andheliocentri cdistribution).Thisinformation ontheparametersofthedustdistributionsosoonafteritisrele asedintothecloudfrom thecatastrophicdisruptionofanasteroid,providesvaluable insightintohowasteroids contributedusttothecloud.Understandingthepropertiesoft hedustreleasedina disruption,beforetheinformationislosttodynamicalandco llisionevolutionofthedust overtime,providesacloserguidetotheparametersofthedust producedintheoriginal disruption.Usingthecross-sectionalareaandsize-distributiono fthenewlyreleaseddust allowsustoinferthemagnitudeofthespikeofdustthatwasrel easedintothecloud, forboththisyoungbandandthethreeolderbands,andassuch,d eterminehowthe brightnessofthecloudmightvarywithtime. Inadditiontoaddressingthequestionsattheforefrontofthee ld,thisworkalso contributestothegoalsofthenextdecadeofstudyofinterpl anetarydust.Therecent decadalsurveywhitepaperoninterplanetarydustsetouttoden ethegoalsofthestudy ofinterplanetarydustoverthenext10years.Ofthefourtople velsciencequestionsthat itdenedasthemajorgoalsoftheeld,threeofthemcanbeaddr essedbythework presentedhere,aswellasfutureworkontheprojectsofthist hesis.Thespecicscience questionsofthedecadalsurveywhitepaperthatthisworkaddr esses(andhowitdoes so)aredetailedinthefollowing.\Howareinterplanetarydust particlesgenerated,how 24

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dotheyevolvedynamically,andwhatarethedominantlossmec hanisms?"Thisquestion isansweredthroughtheunderstandingofhowasteroidscontrib utedusttothecloud (Chapter3)andhowtheorbitsevolveastheydecayinwards(C hapter4).\Whatarethe relativecontributionsofdustparticlesfromeachsourcetot hezodiacalcloudasawhole?" ThisquestionisaddresseddirectlyinChapter2initsestimatio nofthemagnitudeofthe asteroidalcontributiontothecloud.\Whatistheglobalstru ctureofthecloudandhow doesitcomparetoexo-zodiacalclouds?"Understandingthedist ributionandnatureof theasteroidalcomponent(Chapter2)helpsustobegintounde rstandtheglobalstructure ofthecloud.Understandingthedustproductionmechanismsandt emporalvariations (Chapter3)helpstointerpretdataofexo-zodiacalclouds.F urthermore,missionpriorities ofthedecadalsurvey,thatwillguidethefundingofprograms, isfocusedonthecollection ofIDPsneartheEarth(inlower-costmissions)andthenlinkingt hecollectedparticles backtotheirsourcesthroughdynamicalmodelingeorts,suchas thosepresentedinthis thesis. 1.8LayoutofChapters InChapter2,wemodelthethreeknowndustbandsusingdustfromt henew, younger,likelysources|Veritas,KarinandBeagle.Inadditi ontotheupdatedsources, weincludeaparticlesizerangethatextendsfrom1 m{1mm,improvinguponthe earlymodelingattempts(e.g.Groganetal.,2001)thatwere limitedtoparticlesizesof 100 mduetocomputingconstraints.Improvementofcomputingpowe raswellas orbital-evolution-simulationalgorithmsallowsustomode ltheorbitalmigrationofthe dustparticlesinthecloudinto1AU,whereasearlyworkscould onlymodelthedynamics ofthedustparticlesinthemainbelt,andthenhadtoextrapol atethemtotheinnersolar systembasedonassumptionsaboutthecloud.Thesethreeimproveme nts,whichwillbe discussedindetailinChapter2,allowustocreateamorerealist icmodelofthecloud thanearlierattemptswereabletoproduce.Amethodforcomp arisonofthemodeltothe IRASobservationsisdeveloped.Thecomparisonofthemodeland theobservationsisthen 25

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usedtobroadlydeterminehowthedustisdistributed(insize,ar eaandheliocentrically) andthenusedtoestimatethemagnitudeofthetotalasteroidalc ontributiontothecloud. InChapter3,wethenmoveontothemainbodyofthiswork,thea nalysisof thestill-forming,veryyoungdustband.Werstexplainhowweco addtheIRAS ZOHFdatasettorevealthenewbandandgoontodescribehowwedet ermineitis anincompletestructureandlikelyveryyoung.Wediscussthero leofcollisionsinthe dynamicsofthisyoungbandandthengoontocreateafullmode lofthedustband usinganewmodelingtechniquedevelopedspecicallyforthisy oungstructure.Based onthedynamicsofitsconstituentparticles,thedustbandmode lisusedtocharacterize thepropertiesofthedustcomposingthebandandtodeterminea sourcebody.We concludeChapter3withadiscussionofwhythesepartialdustband sareactuallyeven moreinterestingthantheirfullyformeddustbandcounterpar tsandhowtheupcoming WideeldInfraredSurveyExplorer(WISE)willshapethefutur eofdustbandstudies. InChapter4,weinvestigatehowthedustparticleorbitsmaybe alteredastheyreach near-Earthspace,duetogravitationalperturbationsexper iencedfromMarsastheyevolve inward.WendbiasesintheinteractionswithMarsduetothepa rticleinclinations, eccentricities,andsizes.Weestimatethemagnitudeoftheeect anddiscusshowthese biasesmayeecttheorbitaldistributionsofdustneartheEarth ,wheretheparticlespose threatstospacecraftandsatellitesandaectthecompositiona ldiversityofcollectedIDPs (e.gFlynnetal.,1994). InChapter5,wesummarizethemainresultsofthisworkanddiscu sswhythis workisimportantandhowitcontributestotheeld.Weendbye xamininghowthe advancementsofthisthesistintothefuturedirectionsofth eeld,boththroughtaking advantageoftheupcomingtechnicaladvancesandinaddressin gthesciencegoalsofthe nextdecade. 26

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Figure1-1.TheorbitofIRAS.TheInfraredAstronomicalSatell ite(IRAS)wasinapolar orbitaroundtheEarth.Thisorbitallowedforpole-to-pole intensityscansof thethermalemissionofthethezodiacalcloud.Thedatawastak eninboth segmentsofIRAS'orbitaroundtheEarth,fromNorthtoSouthand from SouthtoNorth,resultinginscansintheLeadingdirectionofth eEarth's motionandtheTrailingdirectionofEarth'smotioninitsor bitaroundthe Sun.IRAStookmostofitsobservationsoverasmallrangeofsolare longation angles( 85{95 ).Thesolarelongationangleistheanglebetweenthe Sun-Earthlineandtheviewingdirectionofthetelescope.Th edatawastaken insuchawaythatthesolarelongationanglewasincrementedsyst ematically withthelongitudinalmotionoftheEarth.[Reproducedwith permissionfrom Beichmanetal.,1985.InfraredAstronomicalSatellite(IRAS) catalogsand atlases.Explanatorysupplement(FigureIII.B.1).JetPropul sionLaboratory.] 27

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Figure1-2.Inclinationoftheglobalcloud.Variationofth elatitudeofpeakuxofthe zodiacalcloudwitheclipticlongitudeoftheEarthasobserv edbyCOBEin the25 mwaveband.Theopencirclesrepresentdatatakenintheleadi ng directionoftheEarth'sorbitat90 solarelongationangle,andthesolidcircles arefordatatakeninthetrailingdirectionat90 solarelongationangle.We wouldexpectnovariationofthelatitudeofpeakuxastheEar thmoves arounditsorbitiftheplaneofthesymmetryofthecloudwasth eecliptic. Thesinusoidalvariationofthelatitudeofpeakuxindicatest heorientation oftheplaneofsymmetryofthecloudtotheecliptic.Theeclip ticlongitudes atwhichthelatitudesofpeakuxareequalandoppositeforthe leadingand trailingdataliealongtheintersectionofthetwoplanesand correspondto thelongitudesoftheascendinganddescendingnodeofplaneof symmetry withrespecttotheecliptic.Thelatitudeofpeakuxatthenod esgives theinclinationoftheplaneofsymmetrywithrespecttotheecl iptic.The inclinationisfoundtobe1.49 § 0.07 andthelongitudeoftheascending nodeis58.4 § 2.3 (Dermottetal.,1996).[Reproducedwithpermission fromDermott,S.F.,etal.,1996.SourcesofInterplanetary Dust(Figure1a). InGustafson,B.,Hanner,M.,(Eds.),Physics,Chemistry,andDynam icsof InterplanetaryDust,SanFranciso.] 28

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Figure1-3.Warpoftheglobalcloud.Variationofthemagnit udeofthepolarbrightness fortheNorth(opencircles)andSouth(lledcircles)polaruxes fromthe COBE25 mwaveband.TheNorthandSouthpolarbrightnessesareequalat thenodesoftheplaneofsymmetryofthecloudwithrespecttoth eecliptic. Thelongitudeoftheascendingnodeisfoundtobe70.7 § 0.4 (Dermott etal.,1999).Thesemeasurementsofthepolarbrightnesssample thecloud attheEarth'sorbit(1AU),butthemeasurementsshowninFigure 1-2 areinsteadlookingoutintothecloudandsamplingitat > 1AU.Since thesetwoobservationsnddierentnodesoftheplaneofsymmetry tothe ecliptic,thentheorientationoftheplaneofsymmetrywithr especttothe eclipticischangingwithheliocentricdistance.Thismeans thattheplaneof symmetryofthecloudisnotonlytiltedwithrespecttotheecli pticplane, butisalsowarped.[ReproducedwithpermissionfromDermott,S .F.,etal., 1999.Dynamicalstructureofthezodiacalcloud(Figure6).F ormationand EvolutionofSolidsinSpace,EditedbyJ.MayoGreenbergand AigenLi. KluwerAcademicPublishers.] 29

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Figure1-4.Osetoftheglobalcloud.VariationoftheCOBEmea npolarbrightnessasa functionofeclipticlongitudeofEarthintwoCOBEwaveband s,12 m(left panel)and25 m(rightpanel).AveragingtheNorthandSouthpoledata removesanyvariationsthatwouldbeexpectedtocomefromth einclinationof theplaneofsymmetryofthezodiacalcloudwithrespecttothee cliptic.Ifthe cloudwererotationallysymmetricwiththeSunatthecenter, itisreasonable toexpectthattheminimumoftheaveragedpolarbrightnessesw ouldbeatan extremeoftheEarth'sorbit,eitheraphelionorperihelion ,dependingonhow thematerialisdistributedheliocentrically.However,them inimumintensity isosetfromtheaphelionlocation,whichisexpectedonlyift heSunisnot atthecenterofsymmetryofthecloud.[Reproducedwithpermi ssionfrom Dermott,S.F.,etal.,1999.Dynamicalstructureofthezodia calcloud(Figure 6).FormationandEvolutionofSolidsinSpace,EditedbyJ.M ayoGreenberg andAigenLi.KluwerAcademicPublishers.] 30

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Figure1-5.Schematicofosetoftheglobalcloud.Theosethasb eensuggested (Dermottetal.,1999)tobeduetoseculargravitationalpert urbations,which causethedistributionofzodiacalcloudparticlestobebiased towardsthe samedirection(markedas w f ),asisrepresentedschematicallyhere.Asingle dustparticleorbitismarkedbythedarkline,andthedistribu tionofallthe orbitsresultsinadistributionthatisosetfromtheSun,marke dasS.The complicateddetailsarebeyondthescopehere,butaregiveni nWyattet al.(1999)andDermottetal.(2001).[Reproducedwithpermi ssionfrom Wyattetal.,1999.Howobservationsofcircumstellardiskasymme triescan revealhiddenplanets:Pericenterglowanditsapplicationt otheHR4796disk (Figure2).ApJ527.] 31

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Figure1-6.IRASintensityprole.AnIRASpole-to-poleintensity scanofthethermal emissionofthezodiacalcloudinthe25 mwaveband.Ratherthanasmooth distributionofemission,therecanbeseenasmall\hatandshoulde rs" superimposedonthebroadsmoothemissionofthecloudneartheecl iptic. AfterFourier-lteringtheproletoremovethelow-spatial-fr equency component,thehigh-frequencycomponent,theresidualdustb ands,become evident.Thereareatleastthreeknowndustbandpairs,onepair near § 10 eclipticlatitudeandtwopairstogetherneartheeclipticp laneat § 2.1 and § 1.4 eclipticlatitude.Thesebandsofdustarethoughttoresultfro mthe catastrophicdisruptionsthatcreatedtheVeritas,Karin,and Beagleasteroid familiesrespectively(Dermottetal.,1994,Groganetal.,1 997;2001;Nesvorny etal.,2003;2006;2008).[ReproducedwithpermissionfromGr oganetal., 2001.Thesize-frequencydistributionofthezodiacalcloud: evidencefromthe solarsystemdustbands(Figure1).Icarus152.] 32

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Figure1-7.AsteroidFamilies.Asteroidfamiliesaregroupsofast eroidsthatwerecreated inthedisruptionofalargerasteroid.Theysharecommon(prope r,seesection 2.3.2 fordetails)inclinations,eccentricitiesandsemimajoraxes sincethey shareacommonancestor.Theeclipticlatitudesofthelocatio nsofthethree maindustbands, 10 ,2 ,and1 aremarkedbyhorizontallines.Some additionalproposedbands(e.gSykesetal.,1988)aremarked bydashedlines. Theinclinationsofthethreelargestasteroidfamilies,theHir ayamafamilies (Hirayama,1918)|Eos,Themis,andKoronis,canbeseentobroadlycoincidewiththelatitudesofthedustbands.Theproposedyoun gersources forthebandsarealsomarked|Veritas,KarinandBeagle.[Repr oducedwith permissionfromNesvorny,D.,etal.,2003.Recentoriginofthe solarsystem dustbands(Figure1).ApJ591.] 33

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Figure1-8.Temporalvariationofamodelzodiacalcloud.Sh ownhereisamodelfor thevariationwithtimeofthecross-sectionalareaofdustassocia tedwith thebreakupofamainbeltasteroidthatwaslargeenoughtosupp lyallthe observedcollisionproductsinthebelt(DurdaandDermott,19 97).With eachdisruptionofanasteroid,awaveofdustisinjectedintoth ecloud. Inthismodel,thiswaveofdustthendecayswithtimeduetocol lisional loss(andinreality,todecayoftheorbitsviaP-Rdrag).Theh eightsof thespikesherearesomewhatarbitraryandbasedonanassumedq=1. 9 size-distribution.Butwhataretheactualheightsofthespike s?Arethey largeorsmallcomparedtothebackgrounddustdistribution?Are weseeinga cloudwhichisdominatedbyarecentspikeofdust,orarethespik essmallin comparisontothebackgrounddustproduction?Iftheasteroida lcomponent ofthecloudiscreatedviatheequilibriummodel,withsmall, frequentbreak ups,thenwemightexpectfrequent,smallspikesofdusttobeinje ctedinto thecloud.Thismightresultinacloudwheretheoverallenvel opeofthe dustproduction/injectionremainsinarelativelysteadystat e,uctuating slightlydependingonthetimesinceadisruption.Ifthescenari oisinstead thatofthecatastrophicmodel,thenwemightexpectmorewide lyspaced, largerspikesofdusttobeinjectedintothecloud.Thismightr esultinacloud thatwouldvarydrasticallydependingonthetimesince(andma gnitudeof) alargedisruption.[ReproducedwithpermissionfromGroganet al.,2001. Thesize-frequencydistributionofthezodiacalcloud:evide ncefromthesolar systemdustbands(Figure19).Icarus152.] 34

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Figure1-9.Eectofinclinationdispersionondustbandstructur e.Theeectofdispersion intheorbitalinclinationofthedustbandmaterialontheraw (unltered) dustbandproles.Asthedispersionincreases,theprolesbecomebro ader andthepeaklatitudesmoveinwardstowardstheecliptic.Bo thoftheseeects servetoaddressthediscrepanciesofthemismatchofthemeanoft heEos familyasteroidswiththelatitudeofpeakintensityofthe10 dustbandin theobservations.Adispersionof2.5 intheinclinationprovidedagoodt totheobservations.However,whenparticlesintheinnersolarsy stemwere included,adispersionof3.5 ininclinationwasneededtotthelatitudeof peakuxandthisdispersionresultedinatoo-broadproleascomp aredto theobservations.[ReproducedwithpermissionfromGrogan,K., etal.,1997. OriginofthetendegreeSolarSystemdustbands(Figure4).Pla netaryand SpaceScience45.] 35

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Figure1-10.Possiblesourcesofthe\10degree"band.Theincli nationlocationofasource neededtotthe\10degree"dustbandwasfoundbyGroganetal.( 2001)to beat9.3 .TheisosetslightlyfromthemeanlocationofEos,butisbetter matchedtothelocationoftheVeritasfamily(Nesvornyetal. ,2003).Veritas hasbeenshowntoprovideagoodttotheband,butarecentcolli sionat thelowerinclinationedgeofEosorfromanadditional(notdiscussed)family nearthisinclinationhavenotbeenruledout.[Reproducedw ithpermission fromGroganetal.,2001.Thesize-frequencydistributionoft hezodiacal cloud:evidencefromthesolarsystemdustbands(Figure22).Ica rus152.] 36

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CHAPTER2 THEZODIACALDUSTBANDS 2.1Introduction Inthischapterwepresentamodeloftheasteroidalcomponento fthezodiacalcloud whichisconstrainedbythezodiacaldustbands.Thismodelisba sedonthedynamical evolutionofdustfromtheyoungerfamiliesnowthoughttobet hesourcesofthedust bands|Veritas,Karin,andBeagle.Inadditiontotheuseofthese newlydetermined possiblesources,themodelhasseveralothermarkedimprovement soverearliermodels. Previousattempts(Groganetal.,2001)tomodelthezodiaca lclouddustbandswere limited,bythecomputertechnologyofthetime,toparticle sizesbelow100 mand toorbitsoutsideof2AU.Wenowhavetheabilitytodynamically tracktheorbitsof particlesofallsizesfromafewmicronsuptoacentimeterfro mtheirsourcelocationsin themainbeltintotheinnersolarsystemandwerevisittheproble mwiththesenewtools. Wepresentherethenew,updated,dynamicalmodelofthezodia caldustbandsandthe magnitudeofthetotalasteroidaldustcomponentofthezodiac alcloud. Webeginbypresentingamoredetailedlookatthezodiacalclo uddustbands,which wereintroducedinChapter1.Wewillexplaintheconceptofa steroidfamilies,howtheir agesaredetermined,andtheirrelationtothedustbands.Wewi llalsodiscusswhatis knownaboutthedustbandsandhowtheycanbeusedtoconstrainth emagnitudeof thetotalasteroidalcontributiontothecloud.InSection 2.3 weshowhowthedynamical modelsarecreatedandinSection 2.4 wewilldiscusstheparametersdescribingthemodels andthemethodsbywhichtheseparametersareconstrainedthro ughcomparisonwith theobservations.InSection 2.5 wewilldiscusstheresultsofthemodelingworkandthe resultingmagnitudeoftheasteroidalcomponentofthecloud. Thechapterwillconclude withadiscussionofthefuturedirectionsofworkonthistopic. 37

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2.2WhatisKnownAbouttheZodiacalDustBands Becauseofthewealthofobservationsofthezodiacalcloud(Se ction 1.3 ),wehave informationaboutthestructureandsourcesofthedustbands.Be forewediscuss thesedetails,though,weshouldaskthequestion\whatisazodiac aldustband?". Observationally,azodiacalclouddustbandisapairofbandso fmaterial,aboveand belowtheecliptic,extendingaroundtheskyatalllongitude s.Physically,(asbandsof oatingmaterialwouldofcoursebegravitationalunstable)th edustbandsrepresent apparentover-densitiesattheedgesofatorusofdustthatenc irclestheinnersolar systemattheheliocentricdistanceoftheasteroidbelt.Because thedustbandstructure issuperimposedonthebackgroundcloud,amethodofisolatingt hedustbandsfrom thebackgroundcloudisneeded.Themethodoflteringissomew hatarbitraryand dierentlteringtechniqueswillresultindierentshapesanda mplitudesofthedustband residuals,byincludingmoreorlessofthesmooth(i.elow-frequ ency)componentofthe bandswhichisindistinguishablefromthesmoothcomponentoft hebackgroundcloud. InthisworkweuseaFourierlteringprocesstoseparatethehigh -frequencydustbands fromthelow-frequencybackgroundcloud.Inordertoaccoun tforthesomewhatarbitrary natureofthelteringprocess,weusethesamelteringtechniqueo nthemodelsasonthe observationssothedustbandresidualsofthetwoarecomparable Thezodiacaldustbandsareaby-productofthecatastrophicdi sruptionofan asteroid,onethatalsoproducedanasteroidfamily.Inorderto understandthedust bands,wemustrstunderstandwhatanasteroidfamilyis.Anasteroidf amilyisa groupingofasteroidsinproperorbitalelementspace( a e ,and i ).Thedetailsofforced andproperelementswillbediscussedinSection 2.3.2 ,butfornowitissucientto understandthatanasteroidfamilyisagroupofasteroidswhich ,whilenotphysically togetherinthesky,haveorbitswhichimplythattheywerecre atedinthedisruptionof alarger,parentasteroidatsometimeinthepast.Theagesofthe seasteroidfamilies canbedeterminedthroughbackwardintegrationoftheindiv idualasteroidorbitsto 38

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determineatwhatepochinthepastthesebodieshadcommonperi centersandnodesand werelikelyasingle,largerobject.Muchworkonthisproblem ofdatingasteroidfamilies hasbeenbydonebyNesvornyetal.(e.g.2003).Anexampleofthi sprocessisshownin Figure 2-1 whichshowsthetemporalvariationofthenodallongitude(pa nelA)andthe perihelionargument(panelB)forthemembersoftheKarinfa mily.Therecanbeseen hereacommontimeatwhichallthefamilymembershavecommon nodesandpericenters. Thisepochistakentobethedateofthedisruption|5.8 § 0.2Myr.Throughthis method,wealsoknowtheagesofseveralotherasteroidfamilies, includingtheother familiesthoughttobethesourcesofthedustbands,Veritasand Beagle.Theseagesare summarizedinTable 2-1 .Thisabilitytodatethedisruptionshelpedleadtothecurre nt ideathattheasteroidalcomponentofthezodiacalcloudmayb egeneratedthroughrecent (withinthelast10Myryears)collisionaleventsintheasteroid belt. Buthowdoesthedisruptionofanasteroidleadtoadustband?Whe nanasteroid isdisruptedinacatastrophiccollisionwithanotherbody,the largerpiecescreatedin thedisruptionremainonsimilarorbitstotheparentbodyandf ormanasteroidfamily. Thesmallestproductsofthedisruption,lessthanafewmicronsi nsize,areblownout oftheinnersolarsystembyradiationpressure(Section 2.3.1.1 ).Thedustparticlesin betweenthesetwoextremes,fromafewmicronstoafewcm,areth eparticlesthatwill formazodiacaldustband.Theseparticlesstartoutonsimilaror bitstotheparentbody, buttheeectsofPoynting-Robertson(P-R)dragandsolarwindd rag(Sections 2.3.1.2 2.3.1.3 )willcausetheirorbitstodecayinwardstotheSun.Figure 2-2 showsavery usefulschematictounderstandtheformationofadustband,aswe llaswhyanasteroidal disruptionwillproducesuchastructure.PanelAshowsalatitud e/longitudeskymapthat wouldresultfromtheorbitalorientationoftheparticlessho wninpanelC.Thetopframe ofeachpanelrepresentsthesituationsoonafteracatastrophic disruptionofanasteroid. Followingthedisruption,thefragmentswillhaveslightlydi erentvelocitiesasaresultof 39

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theimpactwhichcanbedescribedas ¢ a a 2 v ej v 0 ; (2{1) where¢ a isthechangeinsemimajoraxis, a isthesemimajoraxisupondisruption, v ej istheejectionvelocity,and v 0 istheorbitalvelocityas v 0 = GM s a 1 = 2 (2{2) where G isthegravitationalconstantand M s isthemassoftheSun.Thevelocitiesofthe fragments, v ej ,areusuallyontheorderoftheescapevelocity,whichfora10k masteroid isabout5m/sandfora100kmasteroidisabout50m/s.Theseeject ionvelocitiesare smallcomparedtotheorbitalvelocityof15{20km/sec,yetresu ltinthefragments spreadingintoaringofmaterialalongtheorbitofthepartast eroidonatimescaleofa fewhundreds{thousandsofyears,thoughifthereissignicantej ectionvelocityimparted totheparticlesinaparticularlyenergeticimpact,thetim escaletospreadaroundthe orbitcanbeasshortasseveralhundredyears.Onalongertimesca le,theparticleswill thenbegintosuerthedrageects(P-Randsolarwinddrag)andsta rttodecayin semimajoraxis.Planetaryperturbationswillcausethenodeso ftheorbitsofparticles atdierentsemimajoraxestoprecessatdierentrates.Thisdier entialprecessionwill spreadtheorbitsoutaroundthesky,asisrepresentedintheseco ndframeofpanelsAand C.Finally,asisshowninthebottomframe,after10 5 {10 6 years,theparticles'nodeswill bespreadallaroundthesky,producingafulldusttorus.PanelBsh owsbothhowand whythisdusttoruswillbeobservedastwoparallelbandsofmat erialatitsedges.The overdensityattheedgesofthetorusisexplainedasfollows:t hemotionoftheparticles aroundtheirorbitsresultsintheirmotioninandoutoftheec lipticplanehavingtheform ofaharmonicoscillator.Theywillthereforespendmoretimes attheextremesoftheir positions,resultinginapparentover-densitiesattheedgesof thetorus.Itcanalsobeseen inpanelBthatthelatitudelocationsofthesebandswillbeasso ciatedwiththeoriginal 40

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inclinationoftheparentbody,aboveandbelowtheirmeanpl ane.Thisresultofthe formationallowsthedustbandstobelinkedbacktotheircorr espondingparentasteroid families. Sincethedustbandsretaintheproperinclinationoftheirpa rentbodyasthey form,theycanbeattributedtoapossiblesource.Referringbac ktoFigure 1-7 ,itcan beseenthatthelatitudesofthedustbands,markedbyhorizonta llines,intersectthe inclinationsoftheasteroidfamilyproducingtheband.Inth ismanner,thebandat approximately10 inclinationisthoughttobeassociatedwiththeVeritasfamil y(Grogan etal.,2001;Dermottetal.,2002;Nesvornyetal.,2003),the 2.11 bandpairisthought tobeassociatedwiththeKarinsub-clusteroftheKoronisfamily (Nesvornyetal.,2003) andthe1.4 bandpairhasrecentlybeenassociatedwithasecondarydisrupti onwithin theThemisfamilyknownastheBeaglecluster(Nesvornyetal., 2008).Theagesofthese familiesaresummarizedinTable 2-1 .Followingtheinitialassociationwithinclination, detailedmodelingisdonetoconrmthecorrespondence.Themo deling,whichwillbe discussedinSection 2.3.3 ,isneededtotakeaccountoftheparticulargeometryofthe observations,astheshapesandpreciselocationsofthedustband svarywithboththe Earth'slongitudeandwiththeelongationangleoftheobserv ations(thereasonsforwhich areexplainedinSection 3.2 ). Inadditiontothiscorrespondenceofthebandlocationwitht hefamilies'inclinations, wehaveotherinformationthatimpliesthatthedustbandsare asteroidalinnature. Bothbrightnesstemperature(Lowetal.,1984)andparallax( Gautieretal.,1984) measurementsputthelocationofthedustbandsbetween2.3and 3.2AU,thedistanceof themainasteroidbelt.Evenfurtherindicationthatthesestru cturesareintheasteroid beltcomesfromtheirplaneofsymmetry.Thedustbandstructure issymmetricabout aplanethatisnottheecliptic,asisshowninFigure 2-3 ,whichshowsthevariationof themedianpointsseparatingtheNorthandSouth 10 dustbandsintheleading(open circles)andtrailing(lledcircles)directionsoftheEarth' sorbitasseenbyIRAS.Asan 41

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aside,andwhichwillbeexplainedinmoredetailinSection 3.6.1 ,theorbitofIRASwas suchthatittookscansinboththeleadingandtrailingdirecti onsoftheEarth'smotion initsorbit.Thesinusoidalvariationofthethemeanlatitude sofFigure 2-3 implyan inclinationoftheplaneofsymmetryofthedustbandmidplanet otheeclipticplane,as novariationofthemeanlatitudewouldbeexpectedifthetwo planeswerethesame. Thelongitudesatwhichthemeanlatitudesareequalandoppo sitefortheleadingand trailingobservationdirectionscorrespondtothenodesofth etwoplanes.Theamplitude ofthebandsatthesepointscorrespondstotheinclinationoft hedustbandmidplane totheeclipticplane.Thus,thenodeandinclinationofthedu stbandmidplanewith respecttotheeclipticarefoundtobe99.9 § 7.8 and1.16 § 0.09 respectively(Grogan etal.,2001).Thesevaluesareveryclosetotheinclinationan dnodeofJupiter'sorbit anddierentfromthevaluesfoundforthebackgroundcloud,a ssummarizedinTable 2-2 Thisindicatesthatthesestructuresareconstrainedtotheaste roidbelt,whereJupiter dominatestheorbitalelementsandcontrolstheplaneofsymm etry.Schematicsofthe inclineddustbandareshowninFigure 2-4 forboththesimpleinclinedcase(idealized dustbands)andthemorerealisticcaseofawarpedcloud(warpedd ustbands),wherethe inclinationvarieswithheliocentricdistanceasdiscussedinS ection 1.4 .Thereasonforthis variationoftheinclinationwithheliocentricdistancewil lbediscussedinSection 2.3.2 Inadditiontothisdatainsupportoftheasteroidaloriginoft hedustbands,ithas furthermorebeenshownthatcometscouldn'tproducetheband structure.Cometary typeorbitshavehigheccentricitiesandtheseculargravita tionalperturbationsofthe planetsproducelargevariationsintheseeccentricitiesth atarecoupledtothevariations intheinclinations.Thus,evenifagroupofcometarytypeorbi tsinitiallyhadidentical inclinations,secularperturbationswoulddispersetheinclin ationsonshorttimescales, makingbandformationimpossible(Liou,1993).Forallthesere asons,itisclearthatthe zodiacaldustbandsmustbeduetoasteroidalsources.Asthecompon entofthecloud 42

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knowntobeasteroidal,thenthedustbandscanprovidethekeyt ounderstandingthe magnitudeofthetotalasteroidalcontributiontothezodiac alcloud. Thislinkbetweenthedustbandsandtheasteroidalcomponento fthezodiacal cloudprovidesthemotivationfortheirstudy.AsdiscussedinCha pter1,therelative proportionsoftheasteroidalandcometarycomponentsofthe cloudarestillasubject ofmuchdebate.Becausethedustbandsrepresentaknownasteroid alcomponent,they provideakeytounderstandingthemechanismsbywhichasteroid scontributedustto thecloud,thepropertiesofthisdust,andultimatelyaconstr aintonthemagnitude ofthetotalasteroidalcomponent.Aswillbediscussedfurtherin Section 2.3.2 ,the dustbandthemselvesrepresentonlyafractionofthetotalaster oidalcomponentof thecloudbecauseoftheirnaturaledgealongtheinnermainbe lt.Theasteroidaldust producedinthecatastrophicdisruptionsthatformedtheband structures,though,also contributesasignicantamountofdustintotheinnersolarsystem .Additionally,as discussedpreviously,thedustbandsarerevealedinaFourierlte ringprocess.Because thislteringmethodisonlysensitivetothehigh-frequencyco mponentofthedustbands, itunderestimatestheirmagnitudebecausethelow-frequency componentoftheband islefttobeincludedwiththebackgroundcloud.Forboththe sereasons,eventhough thedustbandsthemselvesaccountforonlyafewpercentofthez odiacalcloud,they representthetailendofadistributionofdustand,assuch,atot alasteroidalcomponent thatconstitutesamuchlargerproportionofthecloud.Throu ghdynamicalmodelingof thedustbands,wecanputimportantconstraintsonthemagnitud eofthisasteroidal componentofthecloud. 2.3DustBandModeling 2.3.1Forces Followingthecatastrophicdisruptionofanasteroid,thedustsizedparticlescreated inthedisruptionaresubjecttoarangeofradiationandsolarwi ndeectsinadditionto 43

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thegravitationaleectsexperiencedbyallsizebodies.Thesef orces,whichwillnowbe discussed,areradiationpressure,Poynting-Robertson(P-R)dra g,andsolarwinddrag. 2.3.1.1Radiationpressure Radiationpressureisthecomponentoftheradiationforcetha tpointsradiallyaway fromtheSun.Itstemsfromatransferofmomentumduetotheimpa ctofsolarphotons withthedustparticles.Thestrengthoftheforceofradiationp ressurevariesinversely proportionaltothesquareoftheparticles'distancefromtheS un.Radiationpressure servesto\cancelout"someoftheSun'sgravitationpull,resul tingintheparticleorbiting aneectivelylessmassiveSun.ThemassoftheSunthataradiation -pressure-aected particleorbitsisreducedbythefactor1 ,where istheratiooftheradiationforceto thegravitationalforce(Gustafson,1994)as: ( D )= F rad F grav (2{3) Forlargesphericalparticlesinthesolarsystem, canbeapproximatedas ( D ) 1150 D (2{4) where isthedensityoftheparticleinkg/m 3 andDistheparticlediameterin m.This approximationisvalidforparticleswithD > 20 m(Gustafson,1994).Immediatelyafter thedisruptionofaparentbody,whichitselfwastoolargetofe eltheeectofradiation pressure,thefragmentscreatedinthedisruptionwillsuddenly havethisradiationpressure eect\switchedon".Theresultisaninstantaneousalterationo ftheorbitofthedust particle.Theparticledoesn'tphysicallymoveinspace,butth eorbitalelementsdescribing itsorbitwillchangeandtheparticlewillthenbetraveling onanew,alteredorbit.The relativechangestotheorbitfromthiseectwerecalculated byBurns,LamyandSoter (1979)andareasfollows: a 0 = a (1 ¡ ) = [1 ¡ 2 (1+ ecosf ) = (1 ¡ e 2 )](2{5) 44

