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# Massive Star Formation

## Material Information

Title: Massive Star Formation Theory and Observation
Physical Description: 1 online resource (169 p.)
Language: english
Creator: Zhang, Yichen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

## Subjects

Subjects / Keywords: disk -- formation -- massive -- outflow -- radiation -- star -- transfer
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: Massive stars impact many areas of astrophysics, yet there is still no consensus on how they form.  Are they born in a similar way to their low-mass counterparts, i.e., through accretion from gravitationally bound cores (Core Accretion)? Or do they form via a more chaotic competitive accretion process from the surrounding star-cluster-forming clump, or even via protostellar mergers? Besides the complicated theoretical nature of the massive star formation problem, the large distances, high extinction and crowded neighborhoods of typical observed massive star-forming regions all combine to make this a very difficult question to answer observationally. In this dissertation, we make efforts on both theoretical and observational aspects of massive star formation, with the key link being radiation transfer simulations. A model is presented for massive protostars forming from massive dense gas cores that are embedded inside larger star-cluster-forming clumps with high mass surface densities of ~1 g/cm^2.  As stated by Core Accretion theory, such high surface densities are needed for a core to collapse in a time scale of 100,000 yr, reaching accretion rates of 10^{-4} - 10^{-3} Msun/yr, that may be needed to overcome the radiation barrier of massive protostars. In the Core Accretion scenario, relatively large and ordered disks and collimated bipolar outflow are expected to form around massive protostars, helping to transfer angular momentum and reduce radiation pressure on the inflow. Such well-ordered structures are not expected in other formation theories of massive stars.  Therefore, starting with a highly pressurized core, we self-consistently include analytic models for an inside-out expansion wave, a rotating infall envelope, an accretion disk, and a bipolar magneto-hydrodynamic accretion-powered disk wind that sweeps up outflow cavities. The effects of the outflow on the accretion disk are also considered. We also add gas opacities and adiabatic cooling, which are important around massive protostars. Then radiation transfer simulations are carried out for such models. We find the near-facing outflow cavity significantly affects the IR morphology and dominates the mid-IR emission, especially for cores with high surface densities. At 30 - 40 microns, although the outflow cavities are still dominant, lower extinction reveals the fainter far-facing outflow. The dust and gas inside the outflow cavity affect the detailed intensity distribution. For example, the mid-IR emission shows narrower jets while at shorter wavelengths the scattering reveals wide-angle outflow cavities. We also find that the spectral energy distribution (SED) becomes very flat when the system is viewed at an inclination that is near face-on, which may be used to identify such systems. We then study the evolutionary sequence of massive star formation. Based on the analytic outflow model, we consider how the outflow cavities gradually open up and how the star formation efficiency decreases with time. Protostellar evolution is also modeled, utilizing accretion rates that are controlled by the self-consistently calculated formation efficiency. For the fiducial 60 Msun core, we find the final star formation efficiency is ~>0.6. We also find that the colors deduced from the mid-IR to sub-mm SED can be indicators of the evolutionary stages of massive star formation. We carry out observations of an example of a massive protostar, G35.2-0.74, at 30 and 40 $\mu$m with SOFIA-FORCAST. We apply the fiducial radiation transfer model to this source and through fitting both the SED and the intensity profile along the outflow axis simultaneously, constrain the properties of the protostar. Excellent fits between the theoretical model and the observational data are achieved, allowing us to estimate the protostellar mass to be 20 - 30 Msun, the core mass to be ~240 Msun and the clump mean mass surface density to be 0.4 - 1 g/cm^2. These results indicate this is a indeed a massive protostar forming at the center of a high mass surface density core and clump via relatively ordered collapse, accretion and the driving of powerful outflows. At least in this one example, this is evidence in support of the Core Accretion theory, i.e., that a massive star forms similarly to a low-mass star. Finally we discuss future applications of this work. First, this model can be further expanded to a model grid covering ranges of conditions of massive star formation. Second, in order to study the kinematics of the outflow, and the thermal and chemical conditions of the massive young stellar objects, we perform initial explorations of radiation transfer modeling of molecular lines based on the continuum model. Finally, this model can be extended to apply to low-mass star formation in high surface density environments and we present initial explorations of this application.
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 Yichen Zhang.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.

## Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045343:00001

## Material Information

Title: Massive Star Formation Theory and Observation
Physical Description: 1 online resource (169 p.)
Language: english
Creator: Zhang, Yichen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

## Subjects

Subjects / Keywords: disk -- formation -- massive -- outflow -- radiation -- star -- transfer
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: Massive stars impact many areas of astrophysics, yet there is still no consensus on how they form.  Are they born in a similar way to their low-mass counterparts, i.e., through accretion from gravitationally bound cores (Core Accretion)? Or do they form via a more chaotic competitive accretion process from the surrounding star-cluster-forming clump, or even via protostellar mergers? Besides the complicated theoretical nature of the massive star formation problem, the large distances, high extinction and crowded neighborhoods of typical observed massive star-forming regions all combine to make this a very difficult question to answer observationally. In this dissertation, we make efforts on both theoretical and observational aspects of massive star formation, with the key link being radiation transfer simulations. A model is presented for massive protostars forming from massive dense gas cores that are embedded inside larger star-cluster-forming clumps with high mass surface densities of ~1 g/cm^2.  As stated by Core Accretion theory, such high surface densities are needed for a core to collapse in a time scale of 100,000 yr, reaching accretion rates of 10^{-4} - 10^{-3} Msun/yr, that may be needed to overcome the radiation barrier of massive protostars. In the Core Accretion scenario, relatively large and ordered disks and collimated bipolar outflow are expected to form around massive protostars, helping to transfer angular momentum and reduce radiation pressure on the inflow. Such well-ordered structures are not expected in other formation theories of massive stars.  Therefore, starting with a highly pressurized core, we self-consistently include analytic models for an inside-out expansion wave, a rotating infall envelope, an accretion disk, and a bipolar magneto-hydrodynamic accretion-powered disk wind that sweeps up outflow cavities. The effects of the outflow on the accretion disk are also considered. We also add gas opacities and adiabatic cooling, which are important around massive protostars. Then radiation transfer simulations are carried out for such models. We find the near-facing outflow cavity significantly affects the IR morphology and dominates the mid-IR emission, especially for cores with high surface densities. At 30 - 40 microns, although the outflow cavities are still dominant, lower extinction reveals the fainter far-facing outflow. The dust and gas inside the outflow cavity affect the detailed intensity distribution. For example, the mid-IR emission shows narrower jets while at shorter wavelengths the scattering reveals wide-angle outflow cavities. We also find that the spectral energy distribution (SED) becomes very flat when the system is viewed at an inclination that is near face-on, which may be used to identify such systems. We then study the evolutionary sequence of massive star formation. Based on the analytic outflow model, we consider how the outflow cavities gradually open up and how the star formation efficiency decreases with time. Protostellar evolution is also modeled, utilizing accretion rates that are controlled by the self-consistently calculated formation efficiency. For the fiducial 60 Msun core, we find the final star formation efficiency is ~>0.6. We also find that the colors deduced from the mid-IR to sub-mm SED can be indicators of the evolutionary stages of massive star formation. We carry out observations of an example of a massive protostar, G35.2-0.74, at 30 and 40 $\mu$m with SOFIA-FORCAST. We apply the fiducial radiation transfer model to this source and through fitting both the SED and the intensity profile along the outflow axis simultaneously, constrain the properties of the protostar. Excellent fits between the theoretical model and the observational data are achieved, allowing us to estimate the protostellar mass to be 20 - 30 Msun, the core mass to be ~240 Msun and the clump mean mass surface density to be 0.4 - 1 g/cm^2. These results indicate this is a indeed a massive protostar forming at the center of a high mass surface density core and clump via relatively ordered collapse, accretion and the driving of powerful outflows. At least in this one example, this is evidence in support of the Core Accretion theory, i.e., that a massive star forms similarly to a low-mass star. Finally we discuss future applications of this work. First, this model can be further expanded to a model grid covering ranges of conditions of massive star formation. Second, in order to study the kinematics of the outflow, and the thermal and chemical conditions of the massive young stellar objects, we perform initial explorations of radiation transfer modeling of molecular lines based on the continuum model. Finally, this model can be extended to apply to low-mass star formation in high surface density environments and we present initial explorations of this application.
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 Yichen Zhang.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.

## Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045343:00001

Full Text

PAGE 2

r

PAGE 9

6 0 3 0 6 0 6 0 3 0 3 0 60 6 0 60 30

PAGE 10

30 =1

PAGE 11

cl 1gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 10 5 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 )Tj/T1_0 11.955 Tf12.84 0 Td[(10 )Tj/T1_1 7.97 Tf6.6 0 Td(3 M f yr )Tj/T1_1 7.97 Tf6.6 0 Td(1

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60 M f & 0.6 20 )Tj/T1_1 11.955 Tf12.36 0 Td[(30 M f 240 M f

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0 .4 )Tj/T1_0 11.955 Tf12.12 0 Td[(1gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2

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AtacamaLargeMillimeter/submillimeterArray(ALMA) Herschel SpaceTelescope StratosphericObservatoryforInfraredAstronomy(SOFIA) GranTelescopioCanarias(GTC) JamesWebbSpaceTelescope(JWST)

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1.1FormationofLow-massStars IR = d log( F ) = d log =2.2 I R > 0 )Tj/T1_3 11.955 Tf9.24 0 Td(2 < IR < 0 IR < )Tj/T1_3 11.955 Tf9.24 0 Td(2 &

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1.2FormationTheoriesofMassiveStars 10 )Tj/T1_3 7.97 Tf6.6 0 Td(4 )Tj/T1_1 11.955 Tf12.12 0 Td[(10 )Tj/T1_3 7.97 Tf6.6 0 Td(3 M f

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10 8 pc )Tj/T1_2 7.97 Tf6.6 0 Td(3 1 .3TheTurbulentCoreModel

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cl 0.1 )Tj/T1_0 11.955 Tf10.56 0 Td[(1gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 P c l =0.88 G 2 cl =5.9 10 )Tj/T1_1 7.97 Tf6.6 0 Td(8 ( cl = gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 ) 2 dyncm )Tj/T1_1 7.97 Tf6.6 0 Td(2 M c R c =5.7 10 )Tj/T1_1 7.97 Tf6.6 0 Td(2 ( M c = 60 M f )( cl = gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 ) )Tj/T1_1 7.97 Tf6.6 0 Td(1 = 2 pc. t f =1.29 10 5 ( M c = 60 M f )( cl = gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 ) )Tj/T1_1 7.97 Tf6.6 0 Td(3 = 4 yr, 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 )Tj/T1_0 11.955 Tf12.36 0 Td[(10 )Tj/T1_1 7.97 Tf6.6 0 Td(3 M f yr )Tj/T1_1 7.97 Tf6.6 0 Td(1 1.4RadiationTransferSimulations

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cl 1gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 5 10 4 M f 1.5ObservationalEvidenceforCoreAccretion

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1.6SummaryofThisDissertation

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M f M f gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2 cl

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60 M f cl =1gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2 60 0.4 37 M f 0.6

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SOFIA 20 )Tj/T1_2 11.955 Tf12.96 0 Td[(30 M f cl =0.4 )Tj/T1_2 11.955 Tf12.96 0 Td[(1gcm )Tj/T1_6 7.97 Tf6.6 0 Td(2