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e 0 =(1 ¡ ) ¡ 1 p e 2 +2 ecosf + 2 (2{6) Where a 0 and e 0 arethenewsemimajoraxisandeccentricityoftheradiationpressure-aected particle'sorbit, a and e representthevaluesoftheparentbody'ssemimajoraxisand eccentricity,and f isthetrueanomalywhichdenotesthepositionintheorbitatt hetime ofdisruption.Theorbitsofthelargestparticles,thosewithth esmallest ,willexperience theleastperturbationfromradiationpressureeectsandremai nonorbitssimilarto theorbitoftheparentbody.Thesmallerparticleshowever,w illexperienceasignicant orbitalperturbationfromradiationpressure.Thesmallestfra gments,thoseforwhich > 0.5(Gustafson,1994),willenduponhyperbolicorbitsandthu sberemovedfromthe solarsystemonatimescaleofanorbitalperiod.Thesearethesocal led -meteoroids.For asteroidaltypedensities(2{3g/cm 3 ,Hiltonetal.,2003),particleswithdiametersless thanafewmicronsarethepopulationlostfromthesystemduetot heeectofradiation pressure.2.3.1.2Poynting-Robertsondrag P-Rdragisthecomponentoftheradiationforcethatactstan gentialtotheparticle's orbit.TheeectofP-Rdragisanevolutionarydecreaseinboth thesemimajoraxisand eccentricityoftheparticle'sorbit.P-Rdragdoesnotchan getheplaneoftheparticle's orbit,though,andthusresultsinnovariationoftheinclina tionorthenodeofthe orbit.ThesemimajoraxisdecaycausedbytheeectofP-Rdragis themaintransport mechanismoftheparticlesintonear-Earthspace.Largerpart iclesdecayinmoreslowly thansmallerparticlesandausefulscalingisthattherateofth esemimajoraxisdecayis inverselyproportionaltotheparticlesize,thusa100 mparticlewillrequire10timesas longasa10 mparticletodecayintotheSun.Theequationsfortherateof changeofthe semimajoraxisandeccentricityoftheparticleorbitwerede rivedbyWyattandWhipple (1950)andareasfollows: 45

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_ a pr = ¡ a 2+3 e 2 (1 ¡ e 2 ) 3 = 2 = ¡ 2 a + O ( e 2 )(2{7) e pr = ¡ a 2 2 : 5 e (1 ¡ e 2 ) 1 = 2 = ¡ 2 : 5 e a 2 + O ( e 2 )(2{8) where a and e representtheinitialsemimajoraxisandeccentricityofthep articleand =6.24x10 ¡ 4 AU 2 /yr. CombiningEquation 2{7 withEquation 2{4 ,thetimescaleforparticles,asafunction ofsize,todecayintotheinnersolarsystemcanbeapproximateda s t pr = 400 1150 D ( r 2 1 ¡ r 2 2 )(2{9) where t pr isinyears, isinkg/m 3 D isin mand r 1 and r 2 areinAUandrepresent theinitialandnalsemimajoraxis,respectively.Assumingasteroi d-typedensities (2000{3000kg/m 3 ),ausefulapproximationforthetimescaleinyearsforpartic lesof diameter D todecayfromthemainbelt( 2.6AU)intotheEarth(1AU)canbewritten as t pr ( yr ) 5000 D ( m ) : (2{10) 2.3.1.3Solarwind Solarwindcorpuscularforcesarecausedbycollisionsofthedu stparticleswithsolar windprotons.Theresultontheparticles'orbitsisadrageecta nalogoustothatofP-R drag.Themagnitudeofthesolarwinddragonaparticleisestim atedtobe30%ofthe magnitudeoftheeectofP-Rdrag(Gustafson,1994).Solarwind drag,therefore,acts to increase therateofdecayofthesemimajoraxis,decreasingthetimeitta kesfora particletospiralintotheinnersolarsystem.SolarwindLorent zforcesareignoredfor theseparticles,sincethisforceissignicantonlyforparticle slessthan1 mindiameter (Gustafson,1994). 46

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2.3.2DynamicalEvolution Thedynamicalevolutionoftheparticlesisperformedusinga nN-bodycodespecially developedforthepurposeofintegratingtheorbitsoflargep opulationsofdustparticles undertheeectsofP-Rdrag,solarwinddragandplanetarypert urbations(seeKehoeet al.,2003forafulldescription).Numericalintegrationsare carriedoutfortheasteroidal populationsthoughttobethesourcesofthedustbands|Karin, Veritas,andBeagle.It shouldbenotedthattheactualsourceusedintheintegrationsr epresentingtheBeagle clusterwastheThemisfamily,ofwhichBeagleisaveryrecent lydiscoveredsub-cluster. Thedynamicsarebroadlythesame,though,andwedon'texpect thistoaecttheresults signicantly.Theintegrationsallowparticlesofsizesinthe rangeof10 m{1mmtobe trackedastheyevolvefromtheirsourcesintotheinnersolarsy stem.Theseintegrations aredoneforpopulationsof1000particlesandtheparticleo rbitsareusedtobuildthe3-D modelsofthedustdistribution(Section 2.3.3 ).Inordertobuildsmoothmodels,orders ofmagnitudemorethan1000orbitsareneeded,butcomputing timescaleslimitthe numberoforbitsthatcanbetrackedinreasonableamountsoft ime.Therefore,amethod ofcharacterizingtheorbitsisneededtoallowthepopulati ontobearticiallyincreased. Thischaracterizationmethodallowsthe1000integratedpa rticleorbitstopopulateovera millionorbitsinthe3-Dmodel.Thecharacterizationofthe orbitsisdoneinauniqueway, developedbyDermottetal.(1992).Inordertounderstandthe characterizationmethod, itisnecessarytorstunderstandtheconceptsofforcedandprope relements. Forcedandproperelements .Properelementsarethoseinherenttotheinitial conditionsandforcedelementsrepresentthevariationsresu ltingfromtheplanetary perturbations.Giventhesedenitions,wecanalsonowmorepreci selydenethatthedust bandsareseparatedbytwicetheproperinclinationoftheirp arentbody,centeredona planedenedbytheforcedinclination.Thiscanbeseenifwelo okbacktoFigure 2-4 nowthattheseelementshavebeendened.Thetopschematicofth edustbandsshows theforcedinclinationdeningthedustbandmidplanewithresp ecttotheecliptic.The 47

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dustbandcanbeseentobeseparatedbytwicetheproperinclinat ionoftheparentbody andcenteredonthisforced-inclination-denedmidplane.B ecausetheforcedinclinationis actuallyafunctionofheliocentricdistance,thebottomsche maticshowshowthisvariation resultsinawarptothecloud.Becausetheplaneofsymmetryofth edustbands(andthe backgroundcloud)varywithheliocentricdistance,theclou dtakesonawarpedstructure. Theforcedandproperelementshaveavectorialrelationship inwhichtheforcedand propercomponentsoftheinclination/nodeandeccentricit y/pericenteraddvectorially toyieldtheosculating(instantaneous)elements.Thisvectori alrelationshipisshownin Figure 2-5 fortheinclinationandnodeandasimilarrelationshipexistsf ortheeccentricity andpericenter.Theprecessionofthenodes(andpericentersi ntheeccentricity-pericenter component)ofFigure 2-5 resultintheparticleslyingalongacircleinIcos()-Isin() space(orecos( )-esin( )space).Fittingacircletotheosculatingelementsofthepar ticle orbitsallowstheforcedandpropercomponentsoftheorbits tobecharacterized.Thisis knownasthe\particle-on-a-circle"method(Dermottetal. ,1992)andisthemethodused tocharacterizetheresultsofthenumericalsimulations.Anexa mpleofthetechnique isshowninFigure 2-6 .Thisgureshowstheosculatingelementsoutputfromthe simulationsforarangeofsemimajoraxes.Theorbitalelements ateachsemimajoraxis canbeseentoliealongacircleinIcos()-Isin()space.Usingtheve ctorialrelationships showninFigure 2-5 ,theforcedandproperelementscanbedeterminedforeachdi screet semimajoraxisrange.Theosetofthecenterofthecirclefromt heoriginisaresultof themagnitudeoftheforcedelementsandthemagnitudeofthe radiusofthecircleisa resultoftheproperelements.Theforcedandpropercomponent softheinclinationand eccentricityarecharacterizedusingthismethodandenteri ntothemodelalongwitha randomizednodeandpericentertocreate O (10 6 )orbits,theincreaseinorbitsneeded tobuildasmooth3-Dmodel.Theobviousincreaseinthedispersio natthesmaller semimajoraxesofFigure 2-6 shouldbenotedandthecauseofthisdispersionisthenext topicofdiscussion. 48

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Astheparticlesaredecayinginsemimajoraxisacrossthemainb eltduetotheeect ofthedragforces,theyevolvethroughseveralmeanmotionreso nancesandthe 6 secular resonance.Theeectofpassagethroughtheseresonancesisanincr easeinthedispersion oftheproperandforcedelementsoftheparticles.Thiscanbe seeninFigure 2-7 ,which showsthevariationoftheproperinclination(panelA)andfor cedinclination(panel B)fromtheresultsofnumericalsimulations.Thesepanelsshowth evariationofthe inclinationandthedispersionintheinclinationasafunctio nofsemimajoraxisforseveral particlediameters.Theparticles,whichhavebeenreleasedfr omtheVeritasasteroid family(10 inclination,3.16AU),aredecayinginsemimajoraxisthrough theresonances. Themeanproperinclinationisshownwith1 errorbarsfor3particlediameters:20 m (greendiamonds)whichareosetby-5 fromthesourceinclinationforclarity,100 m (redtriangles),and500 m(bluesquares)whichareosetby+5 fromthesource. Thedashedlinesrepresentthelocationsofmean-motionresona nceswithJupiterand thedottedlineisthe 6 secularresonance.Thedispersioncanbeseentoincreaseas theparticlesreachsmallersemi-majoraxisvaluesandhavepa ssedthroughmoreofthe resonanceregions.Theeectoftheresonancepassageisclearlysiz edependent.This sizedependenceisadirectresultofthesizedependenceoftheP -Rdragtimescalesfor theparticlestodecayintotheinnersolarsystem.Becausethela rgeparticles'semimajor axesaredecayingmoreslowly,duetolongerdragtimescales,th eseparticlesspendlonger intheregionswheretheresonancescanaecttheirorbitsandt heeectsarethusmore pronouncedfortheseparticles(Kehoeetal.,2007a).Whilet he20 mparticlesevolveinto theinnersolarsystemrelativelyunchanged,the100 mparticlesshowamarkedincrease indispersioninsideof2AU,andthe500 mparticlesshowanevengreaterdispersion. Theforcedinclination,shownintherightpanel,showsasimila rdependenceonsize. Theexistenceofthedustbandstructureisduetothecommonforc edandproper elementsoftheparticlesproducingtheband(dueinparttot heircommonancestor) andthedispersionoftheseelementsresultsinthelossofthedustb andstructure. 49

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ThiseectcanbeseeninFigures 2-8 { 2-10 whichshowthedustbandstructureat discreetsemimajoraxisincrementsfor20 m,100 m,and500 mdiameterparticles, respectively.Sincethe20 mparticles'orbitalelementsshowlittleperturbation frompassagethroughtheresonancesinFigure 2-7 ,thedustbandstructureofthese particles(Figure 2-8 )remainsclearlydenedintotheinnersolarsystem.Thelarger particles(Figure 2-9 and 2-10 ),though,whichdoexperienceincreaseddispersionfrom theresonancespassages,showadustbandstructurewhichappearsto fadeintothe backgroundcloudaround2AU.Althoughthedustbandstructureis decayingfor theselargerparticles,thedustitselfstillpersistsintotheinne rsolarsystem.Thus, themagnitudeofthedustrepresentedinthedustbandstructurew illonlyaccountfora portionofthetotalcross-sectionalareaofasteroidaldustinth ecloud.Bybuildingmodels oftheasteroidaldustcomponentofthecloudbasedontheintegr ationsofthedustorbits intotheinnersolarsystem,thiseectwillnaturallybeaccount edfor,thusallowingfora modelofthetotalasteroidalcomponent,whichisconstrained bythedustbandstructure. Itshouldbenotedherethatthedescriptionofthedynamicsfor dierentparticlesizes isactuallyadescriptionofdierentvaluesof (Equation 2{3 ).Theapproachisthatthe particlesarerepresentedinthenumericalsimulationsas\ -values",asitisthisproperty oftheparticlethatcontrolsitsdynamicalevolution.These valuesarethenconverted intoparticlediametersbymakingassumptionsabouttheparti cledensityandshape.We usespheresofthestandardasteroiddensityof2{3g/cm 3 (e.g.Hiltonetal.,2002),but notethatiftheparticleswereexceptionallyporousorhada ake-likestructure,thevalues assumedforthedensityandradiationpressureeciencyfactormig htvary.Thiswould notchangetheresultsofthenumericalsimulationsorthedyna micspresentedhere,but mightslightlyvarytheparticlesizesastheyarediscussedinthi swork. 2.3.3CreationofModels Inordertocomparetheorbitaldistributionsfoundfromnume ricalsimulationsto actualobservations,amechanismbywhichtheseorbitaldistribu tionscanbevisualized 50

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isrequired.TheFORTRANcodeSIMUL(Dermottetal.1988;Groga netal.,1997)was developedforthispurpose.Inshort,theSIMULsuiteofcodesall owthecreationofa3-D modelofthecrosssectionalareaofthedistributionofdustthat wouldresultfromagiven orbitaldistribution.This3-Dmodelisthenvisualizedaslin e-of-sightthermalemission proleswhichcanbecompareddirectlywithobservationaldat a.TheSIMULalgorithm isbasedontheideathatacloudcanberepresentedbyalargenum berofdustparticle orbits.Thetotalcrosssectionalareaofthecloudisdividedeq uallyamongtheorbits (whichwillbeweightedtocreateasizeandsemimajoraxisdistr ibutionatalaterstep). Usingtheforcedandproperinclinationandeccentricitychar acterizedinthenumerical simulations,togetherwitharandomlychosensemimajoraxis(fr omagivenrange)and randomizednodesandpericenters,orbitsarecalculated.Th eparticlesaredistributed alongtheorbitsaccordingtoKepler'slaw.The3-Dspaceisdi videdinto O (10 7 )ordered cells,whicharelledwithcross-sectionalarearepresentativeo ftheorbitsthatpass throughthecell.Inthisway,themodelgeneratesalargethr eedimensionalarraywhich describesthespatialdistributionofthecross-sectionalarea.M odelsofthisnatureare madeforeachparticlesizeandthenweightedappropriatelyt orepresentagivensize distribution.Themodelisthenconvertedtoline-of-sightth ermalemissionprolesthat matchtheobservinggeometryofIRAS(oranytelescope)bycalcu latingtheSun-Earth distanceandeclipticlongitudeofEarthattheobservingtime andsettingupappropriate coordinatesystems.Theseprolescanbecompareddirectlytothe IRASscansinorderto constrainthepropertiesofthedustcomposingthebands(Secti on 2.4.1 ). 2.4Models 2.4.1Parameters Themodelsaredescribedbyseveralparametersofthedustdistri bution.These parametersareconstrainedviacomparisonwiththeobservatio nsanddescribethe size-frequencyandheliocentricdistributionsofthedustand thetotalcross-sectionalarea. Themathematicaldenitionsoftheparametersaredescribedh ere. 51

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2.4.1.1Size-frequencydistribution Thesize-frequencydistributionofparticlesresultingfroma catastrophiccollisioncan bedescribedbyacumulativepowerlawoftheform N ( D )= 1 3( q ¡ 1) D 0 D 3( q ¡ 1) (2{11) whereN(D)isthenumberofparticleswithdiameter > D,qisthesizefrequencyindex,D istheparticlediameter,andD 0 isaconstantas D 0 = D e [3(2 ¡ q )] 1 = 3 D 0 D max 2 ¡ q (2{12) where D max isthediameterofthelargestfragmentofthedisruptionand D e isthe equivalentdiameteroftheentiredistribution.Adistributi oninaclosedboxincollisional equilibrium(Dohnanyi,1969)isdescribedby q =1.837and,inthiscase,thecross-sectional areaofthedistributionisdominatedbyparticlesatthesmall endofthesizerange.The valueof q =5/3(1.66)representsaturnovervaluewheredistributionsd escribedbyalarger qwillhaveareadominatedbythesmallestparticlesofthedistr ibutionandadistributions describedbyasmallerqwillhaveareadominatedbythelargestp articlespresentinthe distribution.ThiseectcanbeseeninFigure 2-11 ,inwhichthenormalized,cumulative, cross-sectionalareaisshownasafunctionofparticlesize.Thec ollisionalequilibrium valueofq=1.83canbeseentobedominatedbythesmallestpartic lesinthedistribution. Theturnovervaluefordominationoftheareabysmallparticl es( q> 1.66)andlarge particles( q< 1.66)canbeseenintheshapeofthedistributionsdescribedbyq= 1.6and q=1.7.2.4.1.2Heliocentricdistribution Inordertodeterminehowthematerialisdistributedhelioce ntrically,wemust considerthemethodbywhichtheparticlesarecarriedintoth einnersolarsystem.Recall thatP-Rdragisthemaintransportmechanismofdustparticlesf romtheirsourceregions intotheinnersolarsystem.Sincetheseparticleorbitsaredeca yingatarate_ a pr (Equation 52

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2{7 ),thenthenumberoforbitswithsemimajoraxisintherangea{ (a+da)isgivenby N ( a ) da / 1 a pr / a: (2{13) Thus,thespacingoforbitswillincreaseatsmallersemimajoraxe s,neartheSun.The increaseinspacingwillthusacttodecreasethenumberdensityo ftheparticlesatthese smallersemimajoraxes.Butitmustalsobeconsideredthatboththe circumferenceofthe orbitandtheverticalextentoftheparticledistributionwi llbothdecreaseproportional tosemimajoraxisand,thus,eachwillservetoincreasethenumbe rdensityofparticles withsemimajoraxis.Theresultwhenallthreeeectsareconsider edisthatthenumberof densityofparticleswillincreaseas1 =a .Fornear-circularorbits( a r ),theresultisthat thenumberdensityofparticleswillincreaseinverselywithhe liocentricdistance.IfP-R dragweretheonlyforcecontrollingthedistributionoforbi ts,thenwecoulddescribethe heliocentricdistributionofthenumberdensityofparticles by1 =r .However,weknowthat collisionsareplayingaroleintheorbitsoftheparticlesas theydecay.Thereareseveral reasonswhywebelievethatinter-particlecollisionscouldb eimportant,themainofwhich beingthatwestillseethedustbands.Thisisexplainedinthefol lowingargument.Inan analysisofthemid-infraredISO(InfraredSpaceObservatory )data,Reachetal.(1996) ndthatthecontinuumofinterplanetarydustiswelltbyapopu lationdescribedby particlesfromafew10'stoafew100'sofmicronsindiameter .Yetduetotheagesofthe disruptionsthatproducedthebands,weknowthatalltheparti clessmallerthan1mm fromtheoriginaldisruptionhavealreadyevolvedinsideof1A UundertheeectofP-R drag.So,sincemostofthethermalemissionofthecloudisthough ttocomefromparticles muchsmallerthan1mmandtheseparticlesizesfromtheoriginal disruptionhave beenlosttoP-Rdrag,theninter-particlecollisionsmustbepl ayingaroletoregenerate particlesinthesizesproducingthethermalemission.Toaccou ntfortheseadditional eects,wedescribethedistributionofthenumberdensityofpart iclesinthecloudbyan 53

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inversepowerlawas 1 r (2{14) whereristheheliocentricdistanceinAUand isparametertobedetermined.Any positivevalueof willdescribeadistributionwhichisweightedtowardsmallerse mimajor axes.Figure 2-12 showsthevariationofthenumberdensitydescribedbythisequa tionfor twovaluesof ,normalizedto2AU.Itcanbeseenthatbothdistributionsarewe ighted towardstheSun.Thecurveshavebeennormalizedto2AUtorep resentthedierent amountsofthetotalasteroidaldustcomponentthatwouldbere presentedbyagiven amountofdustbandmaterial(at 2AU)forvaryingvaluesof .Thisplotalsoshows why,giventhisdistribution,thedustbandmaterialoutside2A Urepresentsonlyasmall portionofthetotalasteroidalcomponent.2.4.1.3Cross-sectionalarea Thetotalamountofcross-sectionalareainthedustbandsisusedt odeterminethe magnitudeoftheasteroidalcomponent.Thecomparisonofthem odelstoobservations allowsustoconstrainnotonlythetotalamountofarea,butal sotherelativecontributions fromtheindividualfamilysources.2.4.2ComparisontoIRASdata Althoughtherearenumerousobservationsofthezodiacalclou d,basedonits resolutionandskycoverage,theIRASdatasetremainsthebestfor ourpurposes.Herewe willdiscussthedetailsoftheIRASobservationsandthetechniq uesusedincomparingthe modelstotheobservationstoconstraintheparametersofthed ust. IRASobservations .TheIRASspacecraftwasonapolarsun-synchronousorbit. Thefulldetailsofthesatellite'sobservingcampaignaregiv enintheIRASExplanatory Supplement(Beichmann,1985),butwewilldiscussherethecon ceptspertinenttothis investigation.Ineachorbit,thetelescopescannedtwodiamet ricallyoppositeareasof thesky.ThepathofthesatellitefromtheSouthPoletotheNorth Polewastermed theLeadinglegandthelineofsightofthetelescopewasinthed irectionoftheEarth's 54

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circumsolarmotion.Thesecondhalfoftheorbit,fromtheNorth totheSouthpolewas labeledtheTrailinglegandthelineofsightofthetelescopep ointedinthedirection oppositetheEarth'smotion.Duringeachscantheanglebetwee ntheSun,Earth,and lineofsightofthetelescopewaskeptataconstantangle,known astheelongationangle. Thisanglerangedfrom85 to95 .Inordertoobtaincompleteskycoverage,thecelestial spherewasdividedinto\lunes",denedtobetheareabetweentw oeclipticmeridians 30 apart.Overthecourseoftheapproximatetwoweekperiodrequ iredtoscananentire lune,thesatellitesystematicallysteppedinsolarelongationa ngle.Thevalueofthe elongationanglesuccessivelyincreasedfrom85 to95 inaTrailingluneandsuccessively decreasedfrom95 to85 inaLeadinglune.AswillbediscussedinSection 3.2 ,this aspectoftheobservingstrategyofthetelescopeprovedveryusef ulinourendeavorto coaddtheobservationstosearchforfainterstructures.Thescan sweretakenover4 wavebands, =12,25,60,and100 m.Thedustbandemissionpeaksinthe25 m wavebandandthebandsarealsovisibleinboththe12 mand60 mbands,butthereis toomuchgalacticcontaminationforthebandstobeseeninthe 100 mdata. Comparisonofthemodelstotheobservations .Inordertoconstrainthe size-distributionparameter,q,previousdustbandmodelinge orts(Groganetal.,2001) usedatechniqueofcomparingthemagnitudeofthebandmodels totheobservations inallthreewavebands.Theyfoundthatthemagnitudeofthein tensityinthedust bandmodelsvaried,dependingonthesize-distributionparam eter,inthethreedierent wavebandsinsuchawaythatitallowedaconstraintonthesize-d istributionparameter. Thesemodelsshowedaclearover-intensityofbandmaterialint he12 mbandand under-intensityinthe60 mbandwhenthevalueofthesizedistributionparameter, q,wastoohigh.Thisvariationcorrespondedtotoomanysmallp articlesinthemodels andwasusedasamethodtoconstrainthesize-distributionparam eter.Thesemodels, though,onlycontainedparticles100 minsizeandsmaller,duetocomputerlimitations ofthetime.Asdiscussedpreviously,thecurrentmodelscontainp articleswithsizes 55

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upto1mm.Varyingthesizedistributionwiththislargerandmo rerealisticrange ofsizesunfortunatelyresultedinthiswaveband-dependentintensity-variationeect beingtoosmalltobeusedasadistinguishingfactor.Thisisbeca useparticlescanonly emitthermallyatwavelengthsequaltotheirsizeorsmaller.W henthedistributionis describingparticlesbetween1and100 m,aswasGroganetal.,2001,thentheemission variationseentheinthewavebands(12,25and60 m)couldbeusedtodiscriminatethe thesizedistributionpresent.However,whentheparticlesare >> 60 m(astheyarein ourdistributionofupto1mm),thentheamplitudeoftheemissio nseeninthesethree wavebandsnolongerdiscriminatesbetweenthemodelsofdier entsize-distributions. Thus,inordertobeabletoconstrainthevalueofthesize-distri butionoftheparticles present,anewmethodneededtobedevelopedtodistinguishthet s. Thenewtechniquetoconstrainthesize-distributionparamete risbasedinsteadon thevariationoftheshapeandlocationofthedustbandpeaksfo rdierentsize-distributions. Themethodisbasedontheresultfromthenumericalsimulations thatsmallerparticles retaintheirdustbandstructurefurtherintotheinnersolarsyst emthanlargerparticles (Section 3.6.1 andFigures 2-8 { 2-10 ).Sincethemaximumamountofuxwillalways becomingfromthehottestmaterial,theemissionwillbedomina tedbythematerial thatisclosesttotheobserver.Additionally,recallthatthenu mberdensityofparticles isdistributedas1/a,sosmallersemimajoraxeswillcontainmor ematerialthanlarger semimajoraxes.Thedustbandstructure,then,willbedominated bythesmallest semimajoraxisatwhichthestructureisstillintact.Forverysm allparticles,thosefor whichthedustbandstructurepersistsfartherintotheinnersola rsystem,thisisasmaller semimajoraxisthanforthelargerparticles,wholosetheirstru ctureafterpassingthrough theresonancesofthemainbelt.Thusforahighqvalue(moresma llparticles),thearea isdominatedbyduststructurethatisatsmallersemimajoraxest hanforalowerqvalue (morelargeparticles).Becauseofaparallaxeect,themateri alatthesmallersemimajor axesappearstohaveawiderseparationofthedustbandsthanth atatlargersemimajor 56

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axes,ascanbeseeninFigure 2-8 .Tounderstandtheparallaxeect,considertwoparallel lineswithaconstantseparation.Theselineswillappeartohav emoreseparationifmoved closertotheobserverandtheseparationwilldecreaseiftheyar emovedawayfromthe observer.Thissameeectcanbeseenintheseparationofthedustba ndpeaksand allowsaconstrainttobeplacedonthesizedistributionofpart icles.Ifthedustband modelscontaintoomanysmallparticles,theywillhaveatoo-w ideseparationofthe 10 bandpeakswhencomparedtotheobservations.Thistechniquei sdemonstrated byFigure 2-13 whichshowsacomparisonoftheline-of-sightemissionproleofth e modelwithanaveragedIRASobservation.Thedetailsofaverag ingtheobservations willbeexplainedinChapter3,butitissucientheretoknowth atitisanoise-reduced observation.PanelsAandBofthegurerepresenttwodierentvi ewinggeometriesof IRAS,oneintheleadingdirection(A)andoneinthetrailingdi rection(B).Thismodel hasasize-distributionparameterofq=1.83,whichrepresents dominationbythesmallest particlesofthedistribution.Becausethemodel(red)contai nstoomanysmallparticles, the10 bandpeakscanbeeseentobetoowidelyseparatedascomparedto theIRAS observation(blue).Decreasingthevalueofthesizedistributi onparameterwillweightthe modeltowardslargerparticles,whoseinnermostdustbandedgei satalargersemimajor axis,andwilleectivelydecreasetheseparationoftheuxpeaks. Thiscanbeseenin theimprovedtforthemodeldescribedbyasize-distributionpa rameterwithasmallerq valueofq=1.6inFigure 2-14 Inadditiontothisconstraintonthevalueofq,theamountofc rosssectionalareain thebandsisconstrainedbycomparisonofthemodelswiththeob servations.Thetotal amountofcrosssectionalareaandrelativecontributionsoft hesourcesareevidencedin themagnitudesofthedustbandpeaks.Theareaisconstrainedby comparisonwithall3 wavebandsofIRASdata.Itshouldbenoted,though,thattheamo untofareaneededto provideagoodttotheobservationswillvarywithbothqand 57

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Thevalueoftheheliocentricdistributioncanbeconstrained bycomparisonofthe modeltotheobservations.Becausevarying iseectivelylikeweightingthesemimajor axisslicesof,forexample,Figure 2-10 dierently,theshapesofthedustbandstructurein thedierent modelsshouldvarywiththisparameter.Higher valueswhichputmore relativeemphasisontheinnermostdustbandslicesshouldappear smootherthanlower values,sincethedustbandstructureis\spikey"nearthesourcean dbroadensoutat smallersemimajoraxes. 2.5Discussion 2.5.1Results Theresultsoftheconstraintsontheparametersoftheasteroid aldustcomponent ofthezodiacalcloudarepresentedhere.Throughcomparisono fthemodelswiththe observations,usingthemethodsofconstraintjustdescribed,the resultsfortheparameters ofsize-distribution,heliocentricdistribution,cross-sectio nalareaandthemagnitudeofthe asteroidalcomponentofthecloudarenowdiscussed. Size-distribution .Recallthatthemodelwithasizedistributionofq=1.83 (Figure 2-13 )showedatoo-wideseparationofthe10 bandpeaksintheline-of-sight thermalemissionprolesofthemodelascomparedtothecorrespo ndingobservations andrepresentedatoo-highqvalue.TheexampleofFigure 2-14 ,foralowerqvalueof 1.6,showedanimprovedtandthuswestartourdiscussionhere.Acl oseinspectionof Figure 2-14 showsthat,althoughthismodel,describedasizedistributionp arameterof q=1.6,showsanimprovementoverthemodeldescribedbythehig hervalue,theseparation ofthe10 bandpeaksintheline-of-sightproleofthemodel(red)isstil lslightlytoolarge ascomparedtotheobservation(blue).Sincethisvalueofqsti llappearstoincludetoo manysmallparticles,weneedtoiteratethemodeltowardconta ininglesssmallparticles, whichisasize-distributiondescribedbyanevenlowervaluefo rq.Figure 2-15 shows anexampleoftheresultsforamodelwithasizedistributiondesc ribedbyq=1.5.This modelprovidesareasonablygoodttothelocationsofthe10 bandpeaks.Figure 2-16 58

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showsanexampleofthemodelforasizedistributionofq=1.4.Th ismodelalsoprovidesa reasonablygoodagreementwithobservations,butthe10 bandpeakscannowbeseento liealongtheinnermostedgeoftheobservations.Sinceboththe q=1.4andq=1.5models liealongtheinnerandouteredgesoftheapproximatelocati onofthe10 dustbandin theobservations,theydenetheapproximaterangeofthesizedi stributionofthedust. Thissizedistributionrangealsoprovidesagoodtintheotherw avebands.Anexample ofthelineofsightthermalemissionprolesforboththemodelsa ndobservationsin the12 mand60 mwavebandsareshowninFigure 2-17 ,inpanelsAandB(12 m) andpanelsCandD(60 m).Thus,theobservationsarebesttbyacumulativesize distributionparameterintherangeq=1.4{1.5.Becauseallth eparticlessmallerthan 1mmfromtheoriginaldisruptionhavealreadybeenlosttoP-Rd rag(Section 2.3.1.2 ), thissize-distributionisdescribingthecollisionallyevolve dsecondaryproductsofthe originalasteroidaldisruption.Thissizedistributionimplie sthatthecross-sectionalareaof thedustinthebandsisdominatedbythelargestparticlesinth edistribution.Thisrange ofvaluescorrespondstoacumulativeinversepowerof1.2{1.4 oradierentialnumber inversepowerof2.2{2.5. Previousstudieshavefoundsimilarvaluesforthesize-distrib utionparameter,q.The crateringrecordontheLDEF(Long-DurationExposureFacili ty)satelliteindicatedaq ofapproximately1.2(LoveandBrownlee,1993).Anearliermo delingeortundertaken byGroganetal.(2001),foundabesttqvalueof1.43(howevert heseearlymodelswere limitedbycomputingpowertoonlytrackingtheevolutionof dustparticles100 mand smaller).Nesvornyetal.(2006a)alsolookedatthisproblem,b utinsteadusedabroken powerlawtodescribethesizedistribution.Theyfoundaabesttm odeltothedust bandsthatwasdescribedbyabrokenpower-lawfunctionwhich correspondstoavalueof q=1.36{1.46forthedustparticleswithdiameterssmallertha n100 m,butaverysteep valueofq 1.83fortheparticleswithdiametersbetween100 mand1cm. 59

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Cross-sectionalarea .Thetotalamountofcross-sectionalareaofmaterial associatedwitheachfamilyisfoundfromcomparingtheltered modeldustband magnitudestotheobservedmagnitudesinallthreewavebands. Fromthesourceregion inthemainbeltinto1.2AU(forthesizedistributionofq=1.4) ,thetotalamountof cross-sectionalareaofmaterialis2.90x10 9 km 2 forthe10 Veritasband,1.35x10 9 km 2 and7.0x10 8 km 2 forthecentralbands,KarinandBeaglerespectively.Forasize distributionofq=1.5,theareasdecreaseto2.70x10 9 km 2 forthe10 Veritasband, 8.0x10 8 km 2 and3.5x10 8 km 2 forthecentralbands,KarinandBeaglerespectively. Thedecreaseintheareaforthehighervalueofqisduetothefa ctthatthepopulation withthehigherqvaluehasalargerportionofareainthesmall estparticles.Thesesmall particles,recall,providemoredustbanduxperunitareabeca usetheyretaintheirdust bandstructureintosmallersemimajoraxisvalues(thandolarg erparticles)wherethe materialishotter.Thus,intheq=1.4model,thehighervalue sofcross-sectionalareastill provideagoodttotheobservationsbecauseahigherfractiono fthematerialeectively becomespartofthebackgroundcloud. Theamountofcrosssectionalareathatisneededtomodeltheba ndsisalso dependentonthevaluesoftheheliocentricdistributionofp articles, ,describingthe bands.Moreareaisneededtomodelthedustbandsforhigherval uesofthe distribution sincemorematerialwillbeplacedneartheSun,inaregionpro ducingverylittleifany contributiontothedustbandstructure. Theratiooftherelativecontributionsofthefamiliesisal sodetermined.Forthebest tvaluesofthesizedistribution,q=(1.4{1.5),theratioofth econtributionofareafrom Veritasisapproximatelyafactorof2higherthanthecontri butionfromthecentralband sources,KarinandBeagle.Nesvornyetal.(2006a)alsondasimila rvalueforthisratio. Heliocentricdistribution .Themodelingworkalsohelpsusputsomeconstrainton theheliocentricdistributionoftheasteroidalmaterialint hezodiacalcloud.Asdiscussed inSection 2.4.1.2 ,thedistributionismodeledasaninversepowerlaw.Forhighe rvalues 60

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ofthepowerparameter, ,morematerialislocatedclosertotheSun.Varyingthe parameter is,then,eectivelylikeweightingthesemimajoraxisslicesof ,forexample, Figure 2-10 dierently.Thus,intheory,thedierentvaluesoftheparamet er describing thedistributionshouldresultinmodelswithdustbandsthatapp earmore\spikey"(for lower )or\smooth"(forhigher ).Inpractice,though,themagnitudeofthiseectis unfortunatelynotsignicantenoughtoallowatightconstrain ttobeplacedonthevalue of .Figure 2-12 showswhythisistrueforrealisticvaluesof .Asthegureshows,the magnitudeofmaterialintheinnersolarsystemisenhancedover thatofthedustband region(2{3AU).Thesetwo curveshavebeennormalizedtotheir2AUvalues,but inrealitychangingthevalueof increasesthetotalareainthebackgroundcloudand thedustbands(thewholecurveisshiftedup).Foragiven value,though,therelative variationofthecontributionacrossthedustbandregionisve rysmall,asthecurveis ratheratinthisregion.Sowhilechangingthevalueof willaecthowmuchdustis neededtomodelthedustbands,itonlysubtlychangestheshapeof theband.Because thisdierencecan'tbediscernedthroughcomparisonwiththeo bservations,thevalueof cannotbetightlyconstrained.Beingthisasitis,wewillexpl aintheeectsoftherange =1{2ontheotherparametersandonthetotalasteroidalcontr ibutiontothecloud. Allofthemodelsdiscussedsofarhaveaheliocentricdistribution describedby =1. Modelswithaheliocentricdistributiondescribedby =1.5and =2werealsocreated. Examplesofthemodelsfora =2distributionareshowninFigure 2-18 .Theshapeofthe modeldustbandsdoesn'tvarysignicantlyfrom =1inFigure 2-16 andthusthevalueof cannotbeconstrained.Thusweinvestigatetheeectsofareali sticrangeof =1{2on theotherparameters.Thisrangeischosenbecauseoftheexpect ed =1valueforaP-R dragdistributionoforbitsandbecausepreviousinvestigatio nshavefoundsimilarvalues. Avalueof 1.3wasobservedbythe Helios and Pioneer10/11 spaceprobes(Leinert etal.,1983).Parametricmodelsofthecloudalsopredictava lueof =1.3(Kelsalletal., 1998). 61

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Theamountofcross-sectionalareaneededtotthebands,asexpla inedinthe previoussection,doesvarywiththeheliocentricdistributi on.Becauseoftheweighting towardssmallerheliocentriclocationswherethedustbandstr uctureisfaintorabsent,the totalamountofareacanbeincreasedinthe =2modelssignicantlywhilestillobtaining agoodttothemagnitudeofthebands,sincemostofthematerialb ecomespartofthe low-frequencycomponentofthebands.Thecross-sectionalarea neededforthe =2model toproduceagoodttotheobservationsis4.7x10 9 km 2 forthe10degreeVeritasband, 1.50x10 9 km 2 and7.5x10 8 km 2 forthecentralbands,KarinandBeaglerespectively. Similarplotsarefoundfora =1.5andtheareatis4.50x10 9 km 2 forthe10degree Veritasband,1.50x10 9 km 2 and7.5x10 8 km 2 forthecentralbands,KarinandBeagle respectively.Thus,fora rangeof1{2,thetotalamountofcrosssectionalareaneeded tottheobservationscanincreaseby50%fromtheformertothel atter. 2.5.2TheAsteroidalContributiontoCloud Oneofthemainresearchobjectivesofthisprojectwastodete rmineanestimate ofthemagnitudeoftheasteroidalcomponentofthecloud.Aspr eviouslydiscussedin Section 2.3.2 ,thedustbandstructureisconstrainedtothemainasteroidbelt duetothe dispersionoftheorbitalelementsoftheparticlesastheypass throughthesecularand meanmotionresonances(Figure 2-10 ).Becauseofthis,thedustbandstructureitself representsonlyasmallportionofthetotalcontributionofdu stfromasteroidalsources tothezodiacalcloud.Tocalculatetheactualamount,thedu statsmallersemimajor axeswhichhavealreadylosttheirdustbandsignaturemustalsobe accountedfor. Fordustthatisdistributedheliocentricallyinverselypropo rtionaltosemimajoraxis (magniedbythefactthatmostoftheuxwillcomefromthesmalle stsemimajoraxes wherethedustishottest),thedustbandsrepresentonlythetail endoftheasteroidal contributiontothezodiacalcloudemission.RecallFigure 2-12 ,whichshowshowthe cross-sectionalareaofdustinnear-Earthspaceincreasesforthe dierentvaluesof theheliocentricdistributionparameter, .Thesetwocurvesarenormalizedto2AU 62

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toillustratethechangeinthetotalamountofdustat1AUthatw ouldresultfroma givenamountofdustinthebands(whicharedominatedbytheir 2AUvalues).This exemplieswhatasmallportionoftheasteroidalcontribution thedustbandsrepresent. However,whenthedustinside2AUisaccountedfor,theproporti onoftheclouddueto asteroidalsourceincreasessignicantly.Themagnitudeofthea steroidalcomponentof thezodiacalcloud,accountingforallthematerialfromthe mainbeltinto1.2AUand withthedustparametersdescribedbycomparisonofthemodelst otheobservations, isshowninFigure 2-19 .Theintensityinthe25 mwavebandasafunctionofecliptic latitudeisshownfortheIRASunlteredcloudobservationingre en,themagnitudeof theasteroidalcomponentfromthemodelswiththeheliocentr icdistributiondescribed by =2inred,andthemagnitudeif =1inpurple.Overtheentiresky,thedustbands contribute6{13%ofthezodiacalclouduxfortherangeof valuesshown.Intherange of § 50 aboveandbelowtheecliptic,theasteroidalcontributionac countsfor8{16%of theux,andfortheregion § 10 aboveandbelowtheecliptic,thepercentageincreases evenfurtherto13{24%forthe valuesrangingfrom1{2respectively.Similarvalues werefoundinpreviousworksbyNesvornyetal.(2006a).Theast eroidaldustassociated withthedustbandsourcesrepresentsatleastaminimumvalueoft hemagnitudeof theasteroidalcomponentofthezodiacalcloud.Thereisnore asontothinkthatthe backgroundasteroidpopulationisn'talsoproducingdust{e.g. throughsheddingofdust followingspinupsornon-catastrophicdisruptionswhichrele asesomedustbutdon't disrupttheasteroidintoanasteroidfamily.However,becauseth emechanismofdust productionthatcreatedthebandappearstobethatofrecent catastrophicdisruptions, modelingofthenaturepresentedhereprovidesvirtuallynoi nformationonthedust producedbythoseothermethods.Theimplicationofthisfacti stwofold.Itmeansthat wedetermineonlyaminimumoftheasteroidalcomponentofthe cloudanditalsomeans that,thoughwecansaysomethingabouttheheightofthedust\spi kes"ofFigure 1-8 (andwillinSection 3.6.4 ),wecan't,however,determinethebackgroundenvelopeofd ust 63

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production.Recall(fromSection 1.6 )thatitwasoriginallythoughtthatthefamilyand non-familyasteroidswereproducingdustinthesameway.Since asteroidfamiliesaccount for 30%ofthemainbeltasteroidpopulation,thetotalasteroidal componentofthe cloudwasdeterminedbyincreasingthemagnitudeofdustfound fromthedustbands (andhencethefamilies)byafactorof3toaccountforallaster oidalsources.Sincethis earlyworkdeterminedavalueofabout30%forthedustbandcon tribution,asteroidswere thoughttocontribute90%ofthezodiacalcloudemission(Durd aandDermott,1997). Sincethefamiliesproducingthebandsarenowthoughttobep roducingdustinavery dierentwaytothatofthebackgroundasteroidpopulation,no suchextrapolationcan nowbemade.2.5.3FutureWork Thisworkrepresentsanon-goingiterativeprocessthathasma nyavenuesforfuture work|afewofwhichareexplainedhere.Themainareaoffutur edevelopmentisthe inclusionofinter-particlecollisionsinthedynamicalevol utionofthedustparticles.There alsoexistssomeyet-unstudiedsub-structurewithinthedustbands themselves,manifested inthevariationofthemagnitudesaroundthesky. Inclusionofcollisions .Inter-particlecollisionsareknowntobeimportantinthe detailedevolutionofthezodiacalclouddustparticles,buta renotyetincludedinour model.Includingtheseeectsisadicultprocess,ascomputerli mitationspreventthe trackingofindividualparticlesresultingfromaninter-pa rticlecollision.Althoughitis notpossibletofullyincludethedynamicsofallparticlesund ergoingbothdynamical andcollisionalevolution,characterizationscanbemadeto approximatetheirinclusion. Thereareseveralwaysinwhichwewouldexpectcollisionstova rythedynamicsandthe resultingdistributions.Forasystemundergoingcollisionalevo lution,wewouldexpect thevalueofqtovaryslightlyforeachsemi-majoraxisandfore achsourcepopulation, sincethebodiesdisruptedatdierenttimes.Allowingthisparam etertobeadjusted independentoffamilyandsemimajoraxisisonepossibleimprov ement.Also,thesmaller 64

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particlesaremorelikelytobedisruptedintoevensmallerpar ticlessincethecollisional lifetimeisproportionalto p D (Wyattetal.,1999).Thismayresultinabrokenpower-law distributiondescribingthepopulationofparticles.Inclusio nofdierentqvaluesfor dierentsizesofparticlesinthepopulationcanapproximate this. Itshouldbenotedthat,althoughitmightseemthatasimpleappr oximationto includecollisions,sincethelargerparticlesbreakupintosma llerparticles|creatingmore smallparticlesandlesslargerparticles,istojustincreasethe valueofq.However,there isacollisionalcascadeofparticlesthatextendsfromthesmal lesttothelargestparticles inthepopulation.Theinterplayofthiscascadeisacomplica tedone,asparticlesinthe cascadeareadditionallybeingremovedduetoP-Rdragandrad iationpressure.Although theseprocessespreferentiallyremovethesmallestparticles,th esesmallparticlesactasthe bulletsthatbreakupthelargerparticles,sothewholecascade isaected. Substructurearoundsky .Inthecourseofcreatingthemodelfortheformationof thepartialdustband(whichwillbediscussedinChapter3),tswe redonetodetermine thevariationofthemagnitudeofthe10 bandaroundtheskyandwhatwasrevealed wasthatthe10 bandshowsinterestinglongitudinalvariation.Aninvestigati onofthis substructure,perhapsarelicofformationoftheband,mayhol dadditionalinformation, possiblyaboutthenatureofthedustintheband,thedynamicalst ructureoftheband, andpossiblyevenprovidesomeinformationonthewayinwhichast eroidsinjectdustinto thecloudtoformadustband. 65

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Figure2-1.Datingthefamilies.Theagesoftheasteroidfamil iesaredeterminedthrough backwardintegrationoftheorbitsofthefamilymembers.Anex ampleis shownherefortheKarinfamily.Panelashowsthetemporalvari ationofthe nodallongitudeandpanelbshowsthevariationfortheperihe lionargument forthemembersoftheKarinfamilyfromtheircurrentvalues backwardsin time.Therecanbeseenhereasingleepochatwhichallthefamil ymembers havecommonnodesandpericentersandwerethuslikelyasingl e,larger body.Thisepochistakentobethedateofthedisruption|5.8 § 0.2Myr. Throughthismethod,wealsoknowtheagesofseveralotheraster oidfamilies, includingtheotherfamiliesthoughttobethesourcesofthed ustbands, VeritasandBeagle.TheseagesaresummarizedinTable 2-1 .Thisability todatethedisruptionshelpedleadtothecurrentideathatth easteroidal componentofthezodiacalcloudmaybegeneratedthroughrec ent(withinthe last10Myryears)collisionaleventsintheasteroidbelt.[Repr oducedwith permissionfromNesvornyetal.,2003.Therecentbreakupofana steroidin themainbeltregion(Figure2).Nature417.] 66

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Table2-1.Propertiesofselectedasteroidfamilies FamilyProperinclinationAgeSemimajoraxisPrecursordiame ter Veritas9.35 8.3 § 0.5Myr2.886AU140km Karin2.11 5.8 § 0.2Myr3.169AU27km Beagle1.34 10Myr3.157AU20{62km 67

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Figure2-2.Theformationofadustband.Panel(a)showsalatit ude/longitudeskymap andpanel(c)showsthecorrespondingorbitalorientationfor theasteroid familyparticles(withJupiter'sorbitshownforreference) over3timesteps. Whenanasteroidbreaksup,thematerialspreadsoutaroundthe orbit formingaringofmaterialonatimescaleofafewhundredtoafe wthousand yearsduetothe vofthedisruption(toppanel).Onalongertimescalethe nodesbegintoprecessaroundtheskyduetoperturbationsfrom Jupiterand dustbandstructurebeginstoform(middlepanel).After10 5 {10 6 years,the nodesoftheparticlesarecompletelyrandomizedaroundthe eclipticanda fulldustbandpairhasbeenformed(bottompanel).Thepresenc eofthedust bandstructurestemsfromtheharmonicoscillatormotionofthe particles inandoutoftheplaneof theecliptic,causingthemtospendmoretime attheextremesoftheirpositionandcreatinganoverdensityi nthesurface brightnessasshowninpanel(b),resultinginadustbandpair.[R eproduced withpermissionfromSykesandGreenberg,1986.Theformation andorigin oftheIRASzodiacaldustbandsasaconsequenceofsinglecollisio nsbetween asteroids(Figure1).Icarus65.] 68

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Figure2-3.Inclinationofthedustbandmidplane.Variation softhelatitudesofthe medianpointsseparatingthenorthernandsoutherncomponent oftheten degreebandasseenbyIRASintheleadingandtrailingdirectio ns(openand closedcirclesrespectively).Thesinusoidalvariationimplie saninclination andthelongitudeswheretheleadingandtrailingdataisequ alandopposite correspondtothenodesoftheplanes,withtheamplitudecorre spondingto themagnitudeoftheinclination.[Reproducedwithpermissio nfromGroganet al.,2001.Thesize-frequencydistributionofthezodiacalcl oud:evidencefrom thesolarsystemdustbands(Figure5).Icarus152.] 69

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Figure2-4.Schematicofinclinationofthedustbandmidplan e.Schematicshowing thecross-sectionofthedustbandsforthecaseofaconstant(rstpan el) andheliocentriciallyvarying(secondpanel)valueofthefo rcedinclination. Thedustbands,whichareseparatedbytwicetheproperinclinat ion,are centeredonaplanewhichisinclinedtotheeclipticbythefo rcedinclination. [ReproducedwithpermissionfromKortenkampS.etal.,2001.S ourcesand orbitalevolutionofinterplanetarydustaccretedbyEarth( Figures2and7). In:B.Peucker-Ehrenbrink,B.Schmitz,(Eds.)Accretionofex traterrestrial matterthroughoutEarth'shistory,Kluwer,NewYork,pp.13-3 0.] Table2-2.Observationalfeatures StructuralfeatureAscendingnodeInclination Jupiter'sorbit100 1.31 Dustbands( > AU)99.9 § 7.8 1.16 § 0.09 Backgroundcloud( > 1AU)58.4 § 2.3 1.49 § 0.07 Backgroundcloud(at1AU)70.7 § 0.4 | 70

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I p I I f W f W p W Re(y) = I cos W Im(y) = I sin W Figure2-5.Forcedandproperelements.Thevectorialrelati onshipbetweentheosculating, proper,andforcedelementsinIcos-Isinspace.Theforcedele mentsdene thecenterofthecircle(planeofsymmetry)andtheproperele mentsdene theradius(magnitudeaboveplaneofsymmetry)ofthecircleo nwhichthe particleslie.Thevectorialsumoftheforcedandproperelem entsyieldsthe osculating(instantaneous)elements.Theproperelementsarei nherentto theinitialconditionsofthesystemandtheforcedelementsre presentthe perturbationsinthesystem.Asimilarvectorialrelationshipe xistsforthe eccentricityandpericenter. 71

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-20 0 20 3.17 AU 3.05 AU 2.94 AU 2.82 AU -20 0 20 2.70 AU 2.56 AU 2.42 AU 2.27 AU -20 0 20 -20 0 20 2.11 AU -20 0 20 1.93 AU -20 0 20 1.75 AU -20 0 20 1.51 AU I cos WI sin W Figure2-6.Particle-on-a-circle.Theosculatingelements outputfromthenumerical simulationsareshownatdierentsemimajoraxissnapshotsfor100 m dustparticlesreleasedfromthedisruptionoftheVeritasaster oidfamily. Theelementslieonacircleandtstothecircledenetheforce d(center ofthecircle)andproper(radiusofthecircle)elementsoft hedistribution. Thesecharacterizationsareusedtogenerateordersofmagnit udemoreorbits inthe3-Dgridmodel.Thedispersionintheparticlesthatcause sthemto deviatefromthecircleatsmallersemimajoraxesisthesameeec tthat causesthedustbandstructuretodisperseintothebackgroundinsi milar regions.[ReproducedwithpermissionfromKehoeetal.,2007a. Theeectof inter-particlecollisionsonthedynamicalevolutionofaste roidaldustandthe structureofthezodiacalcloud(Figure1).ESA-SP-643.] 72

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A 2 3 0 10 20 Veritas 4:1 3:1 5:2semimajor axis (AU)inclination (degrees) B 2 3 0 2 4 6 Jupiter Veritassemimajor axis (AU)inclination (degrees) Figure2-7.Properandforcedinclination.Variationofthe orbitalelementswith semimajoraxisforparticlesofdierentdiameters.A)Themeanp roper inclination(leftpanel)with1 errorbarsisshownasafunctionofsemimajor axisforparticlesreleasedfromtheVeritasfamily(at10 inclinationand3.16 AU).The20 mdiameterparticles(greendiamonds)areosetby-5 ,the 100 mdiameterparticles(redtriangles)areshownatthebreakupi nclination, andthe500 mdiameterparticles(bluesquares)areosetby+5 .The dashedlinesrepresentthelocationsofmean-motionresonance swithJupiter andthedottedlineisthesecularresonance.Thedispersioncanb eseento increaseastheparticlesreachsmallersemimajoraxisvalues,w iththeeect morepronouncedforthelargestparticles,whichspendthelong esttimeinthe regionwheretheresonancescanaecttheirorbit,duetotheir slowerdecay inwardsunderP-Rdrag.B)Theforcedinclinationshowsasimil ardispersion dependenceonsizeandsemimajoraxis.[Reproducedwithpermissi onfrom Kehoeetal.,2007a.Theeectofinter-particlecollisionson thedynamical evolutionofasteroidaldustandthestructureofthezodiacalc loud(Figures2 and3).ESA-SP-643.] 73

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20 Micron Diameter Particles -20 -10 0 10 20 Ecliptic Latitude 0 10 20 30 Intensity, arbitrary units Figure2-8.Semimajoraxisvariationofthedustbandsstructu refor20micronparticles. Asthedustbandparticlesevolvethroughthesecularandmean-m otion resonancesattheinneredgeofthemainbelt,around2AU,thefo rcedand properelementsofthedustparticlesbegintodisperse(asFigu re 2-5 ).The smallestparticles(20 mparticlesareshownhere),evolveintotheinner solarsystemrelativelyunperturbedandretaintheirdustbandst ructureinto smallersemimajoraxesthantheirlargerparticlecounterpar ts,whichspenda longertimeintheregionswheretheeectsoftheresonancesca nperturbtheir orbits,resultinginmoredispersionstotheirorbitalelements andlossofthe dustbandstructure. 74

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100 Micron Diameter Particles -20 -10 0 10 20 Ecliptic Latitude 0 5 10 15 20 25 30 35 Intensity, arbitrary units Figure2-9.Semimajoraxisvariationofthedustbandsstructu refor100micronparticles. Asthedustbandparticlesevolvethroughthesecularandmean-m otion resonancesattheinneredgeofthemainbelt,around2AU,thefo rcedand properelementsofthedustparticlesaredispersed(asFigure 2-5 ).Without commonorbitalelementsofthedustparticles,thebandstructu recannot persistanditbeginsto'smear'intothebackgroundcloud.This resultsinthe dustbandsbeingconstrainedoutsideofapproximately2AU,even though thedustitselfpersistsinwardstotheSun.Thus,modelsoftheamo unt ofcross-sectionalareaofdustinthedustbandsunderrepresentth etotal asteroidalcontributionofdusttothecloud.Thedustbandstruc tureofthe smallerparticlescanpersistinfartherthanthatofthelarger particleswhich showamorepronouncedeectduetotheirlongertimespentinthe regions wheretheresonancescaneecttheirorbits,resultinginmoredi spersionsto theirorbitalelements. 75

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500 Micron Diameter Particles -20 -10 0 10 20 Ecliptic Latitude 0 5 10 15 20 25 30 35 Intensity, arbitrary units Figure2-10.Semimajoraxisvariationofthedustbandsstruct urefor500micronparticles. Asthedustbandparticlesevolvethroughthesecularandmean-m otion resonancesattheinneredgeofthemainbelt,around2AU,thefo rcedand properelementsofthedustparticlesaredispersed(asFigure 2-5 ).Without commonorbitalelementsofthedustparticles,thebandstructu recannot persistanditbeginsto'smear'intothebackgroundcloud.This resultsinthe dustbandsbeingconstrainedoutsideofapproximately2AU,even though thedustitselfpersistsinwardstotheSun.Thus,modelsoftheamo unt ofcross-sectionalareaofdustinthedustbandsunderrepresentth etotal asteroidalcontributionofdusttothecloud.Thedustbandstruc tureofthe smallerparticlescanpersistinfartherthanthatofthelarger particleswhich showamorepronouncedeectduetotheirlongertimespentinthe regions wheretheresonancescaneecttheirorbits,resultinginmoredi spersionsto theirorbitalelements. 76

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200 400 600 800 1000 Particle Size (microns) 0 1 2 3 Normalized Cumulative Cross Sectional Area q=1.83 q=1.7 q=1.6 Figure2-11.Sizedistribution-q.Thedistributionofthecum ulativecrosssectional areawithparticlesizeisshownforthreesizedistributioncurv es.Avalue ofq=1.83representsasystemincollisionalequilibriumandthe turnover valueforadistributionwhosecrosssectionalareaisdominated bythesmall particlestoonedominatedbythelargeparticlesisq=1.66, ascanbeseenin thedierencebetweenq=1.6andq=1.7curves. 77

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1.0 1.5 2.0 2.5 3.0 Heliocentric Distance 0 1 2 3 4 r ^g g =1 g =2 Figure2-12.Heliocentricdistribution .Theheliocentricdistributionofarea,described byaninversepowerlaw, ,isshownfor2dierentvalues.Moreof thematerialislocatedclosertotheSunforanypositivevalue of .A distributiondescribedby =1isexpectedifthedynamicsoftheparticles arecontrolledonlybyP-Rdragwithnocollisions.Observation alconstraints fromHelios/Pioneerspaceprobesyieldavalueof =1.3.Thequalityof thecurrentdatapreventsatightconstraintfrombeingplace donthis parameterand,thus =2cannotbeexcludedandisalsoshown.Thevalues arenormalizedat2AUtorepresentagivenamountofmateriali nthedust bands(whichexistprimarilyoutside2AUandwhoseuxisdominat edby theregionjustinside2AU).Thedierenceinthemagnitudeofmat erialin near-Earthspaceresultingfromthesetwodistributionsforthe samedust bandareawouldbequitedierent. 78

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A -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.83 g =1 L 405 B -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.83 g =1 T 303 Figure2-13.Modelwithasizedistributionq=1.83for =25 m.Comparisonofthe models(red)totheaveragedIRASobservations(blue)forasize distribution powerlawparameterofq=1.83.The =25 mscantakenintheleading (panelA)andtrailing(panelB)directionsoftheEarth'sorb itarecompared tomodelswiththesameobservinggeometry.Theseparationofth e10 bandpeaksinthemodelaretoowidecomparedtotheobservatio nandthis indicatesthatthemodelisweightedtooheavilytowardsasma llersemimajor axisduetotoomanysmallparticlesinthedistribution,thusi ndicatingthe valueofqistoohigh. 79

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A -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.6 g =1 L 405 B -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.6 g =1 T 303 Figure2-14.Modelwithasizedistributionq=1.6for =25 m.Comparisonofthe models(red)totheaveragedIRASobservations(blue)forasize distribution powerlawparameterofq=1.6.The =25 mscantakenintheleading (panelA)andtrailing(panelB)directionsoftheEarth'sorb itarecompared tomodelswiththesameobservinggeometry.Theseparationofth e10 bandpeaksinthemodelaretoowidecomparedtotheobservatio nandthis indicatesthatthemodelisweightedtooheavilytowardsasma llersemimajor axisduetotoomanysmallparticlesinthedistribution,thusi ndicatingthe valueofqistoohigh. 80

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A -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.5 g =1 L 405 B -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.5 g =1 T 303 Figure2-15.Modelwithasizedistributionq=1.5for =25 m.Comparisonofthe models(red)totheaveragedIRASobservations(blue)forasize distribution powerlawparameterofq=1.5.The =25 mscantakenintheleading (panelA)andtrailing(panelB)directionsoftheEarth'sorb itarecompared tomodelswiththesameobservinggeometry.Theseparationofth e10 bandsinthemodelareveryslightlytoowidecomparedtotheob servation. Theagreementofthemodelwiththeobservationsshowsthatq=1 .5can'tbe excludedasthesizedistributiondescribingthedust. 81

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A -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.4 g =1 L 405 B -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.4 g =1 T 303 Figure2-16.Modelwithasizedistributionq=1.4for =25 m.Comparisonofthe models(red)totheIRASobservations(blue)forasizedistribut ionpower lawparameterofq=1.4.The =25 mscantakenintheleading(panelA) andtrailing(panelB)directionsoftheEarth'sorbitareco mparedtomodels withthesameobservinggeometry.Theseparationofthe10 bandpeaks inthemodelisveryslightlytoonarrowascomparedwiththeob servations. Theagreementofthemodelwiththeobservationsshowsthatq=1 .4can'tbe excludedasthesizeparameterdescribingthedistributionofd ust. 82

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A -30 -20 -10 0 10 20 30 Ecliptic Latitude 0.0 0.5 1.0 1.5 Intensity MJy/Sr q=1.4 g =1 L 246 l =12 B -30 -20 -10 0 10 20 30 Ecliptic Latitude 0.0 0.5 1.0 1.5 Intensity MJy/Sr q=1.4 g =1 T 303 l =12 C -30 -20 -10 0 10 20 30 Ecliptic Latitude 0.0 0.5 1.0 1.5 Intensity MJy/Sr q=1.4 g =1 L 246 l =60 D -30 -20 -10 0 10 20 30 Ecliptic Latitude 0.0 0.5 1.0 1.5 Intensity MJy/Sr q=1.4 g =1 T 303 l =60 Figure2-17.Modelwithasizedistributionq=1.4for =12,60 m.Comparisonof themodels(red)totheIRASobservations(blue)forasizedistri bution powerlawparameterofq=1.4.The =12 mIRASscans(A,B)and = 60 mscans(C,D)aretakenintheleadingdirection(B,D)andtrai ling direction(A,C)oftheEarth'sorbitandarecomparedtomodel swiththe sameobservinggeometry.Thissizedistributionwelldescribest hedustband structureinallwavebands. 83

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A -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.4 g =2 L 405 B -30 -20 -10 0 10 20 30 Ecliptic Latitude 0 1 2 Intensity MJy/Sr q=1.4 g =2 T 303 Figure2-18.Modelforaheliocentricdistributionof =2at =25 m.Comparison ofthemodels(red)totheaverageIRASobservations(blue)for asize distributionpowerlawparameterofq=1.4.The =25 mscantakeninthe leading(panelA)andtrailing(panelB)directionsoftheEar th'sorbitfora heliocentricdistributionofmaterialdescribedas =2.Themodelwith =2 shouldshowasmoother,less'spikey'proleduetothelargercontr ibution fromthebroader,innerslices.Thiseectistoosmalltodiscernt hevalue and,although =1appearstobeabettert, =2cannotberuledoutwith thecurrentdata. 84

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-50 0 50 Ecliptic Latitude 0 20 40 60 80 Intensity MJy/Sr 25 m m IRAS Scan g =1 g =2 Figure2-19.Asteroidalcontributiontothezodiacalcloud.B ecausethemajorityof materialislocatedneartheSunforainversepower-lawhelio centric distributionandsincethedustbandstructureitselfisconstrain edtothe main-beltregion,thedustbandsactuallyrepresentonlyasmal lportion ofthetotalasteroidalcontributiontothecloud.Whenthedu stinside 2AUisaccountedfor(forthevaluesof fromthemodels),thetotal asteroidalcomponentofthecloudduetoasteroidfamilysource sisshown. Thiscomponentaccountsforallthedustusedtobuildthemodel swhose Fourier-ltereddustbandsmatchthoseoftheFourier-lteredo bservations. 85

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CHAPTER3 AVERYYOUNG,STILLFORMINGDUSTBAND 3.1Introduction InChapter2wediscussedthethreeknowndustbandpairscreatedi nanasteroidal disruptionwhichalsoproducedanasteroidfamily.Giventhenu mberofasteroidfamilies (e.g.Figure 1-7 ),theobviousquestiontoask,then,is\whydoweseeonlythreed ust bands?".Severaladditionaldustbandshavebeenpostulated,b othbySykes(1988)in theIRASdataandbyReachetal.(1997)intheCOBEdata.However ,severalfactors preventedthesepossiblepairsfrombeinginvestigatedfurther .Insomecasesthiswas duetothelackofasucientsignal-to-noiseratiointheobservat ions,andinother casesitwasduetothefactthatnowell-matchedsourceshadyet beenidentied.The recentdiscoveryofseveralnew,veryyoung( < 1Myr)asteroidclusters(Nesvornyetal., 2006b)nowopensuppossiblenewsourcesofthepostulateddustban ds.Theseyoung disruptions,though,havemuchsmallerparentbodies( 10kmindiameter)thanthose producingthedustbandswecurrentlysee( 30{140km).However,becausethesenewly discoveredasteroidfamiliesaresoyoung,theyhavenotyetlost asmuchoftheiroriginal dust(thedustproducedinthedisruptionthatcreatedthefamil y)throughremovalby P-Rdrag,collisions,orradiationpressure,ashavetheirolder ,larger-parent-bodydust bandcounterparts.Inordertosearchforfainterdustbands,ame thodwasdeveloped toallowtheIRASdatasettobecoadded(Jayaraman,1995)provi dinguswithan increasedsignal-to-noiseviewofthethermalduststructureoft hezodiacalcloud.This method,whichwillbediscussedindetailinSection 3.2 ,involvescoaddingvirtuallyall thepole-to-poleintensityscansoftheIRASdatasetusingametho dforcorrectingthe variationsduetoboththeobservinggeometryoftheIRASsatell iteandthestructural variationofthecloud. Thecoaddingprocess,whichproducedasignicantincreaseinsign al-to-noise, revealedtheexistenceofanadditionalsolarsystemdustbandat 17 inclination.Further 86

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investigationofthethecoaddedIRASobservationsalsoreveale dthatthatthenewdust bandispresentatsome,butnotalleclipticlongitudes.Aswillb eexplainedinSection 3.3.2 ,thissuggeststhatthenewsolarsystemdustbandisaveryyoung,pa rtialdustband whichisstillintheprocessofformation. Thischapterwillfocusonthestudyofthisnewbandandtheana lysisofits dynamicalstructure.Webeginbyexplainingtheco-addingpr ocessthatrevealedthe newbandandthengoontodiscussthedynamicsofdustbandformat ion.Inorderto determineasource,wecreateafulldynamicalmodeloftheban d.Previousmodelsof dustbandevolutionhavebeencreated,andtosomeextentbasedo nquitesophisticated numericalsimulations(Vokrouhlickyetal.,2008),butnon ehavehadthecredentialsof anobservationalconstraint.Itisthisobservationalconstrai ntthatallowsthedusttobe characterisedandunderstood.Throughcomparisonofthelongi tudinalintensityvariation ofthedynamicalmodelwiththatofthecoaddedIRASobservatio ns,wedeterminealikely sourceandagefortheband.Thisinvestigationoftheearlystag esofdustbandformation, unveilstheuniquenessofthepartialdustbandstructure.This youngdustband,asit turnsout,containsmuchmoreinformationonitssourceandth enatureofitsprecursor thanitsolderdustbandcounterparts.Becausethisdustbandisn otyetdispersedaround thesky,informationonthenodeand(indirectly)theagecanb eobtained.Thisallowsus, forthersttime,tounambiguouslylinkadustbandwithitssource body.Furthermore, thisnewdustbandissoyoung,itprovidesuswithaglimpseofthe unalteredproducts ofacatastrophicdisruptionofanasteroid;boththequantitya ndsizedistributionofthe dustinjectedintothecloudinsuchadisruption.Thispartiald ustbandisfundamentally dierentfromthepreviouslyknowndustbandsdiscussedinChapter 2andmustbe modeledinacompletelydierentway,whichwedevelophere.Ul timately,comparison ofthedustbandmodelwiththecoaddedobservationsallowsust odeterminetheage, source,size-distribution,andcross-sectionalareaofdustinthe partialband.Weconclude thechapterwillafulldiscussionoftheimportanceofpartiald ustbandsandthenmake 87