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2.1Introduction 60 M f cl =1gcm )Tj/T1_4 7.97 Tf6.6 0 Td(2 8 M f 2 .2MassiveProtostarModel 2.2.1Envelope 2.2.1.1Hydrostaticouterenvelope / r )Tj/T1_7 7.97 Tf6.6 0 Td(k P / r )Tj/T1_7 7.97 Tf6.6 0 Td(k p 10K

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P / r p r p =1 r p =0 k =1.5 r p = 2 3 k p =1 M ( r ) = k p c 2 r G ( r )= (3 )Tj/T1_0 11.955 Tf12 0 Td(k )( k )Tj/T1_5 11.955 Tf12 0 Td[(1) c 2 2 Gr 2 c =( P = ) 1 = 2 M f f m f = f M c ore =30 M f R core =0.057 M core 60 M f 1 = 2 )Tj/T1_6 7.97 Tf6.6 0 Td(1 = 2 c l pc, cl 1g = cm )Tj/T1_6 7.97 Tf6.6 0 Td(2 cl 2.2.1.2Expansionwave

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(1+ H 0 ) H 0 M ( r t )= M non ( r t )(1+ H 0 )= m ( x )(1+ H 0 ) a 3 t t = G ( r t )= non ( r t )(1+ H 0 )= ( x )(1+ H 0 ) 4 Gt 2 m ( x ) ( x ) a t = [ K r p (4 Gt 2 ) 1 )Tj/T1_6 7.97 Tf6.6 0 Td(r p ] 1 = 2 H 0 M (0)= m (0)(1+ H 0 ) a 3 t t = G M (0) / a 3 t t / t 4 )Tj/T1_2 7.97 Tf6.6 0 Td(3 r p M (0) / t 3 )Tj/T1_2 7.97 Tf6.6 0 Td(3 r p / t

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M (0, t ) t f =1.29 10 5 M core 60 M f 1 = 4 )Tj/T1_5 7.97 Tf6.6 0 Td(3 = 4 c l yr M (0, t = t f )= M core =60 M f t ( r t ) u ( r t ) M ( r t ) 2 .2.1.3Rotatinginfall r 1 0 n 1 M r = r d cos 0 sin 2 0 cos 0 )Tj/T1_1 11.955 Tf12 0 Td(cos r d = n 2 1 r 4 1 GM = j 2 1 GM

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r 1 r < r d r d r d r d = 6 a g 5 a i f r = 6 a g 5 a i f M M c ore 1 3 )Tj/T1_3 5.978 Tf5.76 0 Td(k a g =5 j E grav j r = (3 GM 2 )=(5 = 3)(3 )Tj/T1_0 11.955 Tf12.24 0 Td(k ) = (5 )Tj/T1_4 11.955 Tf12.24 0 Td(2 k ) 1.25 a i =2 E rot = ( Mr 2 n 2 )= (2 = 3)(3 )Tj/T1_0 11.955 Tf12 0 Td(k ) = (5 )Tj/T1_0 11.955 Tf11.88 0 Td(k ) 0.286 f = E rot = j E grav j r r d r d = 6 a g 5 a i f M s p M c ore 1 3 )Tj/T1_3 5.978 Tf5.76 0 Td(k M sp M f M f M f ( r ) / 1+ cos cos 0 )Tj/T1_6 7.97 Tf6.6 0 Td(1 = 2 c os 2cos 0 + r d r c os 2 0 )Tj/T1_6 7.97 Tf6.6 0 Td(1 M f

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r 2500 r d 2 r d 4 r d 2.2.2AccretionDisk r d m d = m + m d = (1+ f d ) m f d f d f d 1 = 0 1 )Tj/T1_8 11.955 Tf11.88 17.76 Td(r r r r r e xp n )Tj/T1_2 11.955 Tf13.08 8.04 Td(1 2 z H ( r ) 2 o

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r z r H H = H 0 r r f m d r d ,in r d H 0 f r sub H 0 = r =0.01 H 0 = r = 0.1 H 0 = r =0.01 H 0 = r =0.1 f f H 0 = r = 0.06 =1.75 f =1.08 L acc = Gm m r L disk