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predictionsforthediscoveriesoftheWide-eldInfraredSur veyExplorer(WISE)which hasjustlaunchedandissettorevolutionizeourviewofthedust bands. 3.2CoaddingtheIRASData Inordertosearchforfainterdustbandpairs,weneededtoincre asethesignal-to-noise ratiooftheobservations.Todothis,wecoaddedvirtuallyallo ftheIRAS(Zodiacal HistoryFile)ZOHFscans.Beforethedatacouldbecoadded,though ,weneededto correctforthevariationsinthedata|bothfromstructuralv ariationsoftheclouditself andthosevariationsresultingfromthedierentobservinggeom etriesundertakenbythe IRASsatellite.Throughamethodofcharacterizingandcorrec tingthevariationsfrom theseeects(Jayaraman,1995),wewereabletonormalizeandc oaddthedata.Thereare twomainvariationsofthedatathatneededtobecorrectedan dthesewillbediscussedin thenextsection.Oneisthevariationofthemagnitudeofthese parationofthebandpair seeninobservationstakenatdierentsolarelongationangles.T hiseectstemsfroma parallaxeectduetoobservingthebandsfromdierentdistance s.Thesecondvariationis theshiftinthecenterofsymmetryofthedustbandpairasseenino bservationstakenat dierenteclipticlongitudes.Thiseectresultsfromthefactt hatthedustbandmidplane isinclinedtotheecliptic(Section 2.2 ).Wenowdiscussthesetwoeectsandthetheir corrections.3.2.1Solarelongationvariations Asthespacecraftincrementedthesolarelongationangleofthe observations,the apparentdistancestothedustbandschanged.Thereasonforthe dierencestemsfrom thefactthatmostofthedustbandsignaliscomingfromaround2A U(Section 2.3.2 ).As canbeseeninFigure 3-1 ,observationstakenatsolarelongationanglesgreaterthan9 0 (showningreen),resultinthespacecraftlookingatdustbandstr ucturethatiscloserto itthantheduststructureobservedbythespacecraftwhentheobse rvationshadasolar elongationanglelessthan90 (showninblue).Observingthedustbandsatdierent distancesresultsinaparallaxeect:dustthatisclosertotheob server(higherelongation 88

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angles)willhaveagreaterseparationthandustthatisfarther away(smallerelongation angles).ThiseectcanbeseeninFigure 3-2 ,whichshowsanexampleofthevariationin theseparationofthe10 bandpeaksfortheobservationtakenat84 ,90 ,and95 solar elongationinasinglelune. Eachlunecontainsupto 50usablethermalemissionprolesatelongationangles varyingfromabout85{95 .The10 bandsareusedasmarkersofthedataforthe coaddingprocess.Foreachobservation,systematictsweredonet odeterminetheprecise latitudeofthepeakuxofthenorthernandsoutherncomponent softhe10 bands. Whenthelatitudeswereplottedagainstthesolarelongationa ngle(Figure 3-3 ),itwas foundthatthelocationofthelatitudeofthepeakvariedapp roximatelylinearlywith theelongationangleoftheobservationovertherangeofasing lelune.Intheexample inFigure 3-3 ,foronetrailinglune,thenorthernband(opencircles)andso uthernband (lledcircles)latitudevariationswithelongationanglear eshown.Itcanbeseenthat boththenorthernandsouthernbandsmoveawayfromtheeclipt icforincreasingsolar elongationangles.Foreachlune,theslopeandy-interceptof thelinearvariationwere determinedandusedtonormalizetheseparationofthepeaksin thatlunetotheir90 solarelongationvalue.Anexampleofasolarelongationnormal izedscanisshownat thebottomofFigure 3-2 .Notetheimprovedsignalinthisscan,whichrepresentsthe coaddingofasingleluneofdata.3.2.2Longitudevariations Becausethedustbandmidplaneisinclinedtotheecliptic(Sec tion 2.2 ),thenorthand southdustbandswillbeequallyspacedaboveandbelowtheeclip ticonlyatthenodesof thesetwoplanes.ThisisexplainedwiththeschematicofFigure 3-4 .Thisgureshows thedusttorus(markedbythenorthernandsouthernbandsinred andbluerespectively), relativetotheeclipticplane.Theplaneofsymmetryofthedu stbandsisshowninalight greyandthenodesofthisplanewiththeelliptic(indarkgre y)aremarkedbypurple circles.Onlyforanobservationofthesenodeswouldthenorthe rnandsouthernbandsbe 89

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equallyspacedaboveandbelowtheecliptic.Thisisshownfort heascendingnode(), markedbylightredandblueverticallinesthatrepresentthe distancetotheband.For observationsoflongitudes,forexample,betweentheascendin gnodeanddescendingnode (markedbyagreencircle),thebandpairwillbeshiftedsuchth atthesouthernbandis closertotheeclipticAlternatively,observationstakenonth eothersideofthesky,between thedescendingnodeandascendingnode(markedbyabluecircle )willresultinthe oppositesituationofthedustbandsbeingshiftedsuchthattheno rthernbandiscloser totheecliptic.Thiseectcanbeclearlyseenifwelookatobser vationstakenatdierent longitudesaroundthesky.Figure 3-5 showsexamplesforarangeofobservations,all takeninthedirectionoftheEarth'smotionandallatanelon gationof90 (representing thecenterofeachlune).Theshiftofthecenterofsymmetryoft he10 bandsduetothe inclinationofthetwoplanescanbeseentovaryaroundtheskyw ithlongitudeofthe Earthwhentheobservationsweretaken.Thevariationofthis shiftissinusoidalaround theskyaswasdiscussedinSection 2.2 andcanbeseeninFigure 2-3 .Themagnitudeof theshiftwithlongitudecanbecharacterizedandusedtocorre cttheeectandshiftthe databynormalizingtheobservationsofeachlunetoacenteri ngon0 eclipticlatitude. Thisiseectivelylikeremovingtheforcedinclinationofth edustbandmidplaneand projectingtheplaneintotheecliptic. Oncethedataineachluneisnormalizedto90 solarelongation,thecoaddedlunes arenormalisedto0 eclipticlatitude,andthenvirtuallytheentireIRASZOHFdat aset canthenbecoaddedtoyieldahighsignal-to-noiseratio(Jaya raman,1995;Groganetal., 1997). 3.3ANewDustBandat17 3.3.1ANewBandAppears Thecoaddingprocedurejustdescribedallowedvirtuallythee ntireIRAS25 m ZOHFdatasettobecombinedintoasinglethermalemissionprolesho wingthedustat alllongitudescoaddedtogether.Thisprole,whichisshowni nFigure 3-6 ,revealedthe 90

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existenceofanewdustbandpairatapproximately § 17 latitude,asshownmarkedby horizontallines.Asmentionedbefore,severaladditionaldust bandpairshavepreviously beensuggested.Basedontheinclinationofthisnewbandpair,w ebelieveittobea conrmationoftheM/NpairoriginallyseenbySykesintheIRASd ata(1988)andalso byReachintheCOBEdata(1997).Sykesundertookamethodofc ombiningscansmade atapproximatelythesametime.Sincethescanningmethodofth eIRASsatellitewasto stepinincrementsofsolarelongationangleatagivenlongitu de,scansmadearoundthe sametimewouldhavesimilarlongitudesandelongationangles andcouldbecombined toproduceasmallerscale,morelocalizedversionofcoaddedda tawithoutcorrectingthe variationsinthedataduetodieringlongitudesandsolarelo ngationangles.Through thisprocess,Sykeswasabletoidentifyfouradditionalpossibl ebandpairs,includingthe M/Npair.TheMbandhefoundexistedapproximatelyatageocen triceclipticlatitudeof 15{17.5 andtheNbandhefoundinthenegative17{20 geocentriceclipticlatitude region.Itshouldbenotedalsothatthethreeotherbandpairsh eidentiedallexistat smallerlatitudesthantheM/Npairandwould,thus,beswampedb ytheemissionfrom thethreeknownbandpairs(discussedinChapter2)andlesslikel ytobedetected,soit isnotsurprisingthatwendonlythisonepair.Reachetal.(199 7),usingtheCOsmic BackgroundExplorer(COBE),alsodetectedafaintbandat 17 whichislikelytoalso bethesamestructureweobservehere. Whileournewlyrevealedbandstructureappearstobeanewdust bandandagrees withthatfoundinpreviousworks,wemuststillshowthatitis,inf act,arealdynamic structureandnotarelicoftheFourierlteringprocesswhichse paratesthenestructure dustbandsfromthebroadbackgroundcloud.Inordertotestthi s,Gaussiansweretto boththenorthernandsouthernVeritas10 bandcomponentstodeterminetheirprecise locationandfromwhichthepreciseplaneofsymmetrycouldbed etermined.Theprocess wasrepeatedforthenorthernandsoutherncomponentofthisn ewbandtodetermineif bothbandpairshavethesameplaneofsymmetry,aswouldbeexpe ctedifthenewdust 91

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bandisarealdynamicalstructure.Thecommonplaneofsymmetr ywouldbeexpected forthenewdustbandbecause,intheasteroidbeltwherethestruc turewouldexist,the planeofsymmetryislargelydeterminedbyJupiter.Theresult softheGaussiantting showthatthenewbandandthe10 banddoinfacthaveacommonplaneofsymmetry towithin0.01 ,whichwouldbesurprisingifthebandwassimplyarelicoftheFo urier ltering.3.3.2EvidenceforaPartialBand WhileitiswasnecessarytocoaddtheentireIRASdatasettoclear lyrevealand conrmtheexistenceofthenewband,moreinformationcannowb egainedbylooking backattheindividualcoaddedlunes.RecallfromSection 2.4.2 ,thatalunerepresentsa spanof30 ofeclipticlongitude.Thus,lookingatthenewbandintheind ividualcoadded lunesgivesalookathowthemagnitudeofthebandvarieswith longitudearoundthe sky.Thecoaddedluneseectivelyactas\bins"ofeclipticlong itude.Theindividual coaddedlunesareshowninFigures 3-7 and 3-8 forobservationstakenintheleadingand trailingdirectionsoftheEarth'smotion,respectively.Th eseguresshowtheline-of-sight intensityprolesinthe25 mwavebandcoaddedlunes,osetforclarity.Thelocation ofthenewbandismarkedbyaverticaldashedlineat § 17 latitude.Themeanecliptic longitudeoftheEarthwhentheobservationsweretakenisgiv entotherightaswellas thelunedesignationstotheleft.Itisapparentthatthenewd ustbandisnotpresentat alllongitudesandthattheintensityofboththenorthernand southerncomponentsofthe bandvaries.Forexample,afulldustbandpaircanbeseeninlune L08inFigure 3-7 at 304 longitudeandinluneT11inFigure 3-8 at37 longitude.But,forexample,inthe L11luneat38 longitude,onlyasouthernbandcanbeseenandintheT09luneat 303 longitude,onlyanorthernbandispresent.Thisbehaviourof thebandsgavethersthint thatthenewdustbandat17 maybeaveryyoungstructurethatisstillformingandas such,itsnodesarenotfullydierentiallyprecessedaroundthe sky.Thisreasoningcanbe understoodifweconsidertheformationofadustband. 92

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Figure 3-9 showsthetimestepsofformationofadustband.Theparticlesre leased inthethedisruptionofanasteroidbegintodecayinsemimajora xis,resultingina precessionandadierentialprecessionoftheirnodes,whichresul tinthedustorbits slowlyformingatorusandadustbandpair,aswasrstintroduced intheschematic ofFigure 2-2 .Whenanasteroidbreaksup,thefragmentscreatedinthedisru ptionwill haveslightlydierentvelocitiesandthusslightlydierentsem i-majoraxes.Asmentioned previously,thevelocitiesofthefragmentswillbeontheord eroftheescapevelocity,which fora10kmasteroidisabout5m/sandfora100kmasteroidisabou t50m/s.These ejectionvelocitiesaresmallcomparedtotheorbitalveloci tyof15{20km/sec,yetresult inthefragmentsspreadingintoaringofmaterialalongtheor bitoftheparentasteroid onatimescaleofhundreds{thousandsofyears.Notonlyarethepar ticlesinitiallyspread slightlyinsemimajoraxisfromtheinitialdisruptionbutthey arealsospiralinginwards undertheeectofPoynting-Robertson(P-R)drag(Section 2.3.1.2 ),whichcausestheir semi-majoraxestodecayovertimeatarateinverselyproporti onaltoparticlesize.Thus, therearetwoeectsactingtochangetheparticles'semimajora xes.Whenthematerial hasjustspreadaroundtheorbitintoaring,veryearlyintheev olution,nodustband isevident,justaringofdustalongtheorbitofthesourcebody. Thiscanbeseenin Figure 3-9 ,whichshows,foraseriesoftimesteps,theevolutionofthe Icos { Isin parameterspaceoftheorbitalelements(intheleftcolumn)i nwhichacircleistraced outasthenodesoftheparticlesspread.Therightcolumnshows thecorrespondingdust toriatthoseintervals.Asthenodesbegintoprecess,theorbital elementstraceouta circle(Section 2.3.2 )andthedustbandswillstarttoappearasjustasmallamount ofmaterialattwodierenteclipticlongitudes180 apartinthesky,oneatanorthern latitudeandoneatasouthernlatitude(timestep5x10 4 years).Thedustbandscanbe seenastheoverdensity(yellow)attheedgesofthetorus.Slowl y,asthenodesprecess anddispersearoundtheecliptic,thenorthernandsouthernban dwillspreadinlongitude (timesteps1.5x10 5 and2.2x10 5 years)andeventuallyllintocreateafullbandpair 93

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(timestep2.7x10 5 years)whenthenodesarecompletelydierentiallyprecessed.A t theintermediatestageofformationrepresentedbytheinterm ediatetimesteps,weseea situationsimilartothatofthecoaddeddatainwhichthereexi stsatsomelongitudesafull dustbandpair,atsomeonlyanorthernband,andatsomeonlyasout hernband.Fully dispersednodesandafullyformeddusttorus,asrepresentedbyth enalpanel,arethe situationweseefortheVeritas,Karin,andBeagledustbands,whi cheachhavefullband pairs(Chapter2).However,thenew17 dustbandappearstobeinanintermediatestage offormation,wherethenodesarenotcompletelydispersedand thedustbandsdonot extendallthewayaroundtheskyasbothanorthernandsouthern bandpair,explaining whyweseeabandpairatsomelongitudesbutonlyanorthernband oronlyasouthern bandatothers. Inadditiontothelocationsofthepresenceand/orabsenceoft he17 bandaround thesky,wecanfurtherinvestigatethestructureofthisbandby examininghowthe magnitudeofthebandintensityvarieswithlongitude.Bytti ngGaussianstothe northernandsouthern17 bandprolesineachluneoftheleadingandtrailingcoadded observations,thevariationoftheintensityofthebandemission withlongitudecanbe determined.Theleadingandtrailingobservationseachcove ronlyaportionofthesky, thusinordertoseethebandvariationaroundthewholesky,the seobservationsneed tobecombined.Inordertodothis,theremustbeatransformatio nfromthelongitude oftheEarthwhentheobservationsweretakentothelongitude ofthethestructure beingobserved.Ifthedustbandstructureisconsideredtobeat2 AU,simplegeometric triangulationcanbeusedtodeterminethelongitudevariati onbetweenthelocationof thespacecraftandthelocationofthestructuresitwasobservi ng(inboththeleadingand trailingdirections).Itshouldbenotedthattheassumptiontha tmostoftheuxiscoming from2AUisnotcrucialtotheoutcome,becauseifthebandswer elocatedintherange of1.8AUto2.5AU,thelongitudinallocationofthestructurer elativetotheobservations wouldonlyshiftbyafewdegreesineitherdirection.Usingthis projectionmethod,the 94

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intensityvariationwithlongitudeofthenorthernandsouthe rncomponentsoftheband isshowninFigure 3-10 .Thenorthernbandisshownasredasterisksandthesouthern bandisshownasbluetriangles.Thebandsappeartobestrongove rarangeoflongitudes, butshowareducedintensityatotherlongitudes.Also,thenorthe rnandsouthernbands showthissamepattern,but180 outofphase.Asinecurveisoverlaidtoguidetheeyeto thebandintensityvariationpattern(butisinnowayattothe data).Thispatternof intensityvariationispreciselywhatwouldbeexpectedbythe dynamicsofaformingdust band,ascanbeseeninthemiddlepanelsofFigure 3-9 |thatthenorthernandsouthern bandsbegintoform180 outofphaseandspreadoutwardfromthesepoints.Givensome assumptionsaboutthegapsinthedata,thenorthernbandappea rstobeginatabout 130 longitudeandthesouthernbandappearstobeing180 lateratabout310 ecliptic longitude.Basedonthewayinwhichthedustbandforms,thenort hernbandshouldbe about90 aheadoftheascendingnodeandthesouthernbandshouldbeabout 90 behind it,implyingthatthenodeofthesourceshouldbearound40 .Thus,thevariationofthe dustbandcomponentsrevealsapatternthatbothfurthersugge ststhisnewdustbandis apartialbandstructurethatisstillformingandalsothatallo wsusinformationonthe sourcebodyproducingthestructure. Tobecertainthatthisvariationpatternisafunctionofthe newdustband's structureandnotduetoabackgroundvariation,theintensity variationofthenorthern andsoutherncomponentsofthe10 bandpeakswerealsodeterminedinthesameway. ByttingGaussianstothenorthernandsoutherncomponentsof10 dustbandsinthe leadingandtrailingcoaddedbins(Figures 3-7 and 3-8 )thebandmagnitudevariation ofthe10 Veritasbandaroundtheskycanbecomparedtovariationofthe 17 band. Ifthepatternofvariationseeninthe17 wasduetoabackgroundasymmetry,the10 bandswouldalsobeexpectedtoshowasimilarvariationpattern .Thecomparisonof thebandsisshowninFigure 3-11 ,whichshowsthelongitudinalintensityvariationof thenorthernandsoutherncomponentsofthe10 band,aspurpleasterisksandgreen 95

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diamondsrespectively,ascomparedtothenewband,shownasre dasterisksandblue diamonds.Thevariationofthenorthernandsoutherncomponen tsofthe10 and17 bandsbothshowvariationaroundthesky,butinadierentpatte rn.Infact,theVeritas 10 bandshowsaninterestingpatternofvariationthatwasreferr edtoinSection 2.5.3 willbediscussedmoreinSection 3.7 .Thepointhere,though,isthatvariationpatternsof thetwobandsshowdierentnodesaswelldierentregionsofnor thernorsouthernband componentintensitydomination.Thisimpliesthatthevaria tionpatternseeninthebands isnotmerelyafunctionofabackgroundclouductuationandt hereforeprovidesfurther evidencethatthe17 bandisaveryyoungandstill-formingpartialband. 3.3.3PossibleSources AsdiscussedinChapter2,basedonthewayinwhichthedustbandsfor m(Section 2.2 ), theparticleorbitsretaintheproperorbitalinclinationo ftheparentbodyproducingthe band.Thisprocesscreatesadustbandaboveandbelowtheeclip ticatthelatitudeof theproperinclinationoftheparentbodyandallowsthedustb andstobeattributed topossiblesourcebodiesinthemainbelt.Lookingbacktothelo cationoftheasteroid familiesinFigure 1-7 ,wecanlinkthelatitudeofthenewbandwithasteroidfamilie s atthatproperinclinationtodeterminepossiblesources.Atthi sinclination,the possiblesourcescanbeseentobe1400Tirelaataproperinclinat ionof16.89 ,andthe Emilkowalskiclusterataproperinclinationof17.22 (thoughwithonly3familymembers identied,itistoofainttobeclearlyseenonthisplot).Beca useoftheintermediate natureofthisnewband,wethinkitshouldresultfromaveryrec entdisruption.The Emilkowalskiclusterhasbeenshown,throughbackwardintegra tionoftheorbits (Section 2.2 ),tobe2.2 § 0.3x10 5 yrsold(Nesvornyetal.,2006b)andisatasemi majoraxisof2.6AU,wherethetimescalefornodaldispersionand thusbandformationis ontheorderof10 6 yrs.Thus,wewouldexpectadustbandcreatedfromtheEmilkowal ski disruptiontobeapartialband,muchasweseeinthecoaddedIRAS data.Additionally, theaveragenodeofEmilkowalski(Table 3-1 )isat 41 degreesandthenodeneededto 96

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tthedata,recall,isaround40 .Furthermore,theothersourceat17 ,theTirelafamily, hasnotbeendatedbecauseofcomplicationsofthebackwardin tegrationsfromchaosdue tooverlappingmean-motionresonances(Nesvornyetal,2003) ,thuswehavenomethod todetermineifitshouldproduceafullorpartialband.AsEmil kowalskiisthemostlikely candidateatpresent,wewillbuildafulldynamicalmodeloft hedustbandthatwould beassociatedwiththeEmilkowalskiclusterandcompareittothe coaddedIRASdatato determineifitis,infact,thesourceofthisnewband. Becausethethreepreviouslyknowndustbands(Chapter2)result fromolder disruptions(andrepresentfullyformeddusttori,inwhichthe particleshavefully dierentiallyprecessednodes),onlytheinclinationremainst odeterminethesource body.Thisnewband(whosenodesarenotfullydispersed)howeve r,allowsusmore informationonthesource,becausewecanmodeltheprecessionof thenodesofthedust orbitstoconstrainboththeageandthenodeofthesourcebody. Thus,thisnewpartial bandallowsus,forthersttime,todetermineauniquesourcefor adustbandbecause wecancomparenotonlytheinclinationofthemodelwiththeo bservations,butalso thelongitudinallocationoftheband(whichdeterminesthe node)andtheextentofthe structurearoundthesky(whichyieldsanage). 3.4TheRoleofCollisionsinDustBandFormation Giventhatthisnewdustbandappearstobeveryyoung,itispossi blethatcollisions mightnotyetbeplayingarole.Ifthetimescaleforcollisions islongerthantheage ofthisdustband,thenthisbandwouldberepresentingastructu rewhosedynamics aredominatedonlybyP-Rdragandplanetaryperturbations.I fcollisionsarenotyet aectingthesize-distributionoractingtoremovedust,thenfo rthersttimewecan constraintheamountofdustcreatedinanasteroidaldisruption andthesize-distribution ofthedustthatisproducedinthesecatastrophiccollisions.Ino rdertodeterminetherole ofcollisionsintheearlystagesofdustbandformation,weprese ntthefollowinganalysis. 97

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Assumingthatthesize-distributionofparticlescanbedescribed byasinglepower lawandthatallparticleshaveapproximatelythesamedensity ,Wyattetal.(1999)have shownthatthecollisionallifetimeofaparticleofdiameter D atadistance r fromtheSun canbewrittenas t coll ( D;r )= t per ( r ) f cc ( D;r ) eff ( r ) (3{1) where t per ( r )istheorbitalperiodatr, eff ( r )istheopticaldepth(normaltotheplane)of thezodiacalcloudatr,and f cc ( D;r )issomefunctionofthesize-distributionofparticles and,hence,thenumberofparticlescapableofbreakingupth eparticlewhoselifetimeis beingcalculated.Theparameter f cc eectivelycharacterizestheprobabilityofabreakup anditcanbewrittenas f cc ( D;r )= Z D max D cc 1+ D D 0 2 ( D 0 ;r ) dD 0 (3{2) where D istheparticlediameter, D max isthelargestparticleinthedistribution, D cc isthesmallestparticlecapableofbreakingupaparticleofsiz e D ,and ( D;r )isthe proportionofthetotalcross-sectionalareaperdierentialpa rticlesizeofthediskata distance r thatisinparticlesofsize D .Inordertodeterminetheproportion ( D;r ),it isnecessarytocalculateboththetotalcross-sectionalareaofp articlesofallsizesandthe cross-sectionalareaduetoparticlesofthesizeinquestion D .Thetotalcross-sectional areaofallparticlesinthediskcanbefoundfrom A tot = Z D max D min N ( D 0 ) D 0 2 2 dD 0 (3{3) where N ( D )istheincrementalsizedistributionaccountingforthenumb erofparticlesof size D .Thisincrementalsizedistributionrepresentsthederivativ eofthecumulativesize distributiongiveninEquation 2{11 .Thecross-sectionalareaofparticlesofsize D is 98

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A D = N ( D ) D 2 2 (3{4) whichyieldstheproportionofthetotalcross-sectionalareap erdierentialsizeelementas, ( D;r )=(3 q ¡ 5) D 4 ¡ 3 q D 5 ¡ 3 q min : (3{5) Tosolvefor f cc wealsoneedtocalculatethelowerlimitoftheintegration, D cc ( D )|the minimumparticlesizecapableofcatastrophicallydisrupting aparticleofsize,D.Atthe relativevelocitiesofparticlesinthemainbelt( 5km/sec),Dohnanyi(1969)foundthat theimpactormassneededtoovercomethetensilestrengthandgr avitationalenergy(for thelargerbodies)tocatastrophicallydisruptabodyisgivenb y M imp M body 10 ¡ 4 : (3{6) Assumingthatthebodyandtheimpactorhavethesamedensity,this canbeconverted intoadiameterratiogivenby D imp D body ¡ 10 ¡ 4 ¢ 1 = 3 (3{7) or D cc ( D ) 0 : 046 D (3{8) inthemainbelt.CombiningEquations 3{8 3{5 ,and 3{2 andassumingavalueofq=11/6 (torepresentanold,collisionallyevolvedpopulation)fort hebackgroundcloudparticles, andintegratingyieldstheapproximation f cc 500 p D min p D : (3{9) 99

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Assumingthemeasurednormalopticaldepthofthecloudat1AU( eff =O(10 ¡ 7 ))is alsorepresentativeoftheorderofmagnitudeinthemainbelta ndinsertingthisand Equation 3{9 intoEquation 3{1 yieldsausefulapproximationforthecollisionallifetimeof asteroidaldustparticlesinthemainbelt(r=2.6AUisused)for abackgrounddistribution describedbyq=11/6,as t col 2 : 5 £ 10 4 p D (3{10) where D isthediameteroftheparticleinmicronsand t isinyears.Itshouldbenoted thatthecollisionallifetimeofaparticleiscommensuratewi thsize,andthelargera particleis,thelongeritwilllive.Thisisduetothenatureo fthesizedistribution,for therearelessandlessparticlesinthedistributionwhicharel argeenoughtobreakupa bodythelargerthatbodyis. UsingEquation 3{10 ,Figure 3-12 isproduced.Thesolidredlineisthecollisional lifetimefortheparticles 70microns(theminimumsizeparticlestillcontributing tothedustbandstructureforthisage)withadistributionofba ckgroundparticlesin whichthesmallestparticleremainingfromradiationpressureb lowoutis1micron(as wouldbeexpectedforsilicates,Backmanetal.1995),andthed ottedbluelineisthe collisionallifetimewhentheminimumparticlesizeofthedist ributionis3microns(both distributionsassumeabackgroundsizedistributiondescribedby q=11/6).Theblack dottedlinerepresentstheageoftheEmilkowalskibreakup.Th etimescaleforcollisionsis longerwhenthedistributionhasaminimumparticlesizeof1 mthanwhentheminimum is3 mbecause,forthegivenopticaldepthofmaterialinthecloud describedbypower lawsizedistributionwithq 5/3,mostoftheareaisinparticlesatthesmallestend (Figure 2-11 ).Whenthematerialisdistributeddownintothesmallestparti clesizes thataretoosmalltobreakupanaveragesizeparticleinthedisk ,thenthenumberof actualparticlesthatcouldbreakitupisreducedandthelif etimeincreases.Forparticle sizeswhosecollisionallifetimecurveisabovethecurrentage ofthesystem(dashed 100

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horizontalline),collisionshavenotyetbeguntoplayarole intheirdynamics.Itcan beseenthat,dependingontheminimumparticlesize,collision shavenotyetbecome importantforanyparticleslargerthan 70micronsifthe D min =1 m |aswouldbe expectedforsilicates.Ifthe D min =3 m ,collisionswouldonlybeimportantforparticles betweenabout 70{150microns,asthecollisionallifetimefortheseparticle sislonger thanthecurrentageofthesystem.Theparticlesizesforwhichc ollisionshavebecome importantarenolongercontributingtothedustbandstructur ebecausetheseparticle sizeshavemostlyalreadyevolvedinside2AU.Figure 3-14 showstheheliocentricdistance reachedduetotheP-Rdragdecayoftheparticlesoverthetim esincethedisruption, asafunctionofparticlessize.Itcanbeseenthattheparticle sforwhichcollisionshave becomeimportanthavealreadyevolvedinsideof2AUand,since materialinthisregion isnolongercontributingtothedustbandstructure,wecansafe lyignorecollisionsinthe model. 3.5DynamicalModel 3.5.1CreationoftheModel Toproduceamodelthatcanbecomparedwiththecoaddedobserv ations,wecreate adynamicalmodeloftheevolutionofthedustfromthesourcebo dy,Emilkowalski.We useananalyticalratherthannumericalapproachbecauseital lowsustobetterunderstand thenatureoftheearlystagesofadustbandandthemainforcesc ontrollingitsformation. Thedustorbitsareevolvedundertheeectsofradiationpressur e(Equations 2{5 2{6 ), P-Rdrag(Equations 2{7 2{8 ),solarwinddrag-whichistakentobe30%oftheP-R dragforce(Gustafson,1996),andplanetaryperturbationsfr omJupiter.Itshouldbe notedthat,thoughJupitercontrolstheprecessionrateandSa turncanbeneglectedfrom thisperturbation,thepresenceofSaturnisnecessarytoprodu cethesecularresonance at 2AUthatdispersestheorbitalelementsofthedustparticlesan dmarkstheinner edgeofthedustbands(Section 2.3.2 ).ToaccountforSaturn'spresence,thiseectis approximatedinthemodelbyremovingparticlesatasemimajo raxisthatcorresponds 101

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totheorbitaldispersionoftheinclinationofthatparticled iameter.Thelocationofthe dispersalischaracterizedusingtheoutputofthenumericalsim ulations(Chapter2)and resultsinsmallerparticlescontributingtothedustbandstruc turefartherintotheinner solarsystemthanlargerparticles. Werstcreateamodelbasedonlyonasingleparticlesize(200 m)inorderto determineifEmilkowalskiisasourcecandidate.Wethengoont oproduceafullmodel of 70 m{1cmdiameterparticles(thelowerlimitdeterminedbyP-R dragremovalat theinneredgeofthedustbandfortheageoftheband),describe dbyapower-lawsize distribution.Theanalyticalanalysisofthedustevolutionuse dtoproducethemodelsis derivedinthenextsection.3.5.2DynamicalEvolution Thetimerateofchangeoftheorbitalelementsofaparticlea regivenbythe Lagrangeperturbationequations.Thefullsetofequationsis giveninMurrayand Dermott(1999),butofinteresthereistherateofchangeofth enode,asthedispersionof thiselementcontrolstheformationofthedustbandstructure .Therateofchangeofthe argumentofpericentermayalsopresentinterestingobservable dynamicaleects,butis beyondthescopeofthisthesisandisleftforfuturework.TheL agrangeequationforthe rateofchangeisofthenodeisgivenby d dt = 1 na 2 p 1 ¡ e 2 sinI d < dI ; (3{11) whereisthelongitudeoftheascendingnode, a isthesemimajoraxis, e istheorbital eccentricity, I istheinclination, n isthemeanangularvelocityoftheparticleas n = GM s a 3 1 = 2 (3{12) and < isthedisturbingfunction.Thedisturbingfunctionforapart iclewithorbital elements a e I ,andisgivenbyMurrayandDermott(1999)as 102

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< = na 2 1 2 Ae 2 + 1 2 BI 2 + 2 X j =1 A j ee j cos ( ¡ j )+ 2 X j =1 B j II j cos ( ¡ j ) # ; (3{13) where A =+ n 1 4 2 X j =1 m j m c j j b (1)3 = 2 ( j ) ; (3{14) A j = ¡ n 1 4 m j m c j j b (2)3 = 2 ( j ) ; (3{15) B = ¡ n 1 4 2 X j =1 m j m c j j b (1)3 = 2 ( j ) ; (3{16) B j =+ n 1 4 m j m c j j b (1)3 = 2 ( j ) : (3{17) Theindex j denotestheplanetindexand m c isthemassofthecentralbody(i.e.the Sun).Foranexternalperturbation,i.e. a j (semimajoraxisofperturber) >a (semimajor axisofparticle), j = j = a / a j .TheLaplacecoecients, b ( j ) s ( ),aregivenby 1 2 b ( j ) s ( )= 1 2 Z 2 0 cosj d (1 ¡ 2 cos + 2 ) s : (3{18) InsertingEquation 3{13 intoEquation 3{11 ,ignoringshort-periodvariations,and expandingtheLaplacecoecientsasaseries,wecanwrite(tolo westorderof in theexpansion),theaveragesecularregression(ornegativepre cession)oftheorbitalnode oftheparticlesduetoperturbationsfromJupiteras h i = ¡ 3 GM J a 3 = 2 4 R 3 J p GM s 1+ 15 8 a 2 R 2 J cos I : (3{19) Therateofprecessionofthenodeisafunctionofheliocentric distance,asisplottedin Figure 3-15 whichshowstheprecessionofthenode( peryear)asafunctionofthe semimajoraxis.Theinnerregionsareprecessingslowerthantheo uterregionsdueto theirlargerdistancefromJupiteranditsperturbingeects.E quation 3{19 ,though,is usedtodescribeastatic,non-varying-semimajor-axissituatio n,butthesemimajoraxes 103

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oftheasteroidaldustparticleorbitsaredecayingwithtimeu ndertheeectsofP-Rand solarwinddrag.ThemagnitudeofthesemimajorchangeduetoPRdraginagiventime canbefoundbyintegratingEquation 2{7 ,andthechangeinsemimajoraxisthencanbe writtenas a final [ a 2initial ¡ 4 t ] 1 = 2 : (3{20) Usingtheapproximationfor giveninEquation 2{4 ,wecanwriteausefulexpressionfor a final as a final [ a 2initial ¡ 1150 400 D t ] 1 = 2 (3{21) where a final isthesemimajoraxistheparticlehasreachedattime t a initial isthe semimajoraxisoftheparentbodyfromwhichthedustwasrelease d, isthedensity oftheparticle,and D itsdiameter.Inordertoaccountforthisvariationofthesem imajor axisoftheparticles,weinsertEquation 3{21 forthetemporalvariationof a into Equation 3{19 toyield(tolowestorderin ) h i = ¡ 3 GM J 4 R 3 J p GM s £ a 2o ¡ 4 t ¤ 3 = 4 1+ 15 8 a 2o R 2 J 1 ¡ 4 a 2o t cos I (3{22) whichistheequationusedtogeneratethenodaldispersioninth edynamicalevolution codefortheformingdustbandmodel.3.5.3SingleParticleSizeModel Werstcreateamodelofthedustbandusingonlyasingleparticlesi ze.This singleparticlesizemodelofthe17 dustbandisbasedonthesecularevolutionof theorbitsofthedustparticlesfromtheirsourceregionforasi ngleparticlediameter, 200 m.Wechosetofocusonthisparticlesizeforseveralreasons.First ,particlesizes between10{200 mareproducingmostofthezodiacalemission(e.g.Reachetal., 1996).Secondly,foradisruptionattheageandlocationofEm ilkowalski,particleswith 104

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diameterssmallerthan 100 mwillhaveevolvedinwardsof2AUundertheeectof P-Rdrag.Recallthatinwardsof 2AU,theparticleswillnotcontributetotheuxof thedustbands,asthedustbandstructuredoesnotpersistintothei nnerSolarSystem (Section 2.3.2 ).Finally,LoveandBrownlee(1993)showthepeakinmassofdust particles collectedat1AUisforparticleswithdiametersbetween100 {200 m.Forthesereasons, weuse200 mdiameterparticlesforthesingle-sizetestmodel.Particles ofonlyasingle size,intheabsenceofcollisions,willallbeevolvingtogether underP-Rdragandtheir nodeswillprecessatthesamerateandresultinnodierentialpr ecessionofthenodes andthusthenodeswon'tdispersetoformadustband.Inordertot esttheconcept ofapartialbandwiththissimpletestcasesinglesizemodel,weal lowtheorbitstobe distributedbetweenthesourceandtheP-Rdragdenedsemimajor axislocation(ata giventime)ofthe200 mparticles. Toproducethesingleparticlesizemodel,webeginbyprecessing thenodesof theparentasteroidfamilymembersbacktotheepochofdisrupt ion,allowthedustto bereleased,andthenprecessthenodeforwardintimefordiere nttimesteps.The semi-majoraxisdispersioninthissimplemodelisonlyfromtheP -Rdragoftheparticles, noinitialdispersionduetothe¢vfromtheinitialcollisionorf romradiationpressureis introducedintothesystem,thoughwenotethatradiationpressu rewouldn'thavemuch eectonparticlesofthesizerangebeinginvestigatedhere.At eachtimestepwecalculate thesemimajoraxislocationofthe200 mparticlesandtheamountofprecessionof thenodesoftheseparticles.Additionally,wecalculatetheam ountofprecessionofthe nodeofthesourcebodies.Therangeofsemimajoraxesandnodalv ariationbetweenthe sourcebodiesandthe200 mparticlesrepresentthe¢ a and¢describingthedust torus.Usingthesevaluesaslimits,wecreateaSIMULmodel(Chapte r2)ofthedust distributionandthecorrespondingthermalemissiondusttorust hatwouldresult.An exampleofthethermalemissiondusttorusforthesingleparticl esizemodelthatwould resultfromtheEmilkowalskiclusteratitscurrentageisshowni nFigure 3-13 105

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Ourgoalhereistoconstrainwhatsourceshavetheorbitalorie ntationandageto createthe17 dustbandintheobservedcoaddeddata.WendthatEmilkowalskii sa likelycandidate,asthissimplemodelshowsthat,forthesemim ajoraxisandageofthe cluster,apartialdustbandwouldresult.Thenextstepistobuil dafulldynamicalmodel ofallparticlesizesforcomparisonwiththecoaddedobservati ons. 3.5.4FullModel Thefulldynamicalmodelisbasedontheorbitalevolutionofd ustfromthesource locationofEmilkowalskiandincludesafullrangeofparticl esizesfrom 70 m{1mm (andthenlaterupto1cm,aswillbeexplained),describedbya power-lawsizedistribution. Thesmallestsizeineachmodelisafunctionoftheageofthemode landrepresentsthe smallestsizeparticleremainingfromP-Rdragdecayto 2AUresultinginthatparticle nolongercontributingtothedustbandstructure.Ananalytica ldynamicalevolution codewasdevelopedspecicallyforthepurposeofmodelingthis partialband,usingthe equationsofSection 3.5.2 .ThecurrentsemimajoraxisandnodeoftheEmilkowalski familyareevolvedbackwardsintimetotheepochofthefamil yformation.Atthisepoch thedustparticlesarereleased|oneparticleofeachsizefrom1 0micronsto1mmin stepsof1 m(asizedistributionwillbeimpartedlater).Theirorbitsar ealteredat thedisruptionduetotheeectofradiationpressure(Equations 2{5 and 2{6 ).Thenew orbitalelementsoftheradiation-pressure-eecteddustparti clesarethenallowedtoevolve withtime| a and e accordingtoEquations 2{7 and 2{8 respectivelyandaccordingto Equation 3{22 .Thevaluesof a e ,andarecalculatedforeachparticlesizeateachtime. Becausecollisionsaren'tyetplayinganimportantrole(Sect ion 3.4 ),thesemimajor axislocationofparticlesinthisearlystageofdustbandform ation,isafunctiononly particlesize.Sincetheprecessionrateofthenodeisafunctio nofsemi-majoraxis,the nodelocationoftheparticleorbitsbecomesafunctionofpa rticlesize.Thisresultsin averyinterestingaspectofthisearlystageofformation.Thep articlesaredistributed aroundthesky(inbothnodeandsemimajoraxis)continuouslywit hparticlesize, 106

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resultinginaveryinterestingspiralstructurethatwillpersist onlyforashorttimein theearlystagesofdustbandformation(between10 5 and10 6 years)untilcollisionsbegin todominate.ThisisshownschematicallyinFigure 3-17 inwhich,asfunctionofparticle size(representedbycolor)thelocationofthenodeandsemimaj oraxisoftheparticle areshownforaseriesoftimesteps.Oncetheparticlesarerelease dfromthesource,the smallestparticles(purple)begintodecayawayfromthelarge stparticles(green),which remainnearthesource.Asthesemimajoraxesofthesmallerparti clesdecay,thenodal precessionratesslowduetotheirlargerdistancefromJupitera nditsperturbingeects (Figure 3-15 ).Sincethesesmallerparticlesareprecessingataslowerrate,t heylagbehind thelargerparticlesandthesourcewhichresultsinadispersion ofthenodesaround thesky,sortednicelywithsemimajoraxisandparticlesizeassee ninthespiralplotsof Figure 3-17 .Thesespiralplotsexemplifytheinterestingsituationpresent edbythesevery youngstructures.TheolderdustbandsdiscussedinChapter2repre sentasituationwhere eectivelyparticlesofallsizesexistatallsemimajoraxesand withrandomizednodes.A furtherdiscussionoftheimportanceofthesepartialbandsispr esentedinSection 3.7 Theorbitalelementsresultingfromthisearlyphaseofevolut ionarecharacterized andbinnedintoequalcross-sectionalareabins.Foreachsizedist ributionthatistobe modeled,theparticlesizesaredividedinto10bins,suchthatt heareaineachbinisequal. Therangeofparticlessizesineachbinwillvarywiththesized istribution,butthetotal areaineachofthe10binswillremainequal.Thesebinsareused tocreate10individual SIMULmodels,eachwiththesize,nodeandsemimajoraxisrangede scribingtheparticles inthatbin.EachSIMULmodelisthenconvertedintoathermale missiontorus,described bytheemissionoftheaveragesizeparticleinthatbin.The10th ermalemissiontori arethenaddedtogethertoproduceafullmodelofthepartial dustbandresultingfrom thecontributionsofallsizes.Themodelsofdierentageswill haveaslightlydierent smallestparticlesize,denedbythesmallestparticlewhosedustba ndstructureisstill intact.Theparticlessmallerthanthatminimumsizeareconsid eredlostfromthesystem 107

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duetoP-Rdragdecayandthustheoldermodelshavelostslightl ylargerparticlesthan theyoungermodels.Thismethodofbinningthemodels,withequ alareaacrossallthe bins,allowstheentirenalmodeltobescaledupordowntorepre sentmoreorlesstotal areaandtomatchtheintensityvariationaroundtheskyasseeni ntheobservations. Inthiswaywecanusetheobservations,ascomparedtothemodels, toconstrainthe size-distributionofthedustbymatchingthepatternofthevar iationofthebandintensity withlongitude.Thedeterminationoftheabsoluteamountofa reaisaseparateprocess andwillbediscussedinSection 3.6.4 Theresultingthermalemissiondusttorus(Figure 3-16 )showsmuchmorestructure thanthatofthesimple,singleparticlesizemodel(Figure 3-13 ).Fordustbandsatthis age,mostofmaterialisstilllocatednearthesourceaswasshown in(Figure 3-14 )since ithasn'thadmuchtimetodecayinsemimajoraxis(underP-Rand solarwinddrag). Themajorityofthethermalemission,asshownbythemodels,isco mingfromthe largestparticlesinthedistributionand,thus,theseparticle saredominatingtheresulting structureoftheband.Thevariationofthenorthandsouthband intensitywithlongitude isthenplottedagainstthecoaddedobservations,aswillbedisc ussedinthenextsection.. Throughcomparisonoftheresultinglongitudinalmagnitudev ariationsoftheband structurefromthemodelswiththecoaddedobservations,constr aintscanbeplacedon theparametersofthedustandtheage.Thevariationofthesize distributionparameter, q,controlshowthedustisdistributedintheparticlesizesand thusalsoaroundthesky andtheagecontrolstheextentofthedistribution.Theseconst raintsandtheresultsare discussedinthenextsection. 3.6Discussion 3.6.1ComparisonofModelsWithObservations Usingtheanalyticalmethodpreviouslydescribed,wecreatemod elsofthedust bandstructureresultingfromtheEmilkowalskidisruption.West artthemodelingwith particlesofdiameter70 m{1mmdescribedbyapowerlawsizedistribution,q=1.7. 108

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Thelongitudinalintensityvariationofthenorthernandsout herndustbandsofthismodel isshownpanelAofFigure 3-18 alongwiththecoaddedobservationsforcomparison. Thelongitudinalintensityvariationofthemodelofthenort hernbandisshownasa reddashedlineandthesouthernbandasabluedottedline.Theo bservedlongitudinal variationofthenorthandsouthbandintensityareshownasredst arsandbluediamonds, respectively.Itcanimmediatelybeseenthatthethemodelisn otproducingadustband structurewiththecorrect\phase"(i.e.locationsofthenort handsouthbands)tomatch thecoaddedobservations.Infact,ascanbeenseeninpanelB,th emodeldustbandwould needtobeshiftedbyabout90 tomatchtheobservations.Butourpredictionforthe locationofthenodethatisneededtomatchthecoaddedobserv ations,aswasdiscussed inSection 3.3.3 ,correspondedtothenodeoftheEmilkowalskicluster.Sinceth enode controlsthe\phase"ofthenorthernandsoutherndustbandvari ationpatterns,why,then, doesn'tthismodelmatch?Theexplanationforthisdisconnect liesintheparticlesizes.If welookagainatthespiralplotofthenodallocationsofthedu stfromEmilkowalski(now withthelocationofthelargestbodiesmarkedbyamulti-colo redsquare)inFigure 3-19 itcanbeseenthatthematerialinthesizerangesthoughttobep roducingthebands (andusedinthismodel),thoseupto1mm,havemigratedawayfro mthesource.This migrationisduetothedierentialprecessionresultingfromth e¢ a inducedbytheP-R dragdecayofthe1mmparticles'semimajoraxesrelativetotha tofthesourcebodies. Examinationofthethisgureshowsthatthematerialisabout9 0 awayfromthelarger bodies,theapproximateamountneededtoshiftthenorthernan dsouthernmodelbands tothephaseoftheobservations.Thisspiralshowsparticlesonly upto1mm,butin realitythereisacontinuousdistributionofnodesoflarger andlargerparticlesizesbackto thesource.Thismeansthat,ifparticleslargerthan1mmwere contributingsignicantly tothedustbandthermalemission,thenthemodelforEmilkowalsk iwouldmatchthe coaddedobservations.Butparticleslargerthan1mmwouldnot intuitivelybeexpectedto contributesignicantlytothethermalemissionofthezodiacal cloudduetotheirreduced 109

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areacontributionascomparedtothesmallerparticles.Figur e 3-20 showstheamount ofcrosssectionalareaproducedbyeachparticlesizeforarang eofsizedistributions. Thepercentageofuxcomingfromthe1mmdiameterparticlesi salmostnegligible andthecontributioncontinuestodecreasesforlargerparti cles.Additionally,asisshown inFigure 3-21 theuxcontributedfromtheselargerparticles(whicharealso atlarger semimajoraxes)isreducedevenfromthatoftheparticlesizesb eingcurrentlyconsidered. Thecombinationofthesetwoeectsresultsinverylittleexpec tedcontributionfromthe largestparticles.However,asmentionedbefore,thepartiald ustbandstructurepresentsa uniquesituation.ForthecurrentageoftheEmilkowalskidisru ption(Figure 3-19 )itcan beseenthatthesmallerparticles,100{200 minsize(showninpurple)aredistributed innodefullyaroundthesky,whilethelargerparticlesarebu nchedupnearthesource. So,althoughthetotalamountofcross-sectionalareafrompart icles 1mmandthetotal uxthattheyproducearebothreducedascomparedtotheirsmal lercounterparts,these largerparticlesarebunchedverycloselytogetherinthelon gitudesoftheirnodes,resulting inaneectivelyincreased\ux-density"ascomparedtothesmall erparticles.Couldtheir over-densityatthisveryearlystageofformationallowthemt ocontributesignicantlyto thethermalemissionofthedustbandstructure?Inordertotestth isscenario,wecreate modelsextendingthelargestsizeupto1cm.3.6.2LargerParticleSizeModels Inordertoseeifthelargeparticlescanproduceenoughuxdue totheirlongitudinal overdensitytodominatethebandstructurethermalemission,we includecontributions fromparticlesfrom70 mupto1cm.Webeginwithamodelwhichhasasize-distribution describedbyq=1.7.ThismodelisshowninFigure 3-22 .Themodelnowhasthesame longitudinalphaseastheobservations,meaningthatthelarge rparticles(1mm{1cm) areprovidingasignicantamountofuxduetotheirincreased\u x-density"atthis earlyphaseofdustbandformation,whentheyremainlongitudi nallytogether.The contributionofthelargerparticlesisenoughtoshiftthemo deltothecorrectlocationto 110

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matchtheobservations.Sincethismodelhasshownthatthatthe dustfromEmilkowalski caninfactproducestructureinthecorrectplacestomatchth eobservations,thisnew modelincludingparticlesupto1cmwillnowbeiteratedtoco nstrainthesize-distribution andageoftheband.Additionally,itshouldbenotedthat,since theleadingandtrailing dataismostlyinoppositepartsofthesky,theinitialconstrain tonqismadefrom comparisonofamodelwithallthecoaddeddata(takeninbotht heleadingandtrailing directions).However,becausetheleadingandtrailingdirect ionshaveslightlydierent observinggeometries,theyobserveslightlydierentintensityd istributions.Tomore carefullyrenethevalueofq,modelsofthedustdistributioni nboththeleadingand trailingdirectionsoftheEarth'smotionarecreatedandco mparedseparatelywith observationsmadeinthecorrespondingdirection. Changingthevalueofqiseectivelylikeweightingthecolor softhespiralin Figure 3-19 dierently.Theq=1.7modelcanbeseentobetoo`spikey'(toobu nched upatasmallrangeoflongitudes),asshowninFigure 3-22 .Inordertobroadenout thelongitudinaldistributiontomatchtheobservations,wene edtoincludemoresmall particles,asshiftingtheweightingtowardsthesmallerparti cleswillproducemore dispersion(andbetterttheobservations)sincethesmallerparti clesaremoredispersed aroundtheskythanthelargerparticles.Inordertoincreaseth esmallerparticlesin themodel,asizedistributionwithahigherqvalueisneeded.F igure 3-23 showsthe modelforadistributiondescribedbyq=1.8.Thismodelshowsam uchbetterttothe dataandwelldescribesthedistributionofparticlespresent. Itmightseemadisconnect thatamodeldescribedbyasize-distributioninwhichsmallpart iclesdominateshows agoodttoobservationswhenitwasjustdiscussedthatthelargerp articlesneedto bedominatinginordertotphaseoftheobservations.Theexplan ationisthatthere aretwodierent\domination"atworkhere.Thesizedistributi onthatdescribesthe longitudinalintensityvariationofthispartialband(q=1. 8)isoneinwhichsmallparticles dominatethecross-sectionalareaandthustheux.However,thel argeparticlesupto 111

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1cm(becausetheyarelongitudinallytogether)eectivelyha vemuchmore\ux-density" andsoeventhoughtheydon'tdominatethetotaluxfromtheclo ud,theydodominate thedustbandstructure. Itisinterestingthatthesizedistributionofthisyoungdustpo pulation(q=1.8)is dierentfromthepopulationofdustpresentintheolderdustban ds.Recallthatavalue ofq=1.4isfoundfortheolderdustbandmodels(Chapter2)whi chrepresentolder,more evolvedpopulations.Theseresultsimplythattheareaoftheyo ungerpopulationsis dominatedbysmallerparticlesandthattheolderpopulation saredominatedbylarger particles.Thevalueofq=1.8isalsoofinterestincomparisonto laboratorysimulationsof asteroiddisruptionswhichndasimilarresultastheyaredescrib edbyasizedistribution parameterofq=1.8{1.9(e.g.Flynnetal.,2009).Itshouldbe noted,though,thatmost asteroidsarenowthoughttoberubblepilesofgravelandrock sandnotsolidbodies.A rubblepilemightbeexpectedtocontainmoredustandsmallerp articlesandtherefore mighthaveahighersize-distributionparameterthanwouldbe expectedofasolid body.Theparentbodyofthisfamilythough,isarathersmall 10kmbody.Smaller asteroidsareyounger(duetocollisionallifetimes)andthush aven'tsueredasmanyofthe non-catastrophicimpactsthatareexpectedtogeneratetheg ravelandrocksofarubble pile'sstructure,whichmightexplainthesimilarityofthiso bservedsize-distributiontothe laboratorymeasurements.3.6.3Anupdatedage Asdiscussedpreviously,theerrorbarsonEmilkowalski'sagearel argeduetothe smallnumberofmembers(3).Vockrouhlickyetal.,(inpress-p rivatecommunication) havenowidentieda4thmemberoftheclusterandre-integrate dtheorbits.They ndtwonewlyrenedpossiblevaluesforthefamilyagewithinthe errorbarsofthe previousestimate.Thosetwonewagesare228,0000and236,000 years,withmore statisticalsignicanceontheolderofthetwoages.Inordertofu rthertestthenew modelofEmilkowalskiasthesourceofthepartialdustband,wec reateonenalmodel 112

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(includingthelargeparticlesandusingtheq=1.8distributi on)fortheageof236,000 years.ThismodelisshowninFigure 3-24 .Thenew,olderagecanbeseentoprovide aneven-betteragreementofthemodelswiththecoaddedobser vations,spreadingthe materiallongitudinallytobetterllintheobservations,due tothelongertimefor dierentialprecessionofthenodeswhichspreadthematerialar oundthesky.Thecoadded dataisnotpreciseenoughforustoattempttofurtherrenethe ageofthefamilyusing thismethod,otherthantosaythataslightlyolderagemightpr ovideanevenbettertto thecoaddedobservations,asitproducesslightlymorelongitu dinaldispersion. TheresulthereisthatEmilkowalskiisalikelysourceoftheyou ng,partial,17 dust band.Thedustproducingthebandisdescribedbyaq=1.8powerlawsizedistribution (similartothatproducedinthelaboratorysimulationsofthe initialdisruptionofan asteroid)andmaterialupto1cmiscontributingtotheemission oftheband.Basedon thelongitudinaldistributionofdustintheband,Emilkowalsk iislikelyslightlyolderthan thepreviouslypublished220,000years,possiblycorrespondingt othenew236,000yrage determinedbybackwardintegrationsofthefamilymemberor bitsincludingthenewly discovered4thclustermember.3.6.4Cross-sectionalareacontribution Becausethepartialbandisyoungenoughthatcollisionshaven 'tbeguntoplaya role,modelingofthisstructureallowsus,forthersttime,toc onstraintheamountof dustproducedinthecatastrophicdisruptionofanasteroid.The modelingtodetermine thecrosssectionalareainthisnewbandisdoneinasimilarmann erasthemodeling ofChapter2,inwhichthemodelisaddedtoanobservationalba ckground,Fourier ltered,andthentheline-of-sightprolesofthemodelarecom paredtothelineofsight observations.Forthepartialband,though,itsmorecomplica tedtodeterminetheactual area,becauseeachlineofsightproleisscaledtomatchtheobser vationsandthusthe regionsoftheskywherethedustbandisstrongwillrequiremore areathantheregions whereitisweak.Becausethecoaddedobservationsprovidecov erageofonlyabout70 113

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percentofthesky,wemustestimate,usingthemodelpredictions, theextentofthe strengthofthedustbandinthemissing-dataregions(approxima tely30percentofthe sky).Inthisway,weestimatethecrosssectionalareaofmateria linthe17 dustband tobebetween10 6 {10 7 km 2 .RecallthattheamountofdustassociatedwithVeritas (the10 band)is O (10 9 )km 2 .However,fortheageoftheEmilkowalskidisruption,we knowthatsemimajoraxisdecayduetoP-Rdraghasresultedinth eparticles70 m andsmallerbeinginsidetheregionwherethedustbandstructure exists(approximately 2AU).Therefore,theconstraintonthecross-sectionalareaofou rmodelofthepartial band,whichconsidersonlytheparticlescontributingtothe band,canbeexpandedto accountforthe 70 mdiameterparticles.Withoutcollisionsinthesystem,knowing thesizedistributionfoundfromthemodeling(q=1.8)allowsu stoincludethemissing area.Becausetheareaofasystemwithaqvaluegreaterthan1.66 isdominatedbythe smallestparticles,consideringthemissingparticlesfromthisd istributionincreasesthe crosssectionalareasignicantly.Wendthattheareaofdustgene ratedinthedisruption wasafactorofapproximately4higherthanweseetodaywhenth e 70 mdiameter particlesareincluded.Thus,thecrosssectionalareaofthema terialassociatedwiththe partialdustband,andthuswiththe 10kmdiameterparentbodyoftheEmilkowalski familyisontheorderof10 7 km 2 .Ifthevolumeoftheparentasteroidcanbeusedasa measureoftheamountofdustreleased,then,sincetheparenttot heVeritasfamilywas oforder100kmindiameterandwouldrepresent3ordersofmagn itudemorevolume thanthe10kmEmilkowalskiparent,wemightexpectthatthedi sruptionoftheVeritas familyinitiallyproduced10 10 km 2 ofdust.Thus,implyingthatthecrosssectionalarea ofmaterialoftheasteroidalcomponentofthezodiacalcloud mayhavebeenanorderof magnitudehigherfollowingthedisruptionoftheVeritasfam ily.Furthermore,theamount ofdustreleasedintheEmilkowalskidisruptionwouldcorrespond toaregolithlayerof 3.4metersdeeponthe10kmdiameterparentbodyasteroid'ssur face.Ifthespikeof dustfromtheVeritasdisruptionwasoriginallyanorderofmag nitudehigher,thenthis 114

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wouldsuggestthatthisspikeofdustdominatedthecloud,implyi ngthat,notonlyarewe currentlyinaspike,butthattheheightofthespikewasinitia llyanorderofmagnitude higherthanweseetoday.3.6.5ErrorAnalysis Themaingoalofthismodelingeort,therstofitskind,wasnot necessarilyto preciselyrenetheparametersofthedust,buttoillustratetha t,throughthemodeling, wecouldexplainthestructureseeninthecoaddeddata.Because ofthewayinwhichthe bandforms,thisallowsustoalsoplaceconstraintsonthecross-se ctionalareaandsize distributionofthedust,aswellasthemostlikelysource.Herewe discusstheassumptions andlimitationsoftheresultsasamethodofconstrainingthee rrors. Cross-sectionalarea .Thedeterminationofthecross-sectionalareaisdependent onseveralfactorsthatmayinduceerror.First,thecoaddedda tadoesn'textendallthe wayaroundtheskyandisadditionallydiscretizedfromthecoa ddingprocess.Thusthe completeextentofthestructurearoundtheskyisdeterminedf romthemodelingresults. Inordertodeterminethetotalcross-sectionalofdustpresentin theband,onemusta prioriunderstandtheextentofthisstructure.Weuseourdeter minationoftheamount ofdustpresentineachofthelunestogetherwiththeseparately modeledlongitudinal distributiontodeterminethetotalcrosssectionareaofdustin theband.Secondly, becauseparticlessmallerthan70 mhavealreadyevolvedintotheinnersolarsystem, weaccountfortheseparticlesbyassumingthatthesize-distribu tionofdustfoundfor thelargerparticlesextendsdownintothesesmallestparticle s.Thisassumptioncouldbe untrueiftheoriginalasteroidhadasignicantamountofregol iththatwasdescribedby adierentpower-lawsizedistribution.Becauseoftheseassumptio ns,wedon'treneour estimatefurtherthananorderofmagnitudeestimateforthedu stpresent. Size-distribution .Thedeterminationofthesize-distributionforthepartialb and isdoneinanentirelydierentmannerthanthatoffullbandso fChapter2,which allowedus,throughcomparingthemodelshapesandshiftsofthe dustbandstructure 115

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directlytoindividualobservations,tocarefullydetermine thesize-distributionofthe dustpresent.Becausethefaintnessofthispartialbanddoesnot allowittobeseenin anindividualobservation,weinsteaddeterminethesize-distr ibutioninauniqueway usingthelongitudinalvariationofthestructure(Section 3.6.2 ).Thedetermination ofthesize-distributioninthismannercanbeaectedbyvariat ionsofseveralfactors, namelytheageofthesource,theinclusionofsecondorderpertu rbationeectsfrom alltheplanets(onlyJupiterisusedhere),andtheassumptions aboutthermalemission madeinconvertingthedynamicalmodelsintouxmodels.Additi onally,thecoadding processitselfandtheGaussianttinginannoise-limitedregime, whichwereusedto determinethelongitudinalintensityvariation,couldinvo kesomeerrors.Despiteallthese potentialsourcesoferror,though,theuniquenessofthespira lstructureanddistribution ofparticlespresentinthisyoung,partialbandallowustoun derstandbothhowandwhy thestructurevariesaroundthesky.Furthermore,thislongit udinalintensityvariation turnedouttobeverysensitivetothevalueofthesize-distribut ionoftheparticlespresent, duetotheirdistributionaroundthesky.Thisallowedustoren ethesize-distribution thatbesttthelongitudinalpatternseeninthecoaddeddata.As canbeseeninFigure ~ ?? aq=1.7modelprovidesa\too-spikey"(longitudinallyconde nsed)uxdistribution. Theq=1.9modelyieldedtheoppositeproblem,amuchtoodisper sedstructureproviding almostacompletedustband.Thevalueofq=1.8,asdiscussed,shows thebestt,butas canbeseeninFigure 3-23 ,doesn'tcompletelyexplainthestructure.Thuswecanonly statethatthevalueofqisbetweenq=1.7andq=1.9.Puttingpr eciseerrorbarsonthe size-distributionisbeyondthescopeofthisworkandthedatac urrentlyavailable.The upcomingWISEdata(Section 3.8 )willallowus,inthenearfuture,tofurtherrenethis value. Source .Themodelingpresentedhereisdoneforasourceattheage,semi major axis,node,andinclinationoftheEmilkowalskicluster,themo stlikelysource.Ithasbeen shownherethatEmilkowalskiisnotonlyalikelysource,buthas providedaconvincingt 116

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tothedata,basedparticularlyonitsinclination,andforth ersttime,itsageandnode. Becauseoftheadditionaldataprovidedbythepartialstructu reofthe17 band,the associationofEmilkowalskiwiththisstructureistherstunique solutionforthesource ofadustband,astheolderdustbandshaveonlyinclinationtod iscriminatetheirsource. However,itshouldbenotedthatsuchafaintdustbandcouldbepro ducedbysome yet-undiscoveredsourcebody,beyondthelimitsofcurrentast eroiddetectiontechniques. Ifsuchabodywerethesource,themodelingwouldneedtoberepe atedwiththespecic parametersofthatbodytofullyunderstandthedustseeninthec oaddeddata. 3.7TheImportanceofPartialDustBands Partialdustbands,suchasthisoneat 17 ,areaninterestingphenomenonto studybecausetheyactuallyprovidemoreinformationthanful lyformeddustbands.In acompletedustband,asweseefortheKarin,Veritas,andBeagle bands,thenodesof theorbitsofthedustparticlesarefullydierentiallyprece ssedaroundthesky,erasing anyinformationonthenodeoftheparentbody.Partialdustba nds,though,stillcontain enoughinformation,toconstrainthenodeofthesource.Moreo ver,theamountof dispersioninthelongitudesofthenodesofthedustparticleor bits,providesaconstraint ontheageofthedisruptionthatproducedthem.Older,comple tedustbandsareonly attributedtoasourcebasedontheirinclination,butpartial bandscanbelinkedtoa sourcealsoconstrainedbythenodeandage.Additionally,inthe seyoungformingbands, moreofthedustproducedintheinitialdisruptionisstillprese nt.Figure 3-25 shows theproportionofthecrosssectionalareafromtheoriginaldi sruptionthatremainswith age,asparticlesarebeinglosttoP-Rdrag.Decaycurvesaresh ownfortwodierentsize distributionsandtheagesoftheyoungbandsource,Emilkowal ski,andtheoldersources, KarinandVeritas,aremarkedbydashedline.Itcanbeseenthata greaterproportionof thematerialcreatedinthedisruptionofEmilkowalskiisstill presentascomparedtothe remainingproportionsofKarinandVeritas.Becausefortheol der(Karin,Veritas,Beagle) bands,alloftheoriginaldustsmallerthanabout1mmhasalread yevolvedinsideof1AU 117

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undertheeectofP-Rdrag,theremainingdustmusthavebeencre atedinsecondary inter-particlecollisions.Thus,notonlyismuchoftheorigin aldustlost,butalsothe informationontheoriginal(non-collisionallyevolved)siz e-distributionhasbeenlost. Intheearlystageofformationrepresentedbypartialdustband s,though,inter-particle collisionshavenotyetbeguntoplayanimportantroleandthe size-distributionofthe dustisrepresentativeofthatproducedintheinitialdisrupti on;allowingamuchtighter constraintonthesize-distributionandcross-sectionalareaofd ustproducedinthe catastrophicdisruptionoftheparentasteroid. Throughmodelingofthepartialdustband,wecanevengaininf ormationabout thestructureoftheparentasteroid.Thepartialbandmodelin gallowsaconstraint onboththetotalcrosssectionalareaofdustandthesizedistribu tionoftheparticles createdintheinitialdisruptionofanasteroid.Analysisofthe largerbodiescreatedin thedisruption,thosethatnowconstitutethefamilyorcluster, allowusareasonablygood estimateofthesizeoftheparentbody,sincemostofthevolumewi llcomefromthelarge memberswhicharestillpresentonorbitssimilartothatofthep arentbody.Usingthese twopiecesofthepuzzle(thesizeoftheparentbodyfromobserv ationsofthemembers, andtheamountandsizedistributionofdustfoundinthedustband )onecouldbeginto reconstructthestructureoftheparentasteroid.Thisuniquew aytoviewtwodierent extremesofthesize-distributionpowerlawcouldgivecluesa bouttheprecursorasteroid totheyoungfamilyproducingtheband.Wasitarubblepile?A solidbody?Wastherea regolithlayerofdustandtowhatdepth? Modelingthedustinthepartialbandsandputtingconstraints ontheregolithofthe precursorasteroidcanalsohelpconstrainhowweexpectthemagn itudeofthecloudto varywithtime(e.g.DurdaandDermott,1997).Asteroidsareno longerthoughttobe justthesolidrocksofold.Inastudyofrotationratesofasteroi dsbyPravecandHarris (2000),theyndthattheabsenceoffastrotatingasteroids(less than2.2hourperiods) andthetendencyofthefasterrotatorstohavesphericalshapes isevidencethatasteroids 118

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largerthanafewhundredmetersaremostlylooselybound,grav ity-dominated,\rubble pile"aggregateswithnegligibletensilestrength.Ifalarge percentageoftheasteroidsare rubblepiles,andRichardsonetal.(2002)inasummaryofeviden ce,alsoconcludethat manyifnotmostkilometer-sizedasteroidsmaybe,thenthiscou ldgreatlyaecthowwe expectthemagnitudeofthezodiacalcloudtovarywithtime. Arubblepilehasreceived numerouspreviousimpactseachcontributingtothedepthof theregolithlayerand,thus, increasingtheamountofdustwhichwillbereleaseduponthecat astrophicdisruptionof theasteroid.RecentimagesofItokawa(Fujiwaraetal.,2006 )andEros(Veverkaetal., 2001)revealhowsignicantaregolithlayercanbe.Constraini ngtheparametersofdust releasedinthedisruptionofarubblepilegivesinsightintoho wtheasteroidalpercentage ofthezodiacalcloudwouldvarywithtime,sincelikelyamuch largeramountofdust wouldbeexpectedtocomefromthedisruptionofarubble-pile asteroidofagivensize thanfromasolidbodyasteroidofthesamesize.Forexample,Derm ottetal.(2002a) ndthatifa200kmdiameterasteroid(approximatelythesizeof theprecursortotheEos family),hadaregolithdepthof 70m,thenthewholezodiacalcloud(across-sectional areaofabout2.5x10 10 km 2 )couldhavebeenreleasedfromitsdisruption.Thedepthof regolithonanancientrubblepileislikelytobemuchmoreth an70mandthustherecent disruptionofsuchabodycouldhaveresultedinanincreaseinthe massofdustinthe cloudbyafactorof10 2 andanincreaseinthecross-sectionalareaofdustbyafactorof 10 3 {10 4 (Dermottetal.,2002).Alongwiththeamountofdustproduced, thepresence ofaregolithlayercouldalsoaecthowlongthatdustpersistssinc eitwouldskewthe size-distributionofthedustproducedinthedisruptiontoward thesmallerparticles(and theP-Rdragdecayoftheorbitsisafunctionofparticlesize) Thisworkhasalsorevealed(Figure 3-11 )theapparentsubstructureintheVeritas family.Isthispatternofvariationwithlongitudeofthe10 bandduetosomeremnant oftheformationoradierentdynamicaleect?Canwe,infutur ework,constrainsome informationonthesourceofthe10 bandthoughttohavealreadybeenlost?Perhaps 119

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thereisnosuchthingasa\fullyformeddustband"asolderages mightjustresultin alargerparticlesizewhosenodeshaveyettobedispersedaround thesky.Althoughit willrequiremoreworkinthefuturetodeterminethecauseoft hevariationofthe10 band,ultimatelythemodelingworkonthe17 bandinthethesishaspresentedanew perspectiveondustbandformationandevolution. 3.8TheFuturewithWISE Thiscoaddingprocedurehasgivenusaglimpseofadustbandinf ormation,but WISE(Wide-eldInfraredSurveyExplorer)couldgiveusamuc hmorecompletepicture. Withitsgreatlyincreasedsensitivityoverpreviousdetector s,WISE(whichlaunched inDecemberof2009)shoulddetectmoreofthesepartialdustban dpairs,givingus signicantlymoreinformationontherelationshipsbetweenth edisruptedasteroids andthedustbandstructurestheyproduce.WISEdataoersthree mainbenetsover thecoaddedIRASdatathatwecurrentlyrelyontoconstrainour models:improved sensitivity,moreskycoverage,andmultiplewavebandcoverag e.Withits 500times increasedsensitivity,WISEshouldbeabletodetectstructuremu chfainterthanthatseen byIRAS,allowingittodetectthe17 partialbandinindividuallongitudescansrather thanhavingtoaverageoveraluneaswiththecoaddedIRASdata .Alsoduetothesky coverageofIRASandcontaminationfromthegalacticcenter, ourcoaddedIRASdata ismissingcoverageof 30percentofthesky.WISE,whichwillmaptheentireskyin 6months,canprovideincreasedlongitudecoverageandresolut ion,allowingusabetter viewofthelongitudinalvariations.Thespeciclocationsoft hepresenceandabsenceof thedustbandsaswellashowtheirmagnitudevariesaroundthe skyarekeytofurther constrainingboththenodeofthedustorbits(andthusthesourc e)andtheamountof dispersioninthenode(andthustheageoftheband).Themultip lewavebandcoverage ofthisnewspacecraftisveryimportantforconstrainingthef ormingdustbandmodel. IRASobservedinseveralwavebandsinwhichthethreebrighterd ustbandpairsare clearlyvisible(12,25and60 m),withthestrongestsignalcominginthe25 mband. 120

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Thecoaddingprocedure,whichrevealedthepartialbandint he25 mdata,didnot however,yieldenoughsignal-to-noiseincreaseintheshorterw avebandandonlyyielded ambiguousresultsinthelongerwaveband.Theimportanceoft hedierentwavebands maynotbeimmediatelyapparent,buttheyactuallyprovidea wealthofdataforthis specicsituation. Recallthat,inthisregime,thedynamicalevolutionofthep articlesisdominatedby P-Rdrag,whichcausestheorbitsofdustparticlestodecaytosm allersemi-majoraxesat arateroughlyinverselyproportionaltotheparticlesize(Eq uation 3{21 ).Sincetherateof precessionofthenodeoftheseorbitsisafunctionofthesemi-ma joraxis(Equation 3{22 ), thisresultsintheparticlessemi-majoraxesandnodesbeingso rtedbyparticlesize (Figure 3-17 ).Therefore,weexpectthethermaluxatdierentlongitudes ofthisforming dustbandtobeproducedbyparticlesofdierentsizesand,since thedierentwavebands areprobingdierentparticlesizes,weshouldseestructureindie rentpartsoftheskyin thedierentwavebands.AnexampleofthisisshowninFigure 3-26 ,whichshows,forone ofthemodels,howthedusttoruswouldvaryifviewedat12 mor60 mwavelengths. Viewingthepartialdustbandindierentwavebandscanthuscon rmandfurtherrene thesize-distributionofdustproducingthestructure. AlthoughweonlyseethisonepartialdustbandinthecoaddedIRAS data,the recentdiscoveryofseveralnew,veryyoung( < 1Myr)asteroidclusters(Nesvornyetal., 2006b)opensupnewpossiblesourcesoffaintdustbandsandsevera lmoredustband pairsandpartialbandshavebeenpostulated(Sykes,1988;Rea chetal.,1997).How manymorepartial(orevenfull)dustbandsareyettobediscove red?Theparentbody oftheEmilkowalskicluster,thelikelyprecursortothepartia lband,isestimatedtobe 10kmindiameter(consideringthesizesofthefragmentsandco nvertingthemtoa singlesizebody).Basedoncollisionallifetimes,weexpecttheb reakupofanasteroid thissizetooccuraboutevery10 5 years(Bottkeetal.2005).Sincethetimescalefordust bandformationis10 5 ¡ 10 6 yearsdependingonlocationinthemainbelt(Sykesand 121

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Greenberg,1986),weshouldthereforeexpecttoseeontheorde rofafewformingdust bands,duetothedisruptionofasteroidsofthissize,atanygive ntime.Additionally,since thelifetimeofanasteroidisproportionalto p D asteroid (e.g.Wyattetal.,1999),andsince therearemoresmallerasteroids(duetotheinversepowerlawsiz edistribution),thenthe smallerasteroids(whichwouldproducefaintdustbands)willbr eakupevenmoreoften. SinceWISEshouldbesensitivenotonlytothe10kmdisruptions(t helikelylimitofthe IRAScoadding)butalsoevenfainterandthussmallerdisruption s,weshouldexpectit todetectaminimumofafewformingdustbands,eachofwhichcan modeledusingthe methoddevelopedhere. Modelingtheamountofcross-sectionalareainanyfuturebands willallowusto reneourestimateofthetotalasteroidalcomponentofthezodi acalcloud.Additionally, modelinganyfuturepartialbandswillhelpputconstraintso nthedetailedtemporal evolutionofthezodiacalcloud,sincethesefaintbandscomef romsmallerasteroidswhich breakupmorefrequentlyandtheirdustlikelypersistsforshort eramountsoftime.Future workonthistopicshouldinvestigatehowthetemporalvariati onofthezodiacalcloud wouldcomparetoextrasolardebrisdiskbrightnessvariations, e.g.arethesedisksina steadystate,ordotheyareupinbrightnesswithdisruptionswit hinthesystems(e.g. Telescoetal.,2005;Riekeetal.,2005)?Understandingthetem poralvariationandthe causesofsuchvariationofthezodiacalcloudistherststeptobe tterunderstandingthese extrasolardebrisdisksystems. 122

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Figure3-1.Schematicofsolarelongationobservinggeometry .Adiagramoftheobserving geometryvariationswithsolarelongationangleisshown.Sol arelongation angleistheobservinganglemeasuredfromtheSun-Earthline. TheEarth (includingtheobservingspacecraft)isshowninblueat1AUand thedust bandsarerepresentedas2AU,sincethisregiondominatestheba ndstructure. AsIRASobservedatdierentsolarelongationangles,theeectived istanceto thedustbandvaried,creatingaparallaxeect.Observationst akenatgreater than90 solarelongationangle(showningreen)areclosertotheobserve r thanthosetakenatlessthan90 (showninblue).Thisresultsintheeective distancetothedustbandvaryingwithelongationangle. 123

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Elongation Variation -20 -10 0 10 20 Ecliptic Latitude 1 2 3 4 5 6 Relative Intensity Coadded T08 Figure3-2.Solar-elongation-induceddustbandseparationv ariation.AsIRASobserved atdierentsolarelongationangles,theeectivedistancetothe dustband varied,creatingaparallaxeect(Figure 3-1 ).Observationstakenatgreater than90 solarelongationangleobservedustbandsclosertotheobservert han thosetakenatlessthan90 .Thisresultsinaparallaxeectofdecreasing separationwithincreasingdistance,seenhereasalargersepara tionofthe 10 bandsinthesolarelongation=95 observationsandasmallerseparation inthesolarelongation=84 observations.Thevariationoftheseparationof thepeaksofthenorthandsouth10 bandswasfoundtovarylinearlywith elongationangleoverthesmallrangeofthelune(Figure 3-3 )andthiswas usedtonormalizethedatato90 ,soitcouldbecoadded.Thecoaddedbinfor thisluneisshowninthebottomscan. 124

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Figure3-3.Linearvariationofthelatitudeofthebandswit helongationangle.AsIRAS observedatdierentsolarelongationangles,theeectivedistan cetothe bandsvariedwhichresultedinaparallaxeectcausingthesepar ationofthe bandstochangewiththesolarelongationangleoftheobservat ions.Fitsto thenorthandsouthpeaksofthe10 bandshowhowtheirlatitudevarieswith elongationangleforthenorthern(opencircles)andsouthern (lledcircles) bands,resultingintheapparentseparationvariation.Overth erangeofalune, thiseectwasfoundtobelinear,andwasusedtonormalizethel atitudes tothatexpectedfor90 solarelongation.Thiswasdonebymeasuring thevariationofthepeaks,characterizingtherelationship, andusingitto normalizethedatatoasolarelongationof90 .Becausealltheseobservations aretakeninasinglelune,theyrepresentmaterialphysicallyn eareachother onthesky,thustheeectoftheinclinationofthedustbandmidp lanetothe eclipticinshiftingthecenterofsymmetryofthebandsisvery smallacross alune.Thelocationofthenorthandsouthbands,asmeasuredher e,is alsousedtocharacterizethesinusoidalvariationofthecenter ofsymmetry, asisusedinthenextstageofthecoaddingprocedure.[Reprodu cedwith permissionfromGroganetal.,2001.Thesize-frequencydistrib utionofthe zodiacalcloud:evidencefromthesolarsystemdustbands(Figur e4).Icarus 152.] 125

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Figure3-4.Schematicofaninclineddusttorus.Thedusttorush asaplaneofsymmetry (aplaneaboutwhichthedustorbitsprecess)thatislargelydet ermined byJupiter.TheobservingplatformfollowstheEarthandthee cliptic(the Earth'sorbitalplane),towhichJupiterisinclinedby1.3 .Becauseofthis inclination,thecenterofsymmetryofthenorthernandsouthe rnbandswill varyforobservationstakenatdierenteclipticlongitudes.T henorthernband isshowninred,thesouthernbandinblueandtheintersectionof thedust bandplaneofsymmetry(lightgrey)withtheecliptic(darkgr ey)ismarkedat thenodes(purple).Forobservationstakenofthenodesofthe twoplanes, thenorthernandsouthernbandwillbeequallyspacedaboveand below theeclipticplane(asmarkedattheascendingnode,.Observat ionstaken betweentheascendinganddescendingnodes,(anexampleisshown ingreen) willseeashiftinthebandswiththesouthernbandbeingcloserto theecliptic thanthenorthernband.Forobservationstakenbetweenthede scendingand ascendingnodes(anexampleisshowninblue)theoppositewillb etrue.This resultsinthevariationofthebandstructureshowninFigure 3-5 126

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Longitudinal Variation -15 -10 -5 0 5 10 15 Ecliptic Latitude 2 4 6 8 10 12 Relative Intensity Trailing l E= l E= l E= l E= l E= Figure3-5.Inclination-inducedlatitudeshiftofdustbandm idplane.AsIRASobservedat dierentlongitudes,theinclinationofthedustbandmidplane totheecliptic resultedinashiftofthecenterofsymmetryofthebands(Figure 3-4 ).The variationofthecenterofthesymmetryofthe10 dustbandsisshownfor observationstakenat5dierentlongitudes,eachatasolarelon gationof90 Thesinusoidalvariationoftheshiftaroundtheskywascharacte rizedandused tonormalizethedatatoacenteringonthe0 eclipticlatitude,aswouldbe expectedatthenodesofthetwoplanes.Thiseectivelyremove dtheeectsof theinclinationandallowedthedatatobecoadded. 127

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-20 -10 0 10 20 Ecliptic Latitude 0 5 10 15 20 25 Relative Intensity (MJy/Sr) 25 m m Coadded Data Figure3-6.ThenewdustbandasseeninthecoaddedIRASdata.Whe nvirtually allFourierlteredIRASZOHF25 mscansinbothleadingandtrailing directionsandoveralllongitudesarecorrectedandcoadde dthenewdust bandisrevealed.Thenewdustbandislocatedatabout § 17 degreesecliptic latitude(asmarkedbyverticallines).Thecentraland10 bandsappearto havelargeramplitudesduetothecoaddingprocedure.Fitst othenorthern andsoutherncomponentsofthenewbandandthe10 bandshowtheyhave thesameplaneofsymmetryaswouldbeexpectedforadustbandint he mainbeltandimplyingthattheirexistenceisnotlikelyarel icoftheFourier lteringprocess.[ReproducedwithpermissionfromEspy,A.,etal. ,2009. EvidencefromIRASforaveryyoung,partiallyformeddustband (Figure1). PlanetaryandSpaceScience57.] 128

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-20 -10 0 10 20 Ecliptic Latitude 0 1 2 3 4 Relative Intensity (MJy/Sr) L04 L05 L06 L07 L08 L09 L10 L11 l =247 l =261 l =274 l =292 l =304 l =323 l =31 l =38 Figure3-7.Coaddedleadinglunes.Thevariationofthe17 bandaroundthesky canbefoundfromtheindividuallunes,whicheectivelyactas bins ofeclipticlongitude.Thisgureshowsthedataforalltheusab le (non-galactic-center-contaminated)lunesintheleading directionofthe Earth'sorbit,osetfromeachotherforclarity.Thelunesare markedwith theirlunedesignationsontheleftandtheapproximatelongi tudeoftheEarth whentheobservationsweretaken.Thebandappearsasafullno rth/south bandpairin,forexample,L08,butasasouthernbandonlyin,f orexample, L11,providingevidencethatthestructureisapartial,still -formingband. [ReproducedwithpermissionfromEspy,A.,etal.,2009.Evidenc efromIRAS foraveryyoung,partiallyformeddustband(Figure3).Plane taryandSpace Science57.] 129

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-20 -10 0 10 20 Ecliptic Latitude 0 1 2 3 4 Relative Intensity (MJy/Sr) T04 T05 T06 T07 T08 T09 T11 l =215 l =227 l =246 l =274 l =286 l =303 l =37 Figure3-8.Coaddedtrailinglunes.Thevariationofthe17 bandaroundthesky canbefoundfromtheindividuallunes,whicheectivelyactas bins ofeclipticlongitude.Thisgureshowsthedataforalltheusab le (non-galactic-center-contaminated)lunesinthetrailin gdirectionofthe Earth'sorbit,osetfromeachotherforclarity.Thelunesare markedwith theirlunedesignationsontheleftandtheapproximatelongi tudeoftheEarth whentheobservationsweretaken.Thebandappearsasafullno rth/south bandpairin,forexample,T11,butasanorthernbandonlyin, forexample, T08,providingevidencethatthestructureisapartial,still -formingband. [ReproducedwithpermissionfromEspy,A.,etal.,2009.Evidenc efromIRAS foraveryyoung,partiallyformeddustband(Figure4).Plane taryandSpace Science57.] 130

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-0.4 -0.2 0.0 0.2 0.4 0 100 200 300 -30 -20 -10 0 10 20 30 5x10 4 yrs -0.4 -0.2 0.0 0.2 0.4 -30 -20 -10 0 10 20 30 1.4x10 5 yrs -0.4 -0.2 0.0 0.2 0.4 -30 -20 -10 0 10 20 30 2.2x10 5 yrs -0.4 -0.2 0.0 0.2 0.4 -0.4 -0.2 0.0 0.2 0.4 0 100 200 300 -30 -20 -10 0 10 20 30 2.7x10 5 yrsI sin W I cos W Ecliptic LatitudeEcliptic Longitude Figure3-9.Thetimestepsofformationofthe17 dustband.Foraseriesoftimesteps, theleftcolumnshowsplotsoftheosculatingelementsof200 mdiameter particlesinpolar(I,)space(Dermottetal.,2001)asinFigu re 2-5 .The osculatingelementslieonacirclehere,ofwhichtheradiusi stheproper inclination(I)andtheangleistheproperlongitudeofthea scendingnode ().Asthenodeprecesses,thecircleistracedout.Therightcolu mnshows thecorrespondingall-skymapsoftheuxproducedbytheEmilko walskidust torus,aswellasitsresultingdustbands(whiteattheedgesoft hetorus), wouldappearatthesesametimesteps.Theskymapsrepresenttheint ensity variationwhereblueistheleastintenseandyellowisthemost. Thelasttime steprepresentsafullyprecessednode,asseenintheolderdustban ds,and thethirdtimesteprepresentsthecurrentestimatedageoftheE milkowalski cluster.[ReproducedwithpermissionfromEspy,A.,etal.,2009. Evidencefrom IRASforaveryyoung,partiallyformeddustband(Figure5).Pl anetaryand SpaceScience57.] 131

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0 100 200 300 Heliocentric Ecliptic Longitude -1 0 1 2 3 4 Relative Intensity (Arbitrary Units) Northern Southern 25 m m Coadded Data Figure3-10.Longitudinalvariationofthepartialband.By ttingGaussianstothe northernandsoutherncomponentsofthe17 dustbandintheleadingand trailingcoaddedbins(Figures 3-7 and 3-8 )thebandmagnitudevariation aroundtheskycanbeshown.Thelongitudecoveragearoundthesk yis obtainedthroughcombiningtheobservationsinboththelead ingandtrailing directions.Inordertocombinetheleadingandtrailingobser vations,thets totheintensityvariationofthebandsineachluneareprojec tedontotheir physicallocationonthesky.Thedistancetothedustbandswasassu med tobe2AUinthecalculationoftheprojectedlocation.Thisi sareasonable assumptionasmostoftheuxshouldbecomingfromthisregion,but the projectionisonlyshiftedbyafewdegreeseachwayfordustban dlocations of1.8{2.5AU.Themagnitudeofboththenorth(redstars)andsout h(blue diamonds)bandsappearsstrongoverarangeoflongitudesandt henbegins todecayinintensity.Thenorthernandsoutherncomponentssho wthesame patternbut180 outofphase,aswouldbeexpectedforaformingdustband. Asinecurvehasbeenoverlayedtoguidetheeye,butdoesnotre presentany actualttothedata. 132

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0 100 200 300 Heliocentric Ecliptic Longitude 0 2 4 6 8 10 12 Relative Intensity (Arbitrary Units) Northern Veritas Northern Emil Southern Veritas Southern Emil Figure3-11.Longitudinalvariationcomparisonwiththe10 band.ByttingGaussiansto thenorthernandsoutherncomponentsofthe17 and10 dustbandsinthe leadingandtrailingcoaddedbins(Figures 3-7 and 3-8 )thebandmagnitude variationaroundtheskycanbeshown.Thelongitudecoveragea roundthe skyisobtainedthroughcombiningtheobservationsinboththe leadingand trailingdirections.Inordertocombinetheleadingandtrai lingobservations, thetstotheintensityvariationofthebandsineachlunearep rojected ontotheirphysicallocationonthesky.Thedistancetothedustb andswas assumedtobe2AUinthecalculationoftheprojectedlocation. Thisis areasonableassumptionasmostoftheuxshouldbecomingfromthisregion,buttheprojectionisonlyshiftedbyafewdegreeseac hwayfordust bandlocationsof1.8{2.5AU.Thevariationofthenorthernan dsouthern componentsofthe10 and17 bandbothshowvariationaroundthesky. Sinecurveshavebeenoverlayedonbothstructurestoguideth eeyetothe patternofvariationandshowthedierentnodesofthepattern s.Thesesine curvesdon'trepresentactualtstothedata.TheVeritas10 bandshows astrikinglysimilarpattern,whichwillbediscussedinSection 3.7 ,butit canbeclearlyseenthatthevariationofthetwobandsshowdier entnodes anddierentregionsofdominationofthenorthernversussouth ernband, implyingthatthevariationpatternseeninthebandsisnotme relyafunction ofsomesortofbackgrounductuation. 133

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Table3-1.Emilkowalskiclusterdata AsteroidProperinclinationNodeSemimajor-axisDiameter 14627Emilkowalski17.224 41.57 2.5984AU8.2km 2002DW1017.225 41.39 2.5989AU3.4km 2005WU17817.224 41.34 2.5988AU1.7km Age=2.2 § 0.3x10 5 years Precursordiameter 10km 134

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0 200 400 600 800 1000 Particle Size (Microns) 0 210 5 410 5 610 5 810 5 Collisional Lifetime (Years) Dmin=3 m m Dmin=1 m m Figure3-12.Collisiontimescales.Whencollisionsbecomeimpo rtantinayoungsystemis dependentontheageofthesystemrelativetothetimescaleforc ollisions. Thecollisionallifetimeasafunctionofparticlesizeisshown fortwo dierentvaluesoftheminimumparticlesizeinthebackground population, determinedbytheradiationpressureblowoutthreshold(which isrelated tothedensityassumedfortheparticles).Thebackgroundpopula tion isdescribedbyaq=11/6sizedistributiontorepresentanold,ev olved backgroundpopulation.Thesolidredlineisthecollisionall ifetimefora distributioninwhichthesmallestparticleremainingfromrad iationpressure blowoutis1micron(aswouldbeexpectedforsilicates,Backma netal.1995) Thedottedbluelineisforablowoutminimumparticlesizeof3 microns.The timescaleforcollisionsislongerforaminimumparticlesizeo f1 mbecause, forthegivenopticaldepthofmaterialintheclouddescribed byapowerlaw sizedistributionofparameterq=11/6,mostoftheareaisinpar ticlesatthe smallestend,wheretheyaretoosmalltobreakupanaveragesizep article inthedisk.TheblackdottedlinerepresentstheageoftheEmil kowalski breakupandthusparticleswhosecollisionallifetimeisabov ethislinehave notyethadtimetobreakupovertheageofthissystem.Itcanbese en that,downtotheminimumparticlesizesremainingfromP-Rdr aglossfor thissystem( 70 m),thetimescaleforcollisionsislongerthantheageof systemforallbutafewofthesmallestparticlesdescribedbytheD min =3 system.Sincemostparticleshavelongercollisionallifetimes thantheageof thesystem,theyarenotundergoingcollisionsandthuscollisio nscansafely beignoredinthemodel. 135

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0 100 200 300 Ecliptic Longitude -30 -20 -10 0 10 20 30 Ecliptic Latitude Figure3-13.Singleparticlesizemodel.Amodelofthecurren tageofthedusttorus producingthe17degreebandcomposedof200 mdiameterparticlesis shown.Thedustbandcanbeseenastheoverdensity(showninred)at the edgesofthetorus.Theskymaprepresentstheintensityvariatio nwithpurple beingtheleastintenseandredbeingthemostintense.Fortheage ofthe Emilkowalskidisruption,thenodesofthe200 mparticleshavenotyetfully dierentiallyprecessedandtheresultingstructureisapartial dustband. Observationsoflongitudes 200 wouldshowafullnorth/southbandpair butobservationsof 100 wouldshowonlyasouthernbandandthoseat 300 longitudewouldshowonlyanorthernband. 136

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0.0 0.5 1.0 1.5 2.0 2.5 Heliocentric Distance (AU) 200 400 600 800 1000 Particle Size (microns) Figure3-14.Heliocentricdistributionofparticlesizesresul tingfromtheEmilkowalski breakup.FortheageoftheEmilkowalskidisruption,thelocat ionofthe particlesizesduetotheP-Rdragdecayoftheirorbitsisshown forparticles downto50 mdiameter.Particlesofabout100 mandsmallerarealready insideof2AUandthusnotcontributingsignicantlytothedustb and structure.Particlesbiggerthanabout500 marestilllocatedwithin0.1 AUofthesourceduetotheyoungageofthesystem. 137

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2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Semimajor Axis 0.006 0.008 0.010 0.012 0.014 W dot, degrees/yr Figure3-15.Main-beltnodalprecessionrates.Usingequation 3{22 ,theprecessionrate ofthenodesasafunctionofsemimajoraxisacrossthemainbelt isshown. Theinnersemimajoraxesprecessmoreslowlyduetotheirfurthe rdistance fromtheperturbingeectsofJupiter.Theprecessionrateissho wnasa magnitude,butisactuallyaregression(negativeprecession)r ate.Because therateofprecessionofthenodevarieswithsemimajoraxis,the particles ofdierentsizes,whichareatdierentsemimajoraxesduetoPRdr ag,are precessingatdierentratesandthusdispersinginlongitudearo undthesky, creatingthedustbandstructure. 138

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0 100 200 300 Ecliptic Longitude -30 -20 -10 0 10 20 30 Ecliptic Latitude Figure3-16.Fullmodelthermalemissiontorus.Amodelofthecu rrentageofthedust torusproducingthe17degreebandcomposedof70 m{1mmdiameter particlesisshown.Thedustbandcanbeseenastheoverdensity(sh ownin red)attheedgesofthetorus.Theskymaprepresentstheintensit yvariation withblackbeingtheleastintenseandredbeingthemostintense. Thisfull modelincludingallparticlesizesshowsmuchmorestructureth anthesimple singleparticlesizemodelshowninFigure 3-13 139

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A -3 -2 -1 0 1 2 3 acos( W ) -3 -2 -1 0 1 2 3 asin( W ) 2.0 AU 2.6 AU 1.0E5 yrs B -3 -2 -1 0 1 2 3 acos( W ) -3 -2 -1 0 1 2 3 asin( W ) 2.0 AU 2.6 AU 1.4E5 yrs C -3 -2 -1 0 1 2 3 acos( W ) -3 -2 -1 0 1 2 3 asin( W ) 2.0 AU 2.6 AU 1.8E5 yrs D -3 -2 -1 0 1 2 3 acos( W ) -3 -2 -1 0 1 2 3 asin( W ) 2.0 AU 2.6 AU 2.2E5 yrs Figure3-17.Nodaldispersionofparticlesizes.Thenodaldispersi on,atdierenttime steps,asafunctionofparticlesize(in100 mbins)isshowninI sin / I cos space.Thecolorsrepresent:blue=100{200 m,purple=200{300 m, darkred=300{400 m,red=400{500 m,orange=500{600 m,yellow= 600{700 m,lightgreen=700{800 m,green=800{900 m,darkgreen=900 m{1mm.Theorbitoftheparentbodyisshownatitsorbitof2.6A Uand theapproximateinneredgeofthedustbands(beyondwhichpar ticlesaren't signicantlycontributingtothedustbandstructure)isshownat 2AU. ThepointsrepresenttheNODEoftheparticle'sorbitandnotth ephysical locationoftheparticle.Forthetimestepofthecurrentageo fthe17degree band(panelD),thesmallerparticlesaredispersedaroundthesk y,suggesting somedustbandstructureshouldbepresentinalllongitudes,butth elarger particlesareclumpednearthesource,suggestingavariationo ftheintensity ofthebandwithlongitude. 140

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A 0 100 200 300 10 20 30 40 50 Relative Intensity (Arbitrary Units) B 0 100 200 300 10 20 30 40 50 Relative Intensity (Arbitrary Units) Shift= 90 Degrees Figure3-18.Nodalphasemismatchwith 1mmdiameterparticles.Thevariationofthe longitudinalintensityforthemodelnorthernband(reddashe dline)and thesouthernband(bluedottedline)ascomparedwiththecoad deddata forthenorth(redstars)andsouth(bluediamonds)componentsof the17 dustband.Themodelincludesparticlesizesfrom70 mto1mmandis describedbyapowerlawsizedistributionofq=1.7.A)Thecompar isonof themodeltotheobservations,whereitcanbeseenthatthemodel locations ofthenorthandsouthdustbandstructuredon'tmatchthelocati onsofthe structuresintheobservations.Themodeldustbandhasadierent \phase" oftheintensitypattern.B)Themodelneedstobeshiftedbyabo ut90 in ordertocorrespondtothecorrectphaseoftheobservations. 141

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-3 -2 -1 0 1 2 3 acos( W ) -3 -2 -1 0 1 2 3 asin( W ) 2.0 AU 2.6 AU 2.2E5 yrs Figure3-19.Nodallocationofparticlesrelativetosource.T henodaldispersionforthe dustparticlesatthecurrentageoftheEmilkowalskicluster,a safunctionof particlesizeinI sin /I cos spaceisshown.Thecolorsrepresent100 m binsas:blue=100{200 m,purple=200{300 m,darkred=300{400 m, red=400{500 m,orange=500{600 m,yellow=600{700 m,light green=700{800 m,green=800{900 m,darkgreen=900 m{1mm. Thelocationofthesourcebodiescanbeseenasamulti-colored squareat theorbitof2.6AU.Theapproximateinneredgeofthedustbands (beyond whichparticlesaren'tsignicantlycontributingtothedustb andstructure) isshownat2AU.ThepointsrepresenttheNODEoftheparticle'sor bitand notthephysicallocationoftheparticle.Thesmallerparticl esaredispersed aroundthesky,suggestingsomedustbandstructureshouldbepresent inall longitudes,butthelargerparticlesareclumpednearthesour ce,suggesting avariationoftheintensityofthebandwithlongitude.Thesou rce,asitcan beseenhere,isabout90 behindthe1mmparticles(darkgreen).Although thisplotonlyshowsparticlesupto1mm,inrealitythereisac ontinuous distributionoflargerandlargerparticlesextendingbackt othesource.Since theosetofthesourcefromthe1mmparticlesisequaltotheosetn eeded totthemodeltotheobservations,thelargerparticles(which existinthis regionbetweentheendofthespiralandthesource)areaddedto themodel andcomparedtotheobservations,toseeifinclusionoftheselarg erparticles canshiftthematerialtothecorrectlocationtomatchtheobse rvations. 142

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10 100 1000 Log Particle Size (microns) 0.0 0.2 0.4 0.6 0.8 1.0 Normalized Incremental Cross Sectional Area q=1.8 q=1.7 q=1.6 Figure3-20.Incrementalareadistributionintoparticlesiz es.Forthreedierentpower-law sizedistributionparameters,thenormalizedincrementalare aasafunction ofparticlesizeisshown.Theincrementalareaiscalculatedf romthe incrementalsizedistribution,whichisthederivativeofthe cumulativesize distribution(equation 2{11 ).Forseveralvaluesofthesizedistributionofarea producedinanasteroidaldisruption,themajorityofthearea isinparticles of100 mdiameterandsmaller.Sincelittleareaisfoundintheparti cles greaterthan1mm,thesesizesaren'texpectedtocontributemu chuxto thezodiacalcloudthermalemission.Thelargertheqvalue,th emorethe weightingtowardsthesmallestparticles.Itcanbeseenthatlit tleofthe cross-sectionalareaisexpectedtocomefromparticles 1mm.Inthepartial bandthough,particlesofthissizeandlarger,whileproduci ngonlyasmall proportionofthetotalux,representahighcross-sectional-ar ea/ux density duetotheirlongitudinalbunchingandthisallowsthemtosti lldominatethe dustbandstructure. 143

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1.0 1.5 2.0 2.5 3.0 Heliocentric Distance (AU) 0.5 1.0 1.5 2.0 2.5 3.0 Flux (MJy/Sr) Figure3-21.Thermalemissionuxasafunctionofparticlesizea nddistance.The25 m thermalemissionuxperunitareaasafunctionofdistanceforar angeof particle-sizecurvesisshown.Themostuxcomesfromthesmallest particles inthedistribution.Theuxisdominatedbythesmallesthelioce ntric distancelocations,asthematerialishottestthere.Sincethe particleslarger than1mmproducelessuxandaregreatlydepletedinarea,thep articles inthissizerangewouldn'tbeexpectedtocontributesignican tlytothe zodiacalcloudemissioninmostsituations. 144

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A 0 100 200 300 10 20 30 40 50 60 Relative Intensity (Arbitrary Units) Leading B 0 100 200 300 Heliocentric Ecliptic Longitude 10 20 30 40 50 60 Relative Intensity (Arbitrary Units) Trailing Figure3-22.Longitudinalvariationofthelarge-particle ,q=1.7model.Thevariationof thelongitudinalintensityforthemodelnorthernband(redd ashedline)and thesouthernband(bluedottedline)ascomparedwiththecoad deddatafor thenorth(redstars)andsouth(bluediamonds)componentsofthe 17 band forobservationstakenintheleadingdirection(panelA)andt railingdirection (panelB)oftheEarth'sorbit.Themodelincludesparticlesi zes70 mto 1cmandisdescribedbyapowerlawsizedistributionofq=1.7.Th emodel bandintensityvariationmatchesthelongitudinal'phase'of theobservations, butthemodelistoo'spikey'(toobunchedupatasmallrangeofl ongitudes) indicatingtoomuchemphasisonthelargerparticlesandimpl yingthisvalue ofqistoolow. 145

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A 0 100 200 300 10 20 30 40 50 60 Relative Intensity (Arbitrary Units) Leading B 0 100 200 300 Heliocentric Ecliptic Longitude 10 20 30 40 50 60 Relative Intensity (Arbitrary Units) Trailing Figure3-23.Longitudinalvariationofthelarge-particle ,q=1.8model.Thevariationof thelongitudinalintensityforthemodelnorthernband(redd ashedline)and thesouthernband(bluedottedline)ascomparedwiththecoad deddatafor thenorth(redstars)andsouth(bluediamonds)componentsofthe 17 band forobservationstakenintheleadingdirection(panelA)andt railingdirection (panelB)oftheEarth'sorbit.Themodelincludesparticlesi zes70 mto 1cmandisdescribedbyapowerlawsizedistributionofq=1.8.Th emodel bandintensityvariationmatchesthelongitudinal'phase'of theobservations andalsoiswellttotheamountofnodaldispersionpresentintheb and, makingitthebesttmodel. 146

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A 0 100 200 300 10 20 30 40 50 60 Relative Intensity (Arbitrary Units) Leading B 0 100 200 300 Heliocentric Ecliptic Longitude 10 20 30 40 50 60 Relative Intensity (Arbitrary Units) Trailing Figure3-24.Longitudinalvariationofthelarge-particle ,q=1.8model,atanageof 236kyrs.Thevariationofthelongitudinalintensityforthem odelnorthern band(reddashedline)andthesouthernband(bluedottedline) ascompared withthecoaddeddataforthenorth(redstars)andsouth(bluedi amonds) componentsofthe17 bandforobservationstakenintheleadingdirection (panelA)andtrailingdirection(panelB)oftheEarth'sorbi t.Themodel includesparticlesizes75 mto1cmandisdescribedbyasizedistributionof q=1.8atanageof236kyr.Themodelbandintensityvariationm atchesthe longitudinal'phase'oftheobservationsandiswellttotheam ountofnodal dispersionpresentintheband.Thisslightlyoldermodelprovid esaneven betterttothedatathanthemodelofthepreviouslypublisheda geof220 kyr. 147

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1 10 100 1000 Age (1000s of Years) 0.0 0.2 0.4 0.6 0.8 1.0 Proportion of Cross Sectional Area Remaining (P-R loss) q=1.7 Emilkowalski Veritas Karin q=1.8 Figure3-25.P-Rdragdecayofareawithtime.Asthesemimajora xisofdustparticles decayundertheeectofP-Rdrag,theyeventuallyreachinside 1AU, wheretheyareremovedfromcontributingtoanyobservations madefrom theEarth.Thesmallerparticlesdecayfasterandareremovedm orequickly, thustheproportionoftheareafromadisruptionthathasbeen lostisa functionofthesize-distributionofthedust.Higherqvaluesco ntainmore ofacontributionfromthesmallestparticlesandthusdecayfa sterthan lower-q-valuesystems.ThecurvesshownhereaccountforlossbyP -Rdrag oftheoriginaldisruptiononly,andnotcollisionalloss,which wouldserveto furtherdecreasetheareaatlaterages.Theageofthepossiblesou rceofthe partialband,Emilkowalski,isshownaswellastheagesoftwoo ftheolder bands,KarinandVeritas.Moreoftheoriginaldustremainsinth eyounger disruption,buttheolderdisruptions,forwhomcollisionsarei mportant,will haveevenlessoftheiroriginaldustthanisshownhere. 148

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A 0 100 200 300 Ecliptic Longitude -30 -20 -10 0 10 20 30 Ecliptic Latitude B 0 100 200 300 Ecliptic Longitude -30 -20 -10 0 10 20 30 Ecliptic Latitude C 0 100 200 300 Ecliptic Longitude -30 -20 -10 0 10 20 30 Ecliptic Latitude Figure3-26.Variationofdustbandswithwavelength.Forone ofthemodelsthepredicted variationofthethermalemissionfromthedustbandstructurein =12 m (panelA), =25 m(panelB),and =60 m(panelC)wavebands. 149

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CHAPTER4 INTERACTIONSWITHMARS 4.1Introduction Thepreviouschaptershaveshownhowmodelingthedustbandsca nhelpusconstrain themagnitudeanddistributionoftheasteroidaldustwhoseemissi onproducesthe dustbands.Thesebands,thoughtheyarethekeytodeterminingth emagnitudeof theasteroidalcontribution,areconstrainedoutside2AUandd on'tprovidemuch informationonthedustenvironmentinnear-Earthspace.Under standinghowthe orbitsandpropertiesofdustparticlesevolveastheyreacht heinnersolarsystemisof greatimportancetocharacterizingthethreatthatthesepar ticlesposetospacecraftand satellitesinnear-earthspaceandtounderstandingthenumero usIDPs(Interplanetary DustParticles)thatarecollectedonorneartheearth.IDPsar ecollectedinmany ways,insitucollectionsinspace,fromtheoceanoorsandthepo larices,andinthe atmosphere.IDPscollectedattheEarthrepresent,eectively ,alow-costsamplereturn mission.Eachparticlecontainsinformationabouttheobject fromwhichitcameandthe spaceenvironmentthroughwhichithastraveled.However,col lectingandanalyzingIDPs isoflittleuseiftheycan'tbelinkedbacktoasourcebody.Unde rstandingtheorbitsof asteroidaldustinthisregioncanhelpdeterminewhatproport ionoftheseparticlescome fromasteroidalsources.Abouthalfofthecollectedparticlesh aveelementalabundances thatcloselymatchthebulkabundancesofCIorCMcarbonaceou schondritemeteorites (Rietmeijeretal.,1998).Thespectraofthiscompositionofm eteoritesisverysimilarto thatofC-typeasteroids.Veritas,oneofthefamiliesknowntob econtributingdusttothe zodiacalcloudisaC-typeasteroid.Doesthisbiasinthecoll ectedIDPsrepresentabias towardsdustfromthisfamilyreachingnear-Earthspace,asop posedtotheS-typeKarin family? Inordertocharacterizetheasteroidaldustparticleorbitsn eartheEarth,wemust understandhowthedistributionoforbitalelementschangeas theyevolveinwardsunder 150

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P-Rdragfromtheirsourceregionsinthemainbeltinwardsto1 AU.Theorbitsofthe asteroidaldustparticleschangeastheyevolveduetothreema ineects:thedispersion fromthesecularresonanceat2AU,trappinginmean-motionreson anceswithMars andtheEarth,andscatteringofparticlesbyMarsandEarth.T heseeectsareeach dependentonparticlesizeandaremorepronouncedforlarger particlesthatmigrate inwardmoreslowly.ThetrappinginresonanceswiththeEarthi swellstudied(e.g., Dermottetal.,1994)asisthedispersionfromthesecularandJo vianmean-motion resonances(e.g.,Kehoeetal.,2007b).Wefocushereonthesca tteringeectsofMars onthedustparticleorbitsthroughananalyticalanalysisbase donanextensionofthe theoreticalargumentpresentedby Opik(1951). Outsideof2AU,JupiterandSaturnlargelycontrolthedynamic softhedustand theorbitsoftheparticlesinthisregionaregenerallywell understood.However,as theorbitsoftheseparticlesdecayinwardsof2AU(underthee ectofP-Rdrag),the importanceofthegravitationalperturbationsbytheterre strialplanets,particularlyEarth andMars,greatlyincreasesandthedynamicalbehavioroftheo rbitsbecomesevenmore complicated.Weinvestigateherethegravitationalperturb ingeectsofMarsfollowing themethodoftheseminalpaperby Opik(1951).Inhisanalysis, Opikdeterminesthat veryfewofthemicron{cmsizeddustparticlessueradirectcoll isionwiththeplanet faceastheydecayinwardspastMars.However,wehavere-analyz edthisproblem, consideringadditionallythelikelihoodthatthedustpartic leorbitspassthroughtheHill sphereofMars(tovariousdepths)andexperiencepotentially signicantperturbations totheirorbits.TheHillsphereapproximatesthegravitationa lsphereofinuenceofan astronomicalbody(e.g.,MurrayandDermott,1999).Weinvest igatedthefractionof asteroidaldustparticlesofvariousdiameters,orbitalincli nations,andorbitaleccentricities thatwouldentertheMartianHillsphere.ThedeeperintotheHil lspherethataparticle penetrates,thegreaterthepotentialperturbationtothatp article'sorbit.Someestimate ofthemagnitudeoftheperturbationswillbediscussedinSecti on 4.3.5 151

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4.2Method Beginningwiththemethodof Opik(1951)ondeterminingcollisionprobabilities ofdustparticleswithplanetsoneccentricorbits,wehaveext endedthetheorytoallow foreccentricorbitsofthedustparticles.Thesurvivalfracti on(ofparticlesthatdo notundergoacloseplanetaryencounter), ,iscalculatedfromtheprobabilityofan encounter.Thesurvivalfractionisgivenby = e ¡ ¢ t=T (4{1) where¢ t istheP-Rdragtimescaletodecaythroughtheregionofintere st,and T isthe lifetimefromencounters.TheP-Rdragtimeiscalculatedove rtherangeofsemimajor axesinwhichtheparticlecouldinteractwithMars,thusspeci fyingthetimeinwhichthe particlemightsueranencounter.Thetimescalecanbefoundfr omequation 3{21 andis givenhereas ¢ t = 400 D 1150 ¡ a 2i ¡ a 2f ¢ : (4{2) Sincetheparticleshaveeccentricorbits,thezoneofintera ctionistakenfromwhenthe pericenteroftheparticle'sorbitreachestheouteredgeof Mars'Hillsphere,untilthe apocenteroftheparticlereachestheinneredgeofMars'Hillsp here.Theselocations representtherstandlastandtimestheparticle\sees"Marsandth eregionoverwhich theycaninteract.Theyaregivenas a i = a Mars + R Hill 1 ¡ e 0 (4{3) and a f = a Mars ¡ R Hill 1+ e 0 (4{4) where e 0 istheeccentricityoftheparticle'sorbit, a Mars isthesemimajoraxisofMars' orbitand R Hill istheradiusoftheMars'Hillsphere(.0072AU|about320timest he radiusofMars).Theothertimescaleatworkhereisthelifetim efromencounters T is 152

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givenby T = a 3 = 2 P (1 ¡ ) 1 = 2 (4{5) where T isinyears, a isthesemimajoraxisoftheparticleisinAU,the(1 )term accountsfortheeectsofradiationpressureontheparticles'o rbitalperiodand P isthe probabilityofcollisionperorbitoftheparticleasgivenby P = 2 U sin i ¢j U x j (4{6) where istheradiusofthe\sphereofinteraction"relativetothepl anetsemimajoraxis. Theinclination i istherelativeinclinationoftheparticleorbittotheplan etorbit,asitis usedtodeterminethegeometryoftheinteraction.Thevariab les U and U x representthe relativevelocityfortheinteractionoftheorbitsandareg ivenby, U 2 x =2 ¡ 1 A ¡ A (1 ¡ e 2 )+ 4 9 e 20 ; (4{7) U 2 =3 ¡ 1 A ¡ 2 p A (1 ¡ e 2 )cos i + 4 9 e 20 (4{8) where e istheparticleeccentricity, e 0 istheplaneteccentricity, A is a / a 0 ,theratioofthe particletoplanetsemimajoraxiswhichweassumetobeunitytoa llowforinteraction, and i isagaintherelativeinclinationoftheparticle/planetor bits. InordertodetermineiftheparticlescollidewithMarsanda reremovedfromthe system, Opiksetthevalueofthesphereofaction tothecrosssectionalareaofthe planetface.Wevariedthisvaluefromthatoftheplanetface uptotheHillsphereofthe planet(andvariouspercentagestherein),todetermineift heparticlesarepassingthrough thisregionofpotentialorbitalperturbations.Figure 4-1 showsaschematicofthevalues usedfor inthiswork.Marsisshowninred(andisnottoscale)andtheHill sphere, 50%oftheHillsphere,and10%oftheHillsphereareshowntoscaleto indicatethe dierentpassagedistancesfromtheplanetthattheyrepresent. 153

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4.3Results Wehavedeterminedthefractionofasteroidaldustparticleso fvariousdiameters, orbitalinclinations,andorbitaleccentricitiesthatwoul denterMars'Hillsphereandthus experiencepotentialorbitalperturbations.Recallthatth eHillsphereapproximatesthe gravitationalsphereofinuenceofanastronomicalbody,thus theMartianHillsphere istheregioninwhichMarswouldbeexpectedtocausenon-negl igiblegravitational perturbations.ThedeeperintotheHillspherethataparticlep enetrates(smaller percentagethereof),thegreaterthepotentialorbitaleec tsonthatparticle.Inorder toinvestigateanybiasesintheknownasteroidalsourcesofthec loud,wechosetolookat inclinationsof 2 and 10 ,sincetheserepresenttheapproximatelocationsoftherecent asteroidfamilyformationsofKarinandVeritas,respectively .Thesefamilies,thesources ofthe\near-ecliptic"and\ten-degree"zodiacaldustbands, areknownsourcesofdust thatmigratesintotheinnersolarsystem.Wealsotestaninclinat ionof40 torepresent cometarytypeorbits.Werstconrm Opik'sresultofasurvivalfractionof 1fordirect interactionsofthedustparticlesofallsizesofinterestwith thefaceofMars,meaningthat particlesarenotsueringacollisionwiththeplanet.Wethenv arythesurfaceofaction andndthat,whentheregionofinterestisincreasedfromthefa ceofMarsuptoitsHill sphere,theresultsarequitedierent.Wendthataverylargefr actionofallparticle sizes,attheinclinationsofinterest,arepassingthroughtheHil lspherewheretheycould besubjecttopotentiallysignicantperturbationstotheiror bits.Wediscusstheresults here.4.3.1Inclination Figures 4-2 { 4-4 showthesurvivalfraction, ,asafunctionofinclinationfora rangeofparticlesizesandfordierentregionsofinteractio nwithMars.Figure 4-2 shows thefractionoftheparticlesthatwillentertheHillsphereof Mars.Allofthe > 200 m diameterparticlesentertheHillsphereregardlessoftheincl inationoftheirorbit,but thefractionofsmaller( < 100 mdiameter)particlesthatentertheHillspherewillbe 154

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afunctionofinclination.Thisimpliesthatthepercentage ofparticleswhichexperience potentialorbitaleectswillvaryforthe2 and10 families.Thissameeecttoastronger degreecanbeseeinFigures 4-3 and 4-4 ,inwhichthelowerinclinationparticleshave amuchlowersurvivalfractionthanthehigherinclinationpa rticles.Thisinclination dependenceisduetothegeometryoftheinteraction.Thelow erinclinationparticlesare orbitingin/neartheplaneofMars'interactioncrosssectiona nd,asthus,aremorelikely topassthroughtheperturbationregionsthanarethehigheri nclinationparticleswhoonly passthroughtheorbitalplaneofMars'twiceperorbit(thenod esoftheintersectionof theplanes).Sincethelowinclinationparticlesaremorestro nglyaectedthanthehigher inclinationparticles,thismayintroduceabiasintheastero idalfamilydustparticles reachingtheinnersolarsystemunperturbed,sincelikelymanym oreoftheKarinparticles willsuerorbitalperturbationsthanthehigherinclination Veritasparticles.Decreasing theregionofinterestevenfurthertothatoftheplanetface( theproblemstudiedby Opik) resultsinnoparticles(ofanyinclination)interactingwit htheplanetandthusweconrm Opik'sresultsthatnoparticlesarebeingremovedthroughco llisionswiththeplanet. 4.3.2Size Inadditiontothebiaswithinclination,wealsoseeabiaswith particlesizeforthe fractionoforbitswhichtravelthroughsomefractionofthesp hereofinuenceofMars. Figure 4-5 showstheresultsforallparticles1 mto1mm.Mostparticles 100 mtravel throughtheHillsphereofMars,butasthethepenetrationlevel increases,abiastowards thelargestparticlesenteringtheregionbeginstoshow.Figu re 4-6 showsthatthelargest particles( > 500 m)allpenetrateto50%downintotheHillsphere.Figure 4-7 ,though, showsthatveryfewofparticles < 800 mactuallypenetrateintothe10%leveloftheHill sphere(i.e.passveryclosetotheplanet). Theresulthereis,thelargertheparticle,thehighertheprob abilitytopasscloseto theplanet.Thisisduetothelargerparticles'longerP-Rdra glifetimesandthuslonger timespentevolvingthoughtheregionofinteraction.Sincet hesizerangeof100{200 m 155

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providesmostofthecross-sectionalareaandmassat1AU(Grunet al.,1985),thestrong dependenceofthisparticularparticlesize-rangeoninclin ation( 80%ofthe2 inclination particlespasswithin50%oftheHillsphere,asopposedto 40%ofparticlesfromthe 10 inclinationsource)couldcreateabiasintheasteroidfamily particlesarrivinginto near-Earthspaceunperturbed.4.3.3Eccentricity Wealsoinvestigatedthedependencyoftheeccentricityofthe particleorbitson theinteractionwithMars.Wendthatthesurvivalfractionofp articleswithvarying eccentricitiesiscorrelatedwithparticlesize,andthatth elargestparticleswiththehighest eccentricitiesaremostlikelytoentertheHillsphere.Atvery higheccentricitiesthough, thelikelihoodofinteractionforallparticlesizesconverg es,meaningthatdustonhighly eccentricorbitswouldnotshowthesizebiasinsurvivalratest hatlowereccentricity orbitshave.Additionally,thebiasofthehighereccentrici typarticlesbeingmorelikely tohaveorbitalperturbationscouldcreateabiasinthesourc edistributionofthecloud neartheEarth,ifthehigher-eccentricitycometaryorbits aremoreeectedthanhe lower-eccentricityasteroidorbits.TheresultsareshowninFi gures 4-8 { 4-10 4.3.4NumericalSimulations Figures 4-11 and 4-12 showtheresultsdiscussedhereascomparedwiththeresults ofnumericalsimulations(Kehoeetal.,2007).Theresultsfro mthesimulationsare shownasdiamonds(Karin)andtriangles(Veritas)forarangeo fcolor-codedsizes.The numericalsimulations,whichincludemanymoreeectsthanthe original Opikanalysis, includingeectsofresonancesandperturbationsfromallthe planets,showareasonably goodagreement.Thebesttoftheanalyticalresultstothenume ricalsimulationsfor thedependenceoninclinationandparticlesizeofpassagethro ughtheregionofinterest comesfromassumingaslightlyreducedvalueoftheeccentricit y(e=0.03).Theprevious analysiswasdoneusingaconstantvalueofe=0.05inthetestofth edependenceonsize andinclination.Thisvaluewaschosenasabroadlyrepresenta tivevalue,astheVeritas 156

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andKarinfamilies,thesourcesofthedust,havepropereccentr icitiesof0.064and0.044 respectively(Nesvornyetal.,2003).Theactualvaluesofthe dusteccentricitieswould beexpectedtovaryfromthis,astheyexperiencetheinitiale ectsofradiationpressure (Equation 2{6 ).Additionallythevalueoftheeccentricitywouldbeexpect edtodecayas theparticlesevolveinwards,asP-Rdragalsocausestheorbits tocircularize.Although allofthesevaluesarejustestimates,abrief,back-of-the-env elopecalculationofthewhat theeccentricityvaluesmightdecayto,startingfromtheini tialvaluesofthefamilyand consideringonlythe2-bodyP-Rdragperturbation,resultsin aneccentricityof0.03 andpossiblyexplainstheimprovedttothenumericswiththissm allervalueofthe eccentricity.4.3.5QuantifyingthePerturbation Abriefanalyticalanalysiswasusedtoquantifythemagnitude oftheeccentricity perturbationthatwouldbeexpectedforparticlespassingthr oughthesedierentregions oftheHillsphereandispresentedhere.Inallcases,thelowerthe initialeccentricityof theparticle,thegreatertheperturbationtotheparticleo rbit. ForpassagethroughtheHillsphere,theperturbationisquitesma ll.Forcircular orbits,passagethroughtheHillspherewouldvarytheeccentrici tybyonlyabout ¢e=0.02.Theeccentricityvariationissmallerandsmallerfor particleswithincreasingly eccentricinitialorbitsandeectivelynegligibleonanyor bitswithinitialeccentricity greaterthanaboute=0.01. Passagewithin50%oftheHillspherefromtheplanetwouldresulti nslightlystronger perturbations.Particlesoninitiallycircularorbitsthat passwithinthisdistanceofthe planetwouldhaveaneccentricityvariationofabout¢e=0.08 .Theeectdecreaseswith greaterinitialeccentricitiesandbecomesnegligiblefor particleswithinitialeccentricities greaterthanaboute=0.05. Whentheparticlespasswithin10%oftheHillsphereoftheplane t,though,the eectscanbesignicant|especiallyforcircularorbits.Theeec tinthisregionis 157

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insignicantonlyfororbitswithaninitialeccentricityofe =0.1andgreater.Fororbits withaninitialeccentricityofe=0.03(avaluerepresentati veoftheKarinandVeritas dustintheinnersolarsystem),theperturbationwouldbe¢e=0.04 .Foraneccentricity ofe=0.02,anevenmoresignicantvalueof¢e=0.125isfound.Pa rticlesthatenterthe Hillspheretowithin10%oftheplanet,oninitiallycircularo rbits,wouldexperiencevery extremeeccentricityvariations|upto¢e=1.0. 4.4SummaryandFutureWork WeconcludeherethatMarsmayhaveasignicanteectondustpart icleorbits. Becausetheparticlesdon'tpenetrateverydeeplyintotheMa rtianHillsphere,theresult ofthegravitationalinteractionswilllikelybethatofmod estorbitalchangesratherthan removalthroughejectionfromthesystemoraccretion(aswassh ownbyasurvivalfraction 1fortheplanetface).Wendthat,inthepopulationofpartic lesthatentertheHill sphere,thereisabiastowardslowerinclination,higherecc entricityorbits,andlarger particlesizes(Espyetal.,2008).Inparticular,thebiastow ardeectsonlower-inclination sources,suchastheS-typeKarinrelativetotheC-typeVeritas, maycreateabiasinthe proportionsofasteroidfamilyparticlesthatreachtheinne rsolarsystemandcouldexplain theover-abundanceofIDPsthatarecompositionallysimilart oC-typeasteroids.Thebias towardshighereccentricityparticlesmaycreateabiasint hesourcesofthecloud,withthe cometaryparticlesbeingevenmoreaectedthanlowereccent ricityasteroidalparticles. Thebiaswithparticlesizemayeectthesize-frequencydistrib utionofasteroidalparticles thatreachtheinnersolarsystemandthuseecthowthesize-distri butionvariesas afunctionofheliocentricdistance.Thesesizebiasesmayalsowe llbeevidentinthe compositionanddiversityofIDPscollectedontheEarth(e.g. ,Brownlee,2001;Flynn, 1994). Thetheoreticalresultspresentedhereinformusofthelikeli hoodofaninteraction andananalyticalanalysisyieldssomeconstraintonthemagnit udeoftheexpected perturbation.Infuturework,though,fullnumericalsimula tionsoftheparticleorbitsand 158

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theperturbationstheyundergo,willrevealthefullextent oftheeectsofthegravitational interactionswithMarsonthedustparticleorbits.Inadditio n,thesefullintegrationsof thedustorbitevolutionwillallowustotestwhatpercentageo ftheseparticlesgettrapped intomean-motionresonanceswithMarsandhowthatmightaect theoverallpictureof gravitationalscatteringbyMars.IthasbeensuggestedthatMar smayhavearesonant ring(Kuchneretal.,2000)similartothatofEarth(Dermotte tal.,1994)butnonehas beenseenwithcurrentsensitivityofobservations.Modelingoft hisnaturecanpredicta presenceorabsenceoftheringbydeterminingthelikelihooda ndextentoftheparticles beingtrappedintoco-rotationresonanceswiththeplanet. 159

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Figure4-1.Schematicofpenetrationdepths.Thevaluesof usedinthisanalysisare shown|theHillsphere,50%oftheHillspheredistancefromMars,10%oftheHillspheredistancefromMars,andthefaceofMarsitself(sh ownin redandnottoscale).PassagethroughtheHillspheremayresultino rbital perturbationsandpassagedeeperintotheHillsphere,whichresu ltsincloser passagetotheplanet,maycorrespondtostrongerorbitalpertur bations 160

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0 5 10 15 20 Inclination (degrees) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 100 m m 10 m m 1000 m m 50 m m 200 m m Hill Sphere Figure4-2.LikelihoodofpassagethroughtheHillsphereasafun ctionofinclination.The dependenceofsurvivalfractionontheinclinationofthepar ticlewithrespect totheplanetisshownforarangeofparticlediameters.Asurviv alfactionof 1meansthatnoparticlespassthroughtheHillsphereandasurviv alfraction of0meansthattheyalldo.Itcanbeseenthatmostallofthe > 200 m diameterparticlesentertheHillsphereregardlessoftheincl inationoftheir orbit,butthefractionofsmaller( < 100 mdiameter)particlesthatenterthe Hillspherewillbeafunctionofinclination.Thisimpliestha tthepercentage ofparticlesthatsuerperturbationswilldierforthe2 and10 source families. 161

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0 5 10 15 20 Inclination (degrees) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 100 m m 10 m m 1000 m m 50 m m 200 m m 50% Hill Sphere Figure4-3.Likelihoodofpassagewithin50%oftheHillsphereas afunctionof inclination.Thedependenceofsurvivalfractiononinclina tionisshownfor arangeofparticlediameters.Asurvivalfactionof1meanstha tnoparticles passthroughtheHillsphereandasurvivalfractionof0meanstha tthey alldo.Passagewithin50%oftheHillspherefromtheplanetmayim plya potentiallystrongerperturbation.Thelowerinclinationp articleshavealower survivalfractionthanthehigherinclinationparticlesdue tothegeometry oftheinteraction.Thisimpliesthatthepercentageofpart iclesthatsuer perturbationswilldierforthe2 and10 sourcefamilies. 162

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0 5 10 15 20 Inclination (degrees) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 100 m m 10 m m 1000 m m 50 m m 200 m m 10% Hill Sphere Figure4-4.Likelihoodofpassagewithin10%oftheHillsphereas afunctionof inclination.Thedependenceofsurvivalfractiononinclina tionisshownfor arangeofparticlediameters.Asurvivalfactionof1meanstha tnoparticles passthroughtheHillsphereandasurvivalfractionof0meanstha tthey alldo.Passagewithin10%oftheHillspherefromtheplanetmayim plya potentiallystrongperturbationduetotheproximitytothep lanet.Virtually alloftheparticlesofallinclinationssurviveapassagethisc losetoMars. 163

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0 200 400 600 800 1000 Size (microns) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 10 o 40 o 2 o Hill Sphere Figure4-5.LikelihoodofpassagethroughtheHillsphereasafun ctionofsize.The dependenceofsurvivalfractiononparticlediameterisshown forathree representativeinclinations.Asurvivalfactionof1meanstha tnoparticlespass throughtheHillsphereandasurvivalfractionof0meansthatth eyalldo. The2 and10 inclinationsrepresenttheKarinandVeritasasteroidfamili es, respectively,andthe40 inclinationrepresentscometary-typeorbits.Most particles > 100 m,regardlessofinclination,travelthroughtheHillsphereof Marsandexperiencepotentialorbitalperturbations. 164

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0 200 400 600 800 1000 Size (microns) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 10 o 40 o 2 o 50% Hill Sphere Figure4-6.Likelihoodofpassagewithin50%oftheHillsphereas afunctionofsize. Thedependenceofsurvivalfractiononparticlediameterissh ownforathree representativeinclinations.Asurvivalfactionof1meanstha tnoparticlespass throughtheHillsphereandasurvivalfractionof0meansthatth eyalldo. The2 and10 inclinationsrepresenttheKarinandVeritasasteroidfamili es, respectively,andthe40 inclinationrepresentscometary-typeorbits.The largestparticles( > 500 m)allpenetrateto50%depthintotheHillsphere. 165

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0 200 400 600 800 1000 Size (microns) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 10 o 40 o 2 o 10% Hill Sphere Figure4-7.Likelihoodofpassagewithin10%oftheHillsphereas afunctionofsize. Thedependenceofsurvivalfractiononparticlediameterissh ownforathree representativeinclinations.Asurvivalfactionof1meanstha tnoparticlespass throughtheHillsphereandasurvivalfractionof0meansthatth eyalldo. The2 and10 inclinationsrepresenttheKarinandVeritasasteroidfamili es, respectively,andthe40 inclinationrepresentscometary-typeorbits.Veryfew ofparticles < 800 mactuallypenetrateintothe10%leveloftheHillsphere andpassveryclosetotheplanet. 166

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0.0 0.2 0.4 0.6 0.8 1.0 Eccentricity 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 100 m m 10 m m 1000 m m Hill Sphere Figure4-8.LikelihoodofpassagethroughtheHillsphereasafun ctionofeccentricity. Thedependenceofsurvivalfractiononparticleeccentricit yisshownfora threeparticlediameters.Asurvivalfactionof1meansthatno particlespassed throughtheHillsphereandasurvivalfractionof0meansthatth eyalldo. Thelargestparticleswiththehighesteccentricitiesaremost likelytoenterthe Hillsphere.Atveryhigheccentricities,though,thelikeliho odofinteraction forparticles > 100 mconverges,meaningthatdustonhighlyeccentricorbits wouldnotshowthesizebiasinsurvivalratesthatlowereccentr icityorbits have. 167

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0.0 0.2 0.4 0.6 0.8 1.0 Eccentricity 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 100 m m 10 m m 1000 m m 50% Hill Sphere Figure4-9.Likelihoodofpassagewithin50%oftheHillsphereas afunctionof eccentricity.Thedependenceofsurvivalfractiononpartic leeccentricityis shownforathreeparticlediameters.Asurvivalfactionof1mea nsthatno particlespassthroughtheHillsphereandasurvivalfractionof 0meansthat theyalldo.Thelargestparticleswiththehighesteccentrici tiesaremostlikely topassintothisregion. 168

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0.0 0.2 0.4 0.6 0.8 1.0 Eccentricity 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 100 m m 10 m m 1000 m m 10% Hill Sphere Figure4-10.Likelihoodofpassagewithin10%oftheHillspherea safunctionof eccentricity.Thedependenceofsurvivalfractiononpartic leeccentricityis shownforathreeparticlediameters.Asurvivalfactionof1mea nsthatno particlespassthroughtheHillsphereandasurvivalfractionof 0meansthat theyalldo.Thelargestparticleswiththehighesteccentrici tiesaremost likelytopassintothisregion. 169

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0 5 10 15 20 Inclination (degrees) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 100 m m 10 m m 500 m m 50 m m 20 m m Figure4-11.Survivalfractionversusinclinationascompar edwithnumericalsimulations. Theresultsofthedependenceofthesurvivalfractiononincli nationare shownwiththeresultsfromthenumericalsimulationsasdiamon ds(Karin) andtriangles(Veritas)forarangeofcolor-codedsizes.Thebe stagreementof themodelwiththenumericalsimulationscomesfromaslighter smallervalue oftheeccentricitythanwasoriginallyassumedforthepartic lesbasedonthe families'eccentricities(asdiscussedinthetext)andasshownh ere. 170

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0 100 200 300 400 Size (microns) 0.0 0.2 0.4 0.6 0.8 1.0 Survival Fraction 10 o 2 o Figure4-12.Survivalfractionversussizeascomparedwithnu mericalsimulations.The resultsofthedependenceofthesurvivalfractiononparticle diameter areshownwiththeresultsfromthesimulationsasdiamonds(Kar in)and triangles(Veritas)forthetwodierentcolor-codedinclina tionstowhichthey correspond.Thebestagreementofthemodelwiththenumerical simulations comesfromaslightersmallervalueoftheeccentricitythanwa soriginally assumedfortheparticlesbasedonthefamilies'eccentricities (asdiscussedin thetext)andasshownhere. 171

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CHAPTER5 CONCLUSION Themainaimofthisworkhasbeentounderstandhowasteroidsco ntributedust tothezodiacalcloud,bothfromtherstwaveofdustproducedin adisruption,asseen inthepartialdustband,totheolder,evolveddustpopulation softhethreemaindust bands.Dynamicalmodelingofthethreeoriginaldustbands(Ch apter2)hasallowed ustodeterminewhatproportionofthezodiacalcloudcomesf romasteroidalsources, contributingtothedebateontherelativecontributionsth atremainsattheforefrontof theeld.Identicationofanewdustbandat 17 hasallowedus,forthersttime, toseeadustbandwhileitisstillforming.Subsequentmodelingo fthisbandallows usararelookatthequantityandsizedistributionofdustprodu cedinacatastrophic disruption,beforeithastimetodecayorevolve.Thisallows ustoestimatetheamount ofdustproducedinacatastrophicdisruptionofanasteroid,the structure(depthofthe regolith)oftheparentasteroid,andyieldsinformationonh owtheasteroidalcomponent ofthecloudmightvarywithtime.Aninvestigationoftheevolu tionofdustintotheinner solarsystemthenletsusextendtheanalysistonear-Earthspacea ndlinktheproduction ofasteroidaldustproducedinthemainbelttothepopulationo fIDPscollectedatthe Earth. 5.1SummaryofResults InChapter2webuilddynamicalmodelsofthethermalemissiono fthezodiacal clouddustbandsbasedontheorbitsofthedustcomposingthem.Pr eviousmodels werebuiltundertheassumptionsthatthesourcesofthedustband swereold,large asteroidfamiliesproducingdustthroughaslowcollisionalgri dingprocess.Herewebuild modelsunderthenewthinkingthatthedustbandsareproduced byrecentcatastrophic disruptionsthatinjectedawaveofdustintothecloud.Compar isonofthesemodels withIRASobservationsthenallowsustoconstrainnotonlytheq uantityofasteroidal dustinthecloud,butthephysicalpropertiesofthedustaswell .Wendthatthedust 172

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inthezodiacaldustbandsisbestdescribedbyasize-distributio npower-lawparameter ofq=1.4,whichagreeswellwithpreviousresultsbyGroganet al.,2001.TheVeritas asteroidfamilycontributesabouttwiceasmuchdustasthecen tralbandsourcesKarin andBeagle,andthisndingalsoagreeswiththevaluefoundinr ecentworkbyNesvorny etal.(2006).Thedustisdistributedheliocentricallyasdesc ribedbyaninversepowerlaw parameterintherange =1{2.Althoughthedustbandsthemselvesrepresentonlyafew percentofthecloud,modelingofthebandsallowsustoconstr ainthemuchlarger,total asteroidalcomponent.Wendthatacrosssectionalarea5{7x10 9 km 2 ofasteroidal dustispresentinthezodiacalcloud.Theresultsofcomparisono ftheemissionfromthe dustinthedustbandmodelswiththatofthetotalthermalemissio nofthecloudyields theresultsthat,overtheentiresky,asteroidalsourcescontri bute 6{13%ofthe25 m zodiacalcloudux.Intherangeof § 50 aboveandbelowtheecliptic,theasteroidal contributionaccountsfor 8{16%oftheux,andfortheregion § 10 aboveandbelow theecliptic,thepercentageincreasesevenfurtherto 13{24%forthe valuesranging from1{2respectively. InChapter3wecoaddtheIRASdataanddiscoveranewzodiacaldu stbandat § 17 aboveandbelowtheecliptic.Afterexaminingthebandinsmall erbinsofecliptic longitude,wendthatthedustbandappearsinsomepartsofthesk yandnotothers,in apatternconsistentwiththatofapartial,still-formingband .Thepatternofvariation ofthedustbandaroundtheskypredictsanodeof 40 forthesource.Togetherwith theinclinationandyoungage,weidentityalikelysource|th eEmilkowalskicluster. Webuildafulldynamicalmodeloftheformationofthisdustba ndforcomparison withthecoaddedobservations.Becausethisbandissoyoung,ita llowsusalookatthe amountandsize-distributionofdustproducedintheoriginalc atastrophicdisruptionof anasteroid,beforeitisalteredbytime.Afterdemonstratingt hatcollisionsshouldnot beplayingaroleinthedynamicsofyoungstructures(asthisp artialband),wecreatean analyticdynamicalmodelwhichisconvertedtoathermalemi ssionmodeloftheband. 173

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Comparisonwiththeobservationsyieldstheresultofasize-dist ributionparameterof q=1.8,whichismuchhigherthanthatfoundfortheolderdustb ands(implyingthe presenceofmoresmallparticles)andismuchclosertothevaluef oundtobeproduced inacatastrophicdisruptioninlaboratorymeasurements,furth erconrmingtheyoung natureoftheband.Thedichotomyofthesetwosizedistribution sshedslightonthe dierencesinthepopulationofdustgeneratedinacatastrophi cdisruptionofanasteroid (asseenintheyoungerband)andacollisionallyevolvedpopul ation(asseenintheolder dustbands).Additionallywendthat,intheearlystagesofadustb and,uxfromthe largest( > 1mm)particlesisthedominantcontributortothethermalem issionofthe band.Thisisquitesurprisingduetothemuchreducedamountof areapresentinthe largestparticlesforthissizedistribution,butisexplained duetotheiroverdensityin longitudinalspace,sincetheyareallgroupedtogetheratthe source.Weconrmthe likelihoodofEmilkowalskiasthesourceofthebandfromthego odness-of-tofthemodel totheobservations.Furthermore,sinceanewagehasbeencalcu latedforthefamilyupon discoveryofanadditional(4th)member(Vockrouhlicky,in press-privatecommunication), wealsobuildamodelofthisageandndanevenbetterttotheobse rvations,further conrmingEmilkowalskiasthemostlikelysourceandlendingsupp ortforthenewolder agefoundfromtheintegrations.Wealsondthatthecross-section alareaofdustin thisbandisontheorderof 10 7 km 2 .Thiswouldcomparetoaboutathreeandahalf meterthicklayerofregolithonthesurfaceofthe10kmparent body.Ifthequantityof dustproducedisexpectedtoscalewiththevolumeoftheprecur sor,thenwepredictthat Vertiasshouldhaveproduced,initiallyupondisruption,ano rderofmagnitudemoredust thanweseetoday.Finallyweuseourresultstopredictthepresen ceof,orderafew,more partialdustbandsthatshouldbefoundintheWISEdataset. InChapter4weinvestigatethedynamicaleectsofMarsonthed ustparticleorbits inordertobetterunderstandthenear-Earthspaceenvironmen t.WendthatMarsmay haveasignicanteectondustparticleorbits,asalargepercent ageoftheparticles 174

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passthroughtheHillsphereofMarsastheydecayinpasttheplane tontheirwayto theinnersolarsystem.Sincetheparticlesdon'tpenetratever ydeeplyintotheMartian Hillsphere,though,theresultofthegravitationalinteracti onswilllikelybethatof modestorbitalchangesratherthanremovalthroughejection fromthesystemoraccretion ontotheplanet.Weconrm Opik'soriginalresultthattheparticlesarenotsuering directcollisionswiththeplanet.Theeectsoftheperturbat ionswilllikelyincreasewith depthintotheHillsphereandthoseparticlespenetratingdeep estmayhavethelargest perturbationstotheirorbits.Furthermore,wendthat,inth epopulationofparticlesthat entertheHillsphere,thereisabiastowardslowerinclinatio n,highereccentricityorbits, andlargerparticlesizes.Thebiastowardsthelower-inclina tionsources,suchasKarin, passingthroughtheHillspheremaycreateabiasintheproportio nsofasteroidfamily particlesthatreachtheinnersolarsystemandexplainthecomp ositionalbiasesseenin theIDPscollectedattheEarth.Additionally,thebiastowar dshighereccentricitysources passingthroughtheHillsphereofMarsmaycreateabiasinthesour cescontributingto thenear-Earthspaceenvironment,withcometaryparticlessu eringmoreorbitaleects thanthelower-eccentricityasteroidalparticles.Thebiasw ithparticlesizemayaect thesize-frequencydistributionofasteroidalparticlesthat reachtheinnersolarsystem andalsoaecthowthesize-distributionvariesasafunctionofh eliocentricdistance.We quantifythemagnitudeoftheeectoftheperturbationsandn dthatthemostsignicant perturbationswilloccuroninitiallycircularorbitsthat passdeepintotheHillsphere. 5.2ContributionstotheField Themainresultofthisworkhasbeenthediscoveryof,andmodel for,theyoungest-known zodiacaldustband.Fromthediscoveryinthecoaddeddata,tot heexplanationofthe structureasapartialband,tothelinkingtoasourceandconrm ationthroughdynamical modeling,thisworkhasprovidedtherstlookattheformation ofadustbandstructure thatisconstrainedbyobservations.Previousdustbandmodelsh avebeencreated,and tosomeextentbasedonquitesophisticatednumericalsimulation s(Vokrouhlickyetal., 175

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2008),butnonehavehadthecredentialsofanobservationalc onstraint|aconstraint whichallowedtheparametersofthedusttobecharacterized. Comparisonofthemodel totheobservationshasprovidedtherstobservationallookatt hesizedistributionand amountofdustproducedinthecatastrophicdisruptionofanaste roid,beforeitwaslost toP-Rdragorcollisionallyevolved.Italsoestablishedaregim efortheentirelynew methodofmodelingrequiredforpartialbands,amethodthatc anbeappliedtoany futurebandsdiscoveredbyWISE. Inadditiontotheseconstraints,themodelingoftheolderdustb andsprovidesa contrastinglookatmoreevolvedpopulationsandanestimatef orthemagnitudeofthe asteroidalcomponentofthecloud,includingfulldynamicsi nto1.2AU(ratherthana constraintoutside2AUandanextrapolationinwards,asprevio usmodels)thattsinto theframeworkofothercalculationsofthemagnitudeofthea steroidalcomponent. 5.3ImportanceofThisWork Theimportanceofthisworkisquitewide-reaching.Anunderst andingofthe asteroidalcontributiontothezodiacalcloudandhowasteroi dscontributedustis importantforunderstandinghowthecloudmightvarywithtim e.Howdoesthesuggested spikeytemporalvariation(e.g.DurdaandDermott,1997)oft hecloud(Figure 1-8 ) reallylook?Constrainingtheamountandpropertiesofthedu streleasedinanasteroid disruption,asinChapter3,givesinsightintohowthemagnitu deofthecloudmight areinbrightnesswitharecentdisruption.Theimplicationso fthemodelingofthe partialbandpredictthatthecross-sectionalareaofdustassocia tedwiththeVeritas familymayhavebeenanorderofmagnitudebrighteruponitsd isruption.Eventhe geologicrecordhasrecordedevidenceofdustaccretioneven tsontheEarth.Forexample, Farleyetal.(2006),ndanincreaseintheuxof 3 Heintheseaoorsediment(thought tobeimplantedbytheinterplanetarydustparticles)atthepr eciseageoftheVeritas familydisruption(8.3 § 0.5Myr).Theuxincreasedat8.2 § 0.1Myrtofourtimesthe pre-eventlevelsanddissipatedover 1.5Myr.Thedissipationoftheinitialuxwould 176

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implythattheVeritasdisruptioninitiallyproducedalarge waveofdustbrighterthanits currentstateandhasdecayedtowhatweseetoday,aswehavealso predictedhere.Such awaveofdustcouldalsopotentiallyhave(orhavehad)climati ceectsontheearth. Understandingthenatureofasteroidaldisruptionsalsohelpsto unravelsome questionsinthestudyofextrasolardebrisdisks.Manyofthesedisk sshowfeatures similartothezodiacalcloud,includinganasteroidbeltandK uiperbeltanalogs (e.g.Moro-Martinetal.,2007).Severalofthedisksalsoshowa pparentrecentares ofbrightness(e.g.Telescoetal.,2005;Riekeetal.,2005).C ouldthesebrightness uctuationsbetheresultofarecentcatastrophicdisruptionof ananalogofanasteroid, e.g.areweseeingthesesystemsveryearlyonfollowingadisrupti on?Understanding thequantitiesofdustreleasedinanasteroidaldisruptioncanh elptoestimatethe expectedbrightnessuctuationthatwouldbeassociatedandtoa nswerthequestionof whatsizedisruptionwouldbeneededtoproducetheuctuationse en.Thelikelihoodof suchadisruptioncanthebeusedtodetermineifsuchaneventispl ausibleorifother mechanismsareinsteadatwork. Theparametersandorbitsofthezodiacaldustandhowtheorbi tschangeasthey reachnear-Earthspaceisimportanttocharacterizingtheha zardsinthenear-Earth enviroment.Althoughtiny,thesedustparticlesaremovingwit hveryhighvelocities (km/s)andposetreatstospacecraftandsatellites.Understanding theenvironmentin near-Earthspaceisalsokeytothedevelopmentofthetechnolo giesfortheplannedfuture lunarhabitats. IDPs(interplanetarydustparticles)arecollectednearando ntheearthinamultitude ofways|sweptupinthestratosphere,extractedfromtheoceanoo rs,andfoundinthe arcticices.TheseIDPsrepresentaverycosteectivesampleretur nmission,butonlyif wecancharacterizetheorbitsthatdeliveredthemtonear-E arthspaceanddeterminea sourcebody.ThecollectedIDPsareanalysedandthecompositio nsandpropertiesstudied closely,butthisinformationismuchmoreusefulifitistelli ngusaboutaspecicsource 177

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population.Thus,linkingthecollectedIDPswiththeirlike lysourcebodiesthroughthis typeofmodelingiskeytomaximizingtheinformationgained fromtheirstudy. Theconstraintsonthesizedistributionofdust(foundfromthep artialband modeling)yield,forthersttime,observationalconstraintso nthedustreleasedinthe catastrophicdisruptionofasteroid|inasizerangethatcan'tb ereproducedinlaboratory simulations.Combiningthisinformationonthesizedistributi onofthedustparticleswith thesizedistributionofthelargerbodiesproducedinthedisru ption,givesusinformation onthelikelystructureoftheparentbody.Diditbreakupaswo uldbeexpectedfora solidbody,arubblepile,wastherealikelyregolithlayer?Ho wdoestheamountofdust producedscalewiththesizeoftheparentbody? CoaddingtheIRASdataalsogivesusaglimpseofwhattheupcomin gWISE spacecraftmightseeandallowsustomakepredictionsfortheW ISEdataset.Thepartial dustbandmodelllsintheholesintheIRASdatacoverageandpre dictswhatWISE shouldseeintheseregions.Thepartialdustbandalsoreveals,fort hersttime,thatvery smallasteroiddisruptionsshouldbevisibleintheseearlystageso fdustbandformation. Thesedustbandslikely\disappear"whentheirdustbeginstosuer collisions,P-Rdrag loss,andlongitudinaldistribution.Thenatureoftheearlysta gesofdustbandformation, asthe17 bandhasshown,allowsustoseesmall,faintdisruptionsthatwew ouldn't expecttodetectasfullbandpairs. 5.4FutureDirections Thisworktsinwellwithcurrentandfuturedirectionsofthe eldofinterplanetary dust|ittakesadvantageofthenewtechnologydevelopmentsa ndprovidesinsightto addressingthemajorquestions. Thereareseveralnewtelescopes,detectors,andprogramsonthe horizonthatare poisedtoprovideavirtuallyinniteamountofnewdatatothest udyoftheproblems coveredinthiswork.WISE,whichjustlaunchedinDecember20 09,willmaptheentire skyin6monthsat 500timesthesensitivityofIRASandshoulddiscover(atleast)a 178

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fewmorepartial(andfull)dustbands,whilealsollingintheho lesintheIRASview ofthecurrentpartialband.AKARI(formerlyASTRO-F),isaJapa nesesatellitewhose mainobjectiveistoperformanall-skysurveywithbetterspati alresolutionandwider wavelengthcoveragethanIRAS,mappingtheentireskyinsixinf raredbandsfrom9 to180microns(e.g.Murakamietal.,2008).Itwillprovidec omplimentarydatato WISEandatmorewavelengths(which,recall,isimportantfo rconrmingandfurther constrainingthesize-distributionofthepartialbands). Asthesenewfaintdustbandsandpartialbandsarediscovered,th eywillneedtobe matchedtosourcefamilies.Sincetheyrepresentfaint,young, structures,theyarelikelyto beduetosmall,recent,disruptionsofasteroidfamiliesthatm aynothavebeenidentied asyet.Twogroundbasedcampaignswillndmanymoresmall( fewkm)asteroids. Manyoftheseasteroidswillconstitutenewasteroidfamiliesor additionalmembersof currentfamilies,allowingtheiragestoberenedandprovidi ngsourcecounterpartsforthe newfaintbandsdiscoveredbyWISE.Pan-STARRS,thePanoramic SurveyTelescopeAnd RapidResponseSystem(e.g.,Jedickeetal.,2009;Morganetal. ,2008),andLSST,the LargeSynopticSurveyTelescope(e.g.Ivezicetal.,2009),w illalsondmanymoresmaller asteroids.Pan-STARRSisexpectedtondalloftheremainingaste roidsdownto1kmin sizeandLSSTwillnd90%ofthebodiesdownto140m. Additionally,asdiscussedintheintroduction,theworkpresent edherehasapplications tothetoplevelsciencequestionsdenedbythelatestdecalsurve yoninterplanetarydust. Thus,inadditiontomakingimportantcontributionstothecu rrentstateoftheeld,the investigationspresentedinthisworkarepoisedtocontinueto addressthemaingoalsand issuesofthenextdecadeofscience. 179

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REFERENCES [1]Backman,D.,Dasgupta,A.,Stencel,R.,1995.ModelofaKui perBeltsmallgrain populationandesultingfar-infraredemission.ApJLetters450 ,L35. [2]Backman,D.,Werner,M.,Rieke,G.,VanCleve,J.,1997.E xploringplanetarydebris aroundsolar-typestars.FromStardusttoPlanetesimals.ASPConfe renceSeries122, 49. [3]Beichmann,C.A.,1985.InfraredAstronomicalSatellite(I RAS)catalogsandatlases. Explanatorysupplement.In:C.A.Beichmann,(Ed.),JetPropu lsionLaboratory, Pasadena. [4]Beichmann,C.,1987.TheIRASviewoftheGalaxyandthesola rsystem.Annual ReviewofAstronomyandAstrophysics25,521{563. [5]Boggess,N.,and19coauthors,1992.TheCOBEmission-Itsdesign and performancetwoyearsafterlaunch.ApJ397,420{429. [6]Bottke,W.F.,Durda,D.D.,Nesvorny,D.,Jedicke,R.,Mor bidelli,A.,Vokrouhlicky, D.,Levison,H.F.,2005.Linkingthecollisionalhistoryofthem ainasteroidbeltto itsdynamicalexcitationanddepletion.Icarus179,63{94. [7]Brownlee,D.2001.Theoriginandpropertiesofdustimpac tingtheEarth.In: AccretionofExtraterrestrialMatterThroughoutEarth'sHisto ry,Kluwer(New York),1-12. [8]Burns,J.A.,Lamy,P.L.,Soter,S.,1979.Radiationforces onsmallparticlesinthe solarsystem.Icarus40,1{48. [9]Dermott,S.F.,Nicholson,P.D.,Burns,J.A.,Houck,J.R.,198 4.Originofthesolar systemdustbandsdiscoveredbyIRAS.Nature312,505{509. [10]Dermott,S.,Nicholson,P.,Kim,Y.,Wolven,B.,1988.TheI mpactofIRAS onAsteroidalScience.In:Lawrence,A.(Ed.),LectureNotesinP hysics297 Springer-Verlag,Berlin,pp.3. [11]Dermott,S.F.,Gomes,R.S.,DurdaD.D.,Gustafson,B. A.S.,Jayaraman,S.,Xu, Y.-L.,Nicholson,P.D.,1992.Dynamicsofthezodiacalcloud.I n:Ferrax-Mello,S. (Ed.),Chaos,ResonanceandCollectiveDynamicalPhenomenai ntheSolarSystem, KluwerAcad.Publ.,Dordrecht,pp.333{347. [12]Dermott,S.F.,Jayaraman,S.,Xu,Y.L.,Gustafson,B. A.S,Liou,J.C.,1994.A circumsolarringofasteroidaldustinresonantlockwiththeEar th.Nature369, 719{723. [13]Dermott,S.,Grogan,K.,Gustafson,B.,Jayaraman,S.,Ko rtenkamp,S.,Xu,Y., 1996.SourcesofInterplanetaryDust.In:Gustafson,B.,Hanner ,M.,(Eds.),Physics, Chemistry,andDynamicsofInterplanetaryDust,SanFrancisco ,pp.143. 180

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[14]Dermott,S.,Grogan,K.,Holmes,E.,Wyatt,M.,1998.Sign aturesofplanets. ExozodiacalDustWorkshop,59. [15]Dermott,S.,Grogan,K.,Holmes,E.,Kortenkamp,S.,1999 .Dynamicalstructure oftheZodiacalcloud.In:J.MayoGreenbergandAigenLi,(Eds. ),Formationand EvolutionofSolidsinSpace,KluwerAcademicPublishers,p.56 5. [16]Dermott,S.F.,Grogran,K.,Durda,D.D.,Jayaraman,S. ,Kehoe,T.J.J., Kortenkamp,S.J.,Wyatt,M.C.2001.Orbitalevolutionofin terplanetarydust. In:Grun,E.,Gustafson,B. A.S.,DermottS.F.,Fechtig,H.,InterplanetaryDust, Springer,Heidelberg,pp.569{639. [17]Dermott,S.F.,Kehoe,T.J.J.,Durda,D.,Grogan,K.,Nesv orny,D.,2002.Recent rubblepileoriginofasteroidalsolarsystemdustbandsandastero idalinterplanetary dustparticles.ProceedingsofACM,319{322. [18]Dohnanyi,J.S.,1969.Collisionalmodelofasteroidsand theirdebris.JGR74, 2531{2554. [19]Domson,D.,1972.NicolasFatiodeDuillierandtheProphe tsofLondon:AnEssay intheHistoricalInteractionofNaturalPhilosophyandMillenn ialBeliefintheAge ofNewton.PhDThesis,Yale. [20]Durda,D.,Dermott,S.F.,1997.Thecollisionalevoluti onoftheasteroidbeltandits contributiontothezodiacalcloud.Icarus130,140{164. [21]Espy,A.J.,Dermott,S.F.,Kehoe,T.J.J.,2008.Dynamica leectsofMarson asteroidaldustparticles.Earth,MoonandPlanets102,199{20 3. [22]Espy,A.J.,Dermott,S.F.,Kehoe,T.J.J.,Jayaraman,S., 2009.EvidencefromIRAS foraveryyoung,partiallyformeddustband.PlanetaryandSp aceScience57, 235{242. [23]Farley,K.A.,Vokrouhlicky,D.,Bottke,W.F.,Nesvorny ,D.,2006.Alatemiocene dustshowerfromthebreak-upofanasteroidinthemainbelt.Natu re439,295{297. [24]Flynn,G.J.,1994.Interplanetarydustparticlescolle ctedfromthestratosphere: physical,chemicalandmineralogicalpropertiesandimplic ationsfortheirsources. PlanetaryandSpaceScience42,1151{1161. [25]Flynn,G.,Wirick,S.,Keller,L.,Jacobsen,C.,Sandfor d,S.,2009.CarbonateGrains inAnhydrousIDPs.MeteoriticsandPlanetaryScienceSupplem ent,5296. [26]Fujiwara,A.,and21coauthors,2006.TheRubble-PileAster oidItokawaasObserved byHayabusa.Science312,1330{1334. [27]Gautier,T.,Hauser,M.,Low,F.,1984.ParallelMeasureme ntsoftheZodiacalDust BandswiththeIRASSurvey.BulletinoftheAmericanAstronomica lSociety16, 442. 181

PAGE 182

[28]Giese,R.,Kneissel,B.,Rittich,U.,1986.Three-dimension almodelsofthezodiacal dustcloud-Acomparativestudy.Icarus68,395{411. [29]Grogan,K.,Dermott,S.F.,Jayaraman,S.,Xu,Y.L.,1997. Originofthetendegree SolarSystemdustbands.PlanetaryandSpaceScience45,1657{1 665. [30]Grogan,K.,Dermott,S.F.,Durda,D.,2001.Thesize-fre quencydistributionofthe zodiacalcloud:evidencefromthesolarsystemdustbands.Icarus 152,251{267. [31]Grogan,K.,Price,S.,2003.ConstrainingtheOriginand StructureoftheZodiacal DustBandswiththeMSXCelestialBackgroundsData.AASDPSBulle tin35,1488. [32]Gustafson,B. A.S.,1994.Physicsofzodiacaldust.AnnualRev.EarthandPlane tary Science22,553{595. [33]Hilton,J.,2002.AsteroidMassesandDensities.In:BottkeW., Cellino,A., Paolicchi,P.,Binzel,R.(Eds.),AsteroidsIII,W.F.BottkeJr .,A.Cellino,P. Paolicchi,andR.P.Binzel(eds),Univ.ofArizonaPress,Tucson,p p.103{112. [34]Hirayama,K.,1918.Groupsofasteroidsprobablyofcommo norigin.AJ31,185{188. [35]Ivezic,Z.,Tyson,J.,Axelrod,T.,Burke,D.,Claver,C., Cook,K.,Kahn,S.,Lupton, R.,Monet,D.,Pinto,P.,Strauss,M.,Stubbs,C.,Jones,L.,Saha ,A.,Scranton,R., Smith,C.,2009.LSST:FromScienceDriversToReferenceDesi gnAndAnticipated DataProducts.BulletinoftheAmericanAstronomicalSociety41 ,366. [36]Jayaraman,S.,1995.Resonantstructureofthezodiacalc loud.PhDThesis, UniversityofFlorida. [37]Jedicke,R.,Morbidelli,A.,Spahr,T.,Petit,J.M.,Bot tke,W.,2003.Earthand space-basedNEOsurveysimulations:prospectsforachievingthespa ceguardgoal. Icarus161,17{33. [38]Jedicke,R.,2009.FirstResultsfromPan-STARRS1.AASDPSMe eting41,43.04. [39]Kehoe,T.J.J.,Murray,S.D.,Porco,S.S.,2003.Adissipa tivemappingtechniquefor theN-bodyproblemincorporatingradiationpressure,Poyntin g-Robertsondragand solarwinddrag.AJ126,3108{3121. [40]Kehoe,T.J.J.,Dermott,S.F.,Mahoney-Hopping,L.,200 7a.Theeectof inter-particlecollisionsonthedynamicalevolutionofaste roidaldustandthe structureofthezodiacalcloud.ESA-SP-643,81{85. [41]Kehoe,T.,Espy,A.,Dermott,S.,2007b.GravitationalSc atteringofAsteroidalDust ParticlesbyMars.BulletinoftheAmericanAstronomicalSociet y39,516. [42]Kortenkamp,S.J.,Dermott,S.F.,1998.Accretionofint erplanetarydustparticlesby theEarth.Icarus135,469{495. 182

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[43]KortenkampS.J.,DermottS.F.,FogleD.,GroganK.,200 1.Sourcesandorbital evolutionofinterplanetarydustaccretedbyEarth.In:B.Pe ucker-Ehrenbrink, B.Schmitz,(Eds.)Accretionofextraterrestrialmatterthrou ghoutEarth'shistory, Kluwer,NewYork,pp.13-30. [44]Kuchner,M.J.,Reach,W.T.,Brown,M.E.,2000.Asearchf orresonantstructuresin theaodiacalcloudwithCOBEDIRBE:theMars'wakeandJupiter 'sTrojanclouds. Icarus145,44{52. [45]Leinert,C.,Roser,S.,Buitrago,J.,1983.Howtomainta inthespatialdistributionof interplanetarydustparticle.AA118,345{357. [46]Liou,J.C.,1993.Dynamicalevolutionofasteroidaland cometaryparticlesandtheir contributiontothezodiacalcloud.PhDThesis,UniversityofFl orida. [47]Love,S.G.,Brownlee,D.E.,1993.Adirectmeasuremento ftheterrestrialmass accretionrateofcosmicdust.Science262,550{553. [48]Low,F.J.,Young,E.,Beintema,D.A.,Gautier,T.N.,Beic hman,C.A.,Aumann, H.H.,Gillett,F.C.,Neugebauer,G.,Boggess,N.,Emerson,J.P.,19 84.Infrared cirrus:newcomponentsoftheextendedinfraredemission.ApJ27 8,L19{L22. [49]Meadows,V.,Bhattacharya,B.,Reach,W.,Grillmair,C., Noriega-Crespo,A., Ryan,E.,Tyler,S.,Rebull,L.,Giorgini,J.,Elliot,J.,20 04.TheSpitzerFirst LookSurvey-EclipticPlaneComponent:AsteroidsandZodiaca lBackground.ApJ Supplement154,469{474. [50]Morgan,J.,Burgett,W.,Teran,J.,2008.ThePan-STARRS PS4telescopesuite. In:L.Stepp,R.Gilmozzi,(Eds.).Ground-basedandAirborneTe lescopesII. ProceedingsoftheSPIE7012,70122R-70122R-10. [51]Moro-Martn,A.,Malhotra,R.,2002.Astudyofthedynami csofdustfrom theKuiperbelt:spatialdistributionandspectralenergydistr ibution.AJ124, 2305{2321. [52]Murakami,H.,Matsuhara,H.,2008.Theinfraredastronomic alsatelliteAKARI: overview,highlightsofthemission.SpaceTelescopesandInstr umentation2008: Optical,Infrared,andMillimeter,ProceedingsoftheSPIE 7010,70100A{70100A-10. [53]Murray,C.D.,Dermott,S.F.1999.SolarSystemDynamics. CambridgeUniversity Press,UK. [54]Nesvorny,D.,Bottke,W.,Dones,L.,Levison,H.,2002.Ther ecentbreakupofan asteroidinthemainbeltregion.Nature417,720{771. [55]Nesvorny,D.,Bottke,W.,Levison,H.,Dones,L.,2003.Rece ntoriginofthesolar systemdustbands.ApJ591,486{497. 183

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[56]Nesvorny,Vokrouhlicky,D.,Bottke,W.,Sykes,M.,2006 a.Physicalpropertiesof asteroiddustbandsandtheirsources.Icarus181,107{144. [57]Nesvorny,D.,Vokrouhlicky,D.,2006b.Newcandidatesf orrecentasteroidbreakups. AJ132,582{595.nesnewNesvorny,D.,Bottke,W.,Vokrouhlick y,D.,Sykes,M., Lien,D.,Stansbery,J.,2008.OriginoftheNear-EclipticCir cumsolarDustBand.AJ 679,L143{L146. [58] Opik,E.J.,1951.Collisionprobabilitieswiththeplanetsa ndthedistributionof interplanetarymatter.Proc.oftheRoyalIrishAcademy54,16 5{199. [59]Pravec,P.,Harris,A.,2000.FastandSlowRotationofAsteroi ds.Icarus148,12{20. [60]Price,S.D.,Noah,P.V.,Mizuno,D.,Walker,R.,Jayarama n,S.,2003.Midcourse SpaceExperiment;mid-infraredmeasurementsofthethermal emissionfromthe zodiacaldustcloud.AJ125,962{983. [61]Price,S.,Noah,P.,Mizuno,D.,Walker,R.,Jayaraman,S .,2006. MSXZodiacalDustDataV1.0.In:NASAPlanetaryDataSystem,MSX-D-SPIRIT3-3-MSXZODY-V1.0. [65]Price,S.D.,2009.Infraredskysurveys.SpaceScienceRev iews142,233{321. [63]Reach,W.T.,Abergel,A.,Boulanger,F.,Desert,F.X.,Pera ult,M.,Bernard,J.P., Blommaert,J.,Cesarsky,C.,Cesarsky,D.,Metcalfe,L.,Puget, J.L.,Sibille,F., Vigroux,L.,1996.Mid-infraredspectrumofthezodiacalligh t.AA315,L381{L384. [64]Reach,W.T.,Franz,B.A.,Weiland,J.L.,1997.Thethree -dimensionalstructureof thezodiacaldustbands.Icarus127,461{484. [65]Rietmeijer,F.J.M.1998.Interplanetarydustparticle s.In:Papike,J.J.(Ed.), PlanetaryMaterials,ReviewinMineralogy36,Mineralogica lSoc.ofAmerica, Washington. [66]Richardson,D.,Leinhardt,A.M.,Melosh,H.J.,Bottke,W.F .,Asphaug,E.,2002. Gravitationalaggregates:evidenceandevolution.In:Bott keW.F.,Cellino,A., Paolicchi,P.,Binzel,R.P.,(Eds.)AsteroidsIII,Univ.ofArizo naPress,Tucson,pp. 501{515. [67]Rieke,G.H.,Su,K.Y.L.,Stansberry,J.A.,Trilling,D.,Br yden,G.,Muzerolle,J., White,B.,Gorlova,N.,Young,E.T.,Beichman,C.A.,Stapelfe ldt,K.R.,Hines,D.C., 2005.Decayofplanetarydebrisdisks.ApJ620,1010{1026. [68]Sykes,M.,Greenberg,R.,1986.Theformationandorigin oftheIRASzodiacaldust bandsasaconsequenceofsinglecollisionsbetweenasteroids.Ic arus65,51{69. [69]Sykes,M.,1988.IRASobservationsofextendedzodiacalstr uctures.ApJ334, L55{L58. 184

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[70]Sykes,M.,1990.Zodiacaldustbands:theirrelationtoaste roidfamilies.Icarus85, 267{289. [71]Sykes,M.,Walker,R.,1992.Cometarydusttrails.I-Surve y.Icarus95,180{210. [72]Telesco,C.,Fisher,R.S.,Wyatt,M.C.,Dermott,S.F.,Ke hoe,ThomasJ.J.,Novotny, S.,Marinas,N.,Radomski,J.T.,Packham,C.,DeBuizer,J.,Hayw ard,T.L.,2005. Mid-infraredimagesof Pictorisandthepossibleroleofplanetesimalcollisionin thecentraldisk.Nature433,133{136. [73]Veverka,J.,and32coauthors,2001.ImagingofSmall-Sc aleFeatureson433Eros fromNEAR:EvidenceforaComplexRegolith.Science292,484{4 88. [74]Vokrouhlicky,D.,Nesvorny,D.,Bottke,W.F.,2008.Ev olutionofdusttrailsinto bands.ApJ672,696{712. [75]Wyatt,S.Whipple,F.,1950.ThePoynting-RobertsonEec tonMeteorOrbits.ApJ 111,134{41. [76]Wyatt,M.C.,Dermott,S.F.,Telesco,C.M.,Fisher,R.S., Grogan,K.,Holmes,E.K., Pina,R.K.,1999.Howobservationsofcircumstellardiskasymmet riescanreveal hiddenplanets:PericenterglowanditsapplicationtotheHR4 796disk.ApJ527, 918{944. 185

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BIOGRAPHICALSKETCH AshleyJeanneEspywasbornApril18,1978andraisedinSummervill e,GAbyGene andLindaEspy.Shehasoneolderbrother,JasonEspy.Shegradua tedfromChattooga HighSchoolin1996,whereshewasamemberofthetrackandeld,c rosscountry, basketball,andscholarbowlteamsandwaspresidentofthemath club.Afterhighschool shemovedtoAtlanta,GAtoattendGeorgiaTech.Duringhertim eatGeorgiaTech shewasamemberoftheindoor/outdoortrackandeldandcrossco untryteams.While atTechshespentasemesterabroadinSt.Petersburg,Russiaandsemest eratanNSF REUprogramatStanford.In2000shereceivedaB.S.inPhysics( HighestHonors) fromGeorgiaTech.Followingafewmonthsofwaitingtablesa tSchroedersinRome, GA,shethenmovedtoGainesville,FLtoattendgraduateschoolat UF.In2003she receivedanM.S.inAstronomyforprojectonlightscatteringby Miespheresunderthe advisementofDr.BoGustafson.Shethenchangedpathstoworkon thesolarsystem dynamicspresentedhere,undertheguidanceofDr.StanleyDe rmott.Thisdissertation wasdefendedonMarch16th,2010.Throughoutgradschool,shec ontinuedtorunand raceinroadracesandmarathonsandcompletedanIRONMANin200 5.Theworkfor thisdissertationwasfundedbyaUFAlumniFellowshipandaNASAGrad uateStudent ResearchersFellowship.UpongraduationinMay2010,shewillre maininGainesvilleto beginajointpostdocpositionbetweenUFandUCFworkingonthedu stdynamicsofthe outersolarsystem. 186