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L h otspot L disk = L hotspot = 1 2 L a cc r d ,in L disk ( r d ,in )= Gm m 2 r d in 3 )Tj/T1_2 11.955 Tf11.88 0 Td(2 ( r = r d ,in ) 1 = 2 m 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 )Tj/T1_2 11.955 Tf12.6 0 Td[(10 )Tj/T1_1 7.97 Tf6.6 0 Td(3 M f 2.40 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 M f M f M f m = p 18 3 d isk V c 0 H 3 0 = r V c =( Gm = r ) 1 = 2 disk =1.43 d isk 1.0 )Tj/T1_2 11.955 Tf11.88 0 Td[(1.6 L w 2.2.3OutowCavity

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p w / (sin w ) )Tj/T1_6 7.97 Tf6.6 0 Td(2 w > w 0 w w 0 10 )Tj/T1_6 7.97 Tf6.6 0 Td(2 d_ p w dn = p w 4 ln(2 = w 0 )(1+ 2 w 0 )Tj/T1_3 11.955 Tf11.88 0 Td[(cos 2 w ) w esc w > w ,esc f w ,esc f w ,esc m m w m d m d = f d m f w =_ m w = m f w ,esc t 1 m ( t 1 ) m d ( t 1 ) t 1 =0 t < t 1 m d ,0 ( t 1 )= m d ( t 1 )= m ( t 1 )+ m d ( t 1 )=(1+ f d ) m ( t 1 ), m d ,0 t 1 t f m +_ m d + f w ,esc m w =cos w ,esc m d ,0

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cos w ,esc d m d m d 0 = m d ( t f ) )Tj/T1_6 11.955 Tf11.88 0 Td(m d ( t 1 ) M c ore )Tj/T1_6 11.955 Tf12 0 Td(m d ,0 ( t 1 ) = (1+ f d )cos w ,esc 1+ f d + f w f w esc d m d ( t f ) m d 0 ( t f ) = m d ( t f ) M c ore m f = m ( t f )+ m d ( t f ) 1+ f w = 1 + f d + f w (1+ f w )(1+ f d ) m d ( t f ), m f M core f m f M c ore = 1+ f d + f w (1+ f w )(1+ f d ) d = 1 2 m ( t 1 )=8 M f m d ( t 1 )=10.67 M f w esc f w ,esc f =0.5 f d =1 = 3 f w =0.1 0.8 f w ,esc f w f w =0.6 f w ,esc =0.86

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2.2.4Protostar m d ,0 12 M f m =8 M f M f m =8 M f cl = 1gcm )Tj/T1_4 7.97 Tf6.6 0 Td(2 r =12.05 R f L =2.81 10 3 L f T =1.22 10 4 T ,hotspot =1.43 10 4 cl )Tj/T1_4 7.97 Tf6.6 0 Td(2 r = 11.3 R f T =1.25 10 4 T ,hotspot =1.37 10 4 cl

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)Tj/T1_1 7.97 Tf6.6 0 Td(2 r =5.93 R f T =1.74 10 4 T ,hotspot =2.62 10 4 2.2.5ModelSeries M f M f / r k 52 M f 8 M f r =0.0408 52 M f H 0 = r =0.01 r sub r s ub = r ( T sub = T ) )Tj/T1_1 7.97 Tf6.6 0 Td[(2.1 T sub T sub =1600 r =0.0494 m + m d =10.67 M f 49.33 M f 29 M f

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98.4 r L disk =25.29 L f L hotspot =2.45 10 3 L f + H 0 = r =0.1 T > 1600 H 0 f H 0 = r =0.06 =1.75 f =1.08 z 2 10 )Tj/T1_4 7.97 Tf6.6 0 Td[(15 gcm )Tj/T1_4 7.97 Tf6.6 0 Td(3 r d ,in = r sub

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cl =0.316 2 2.3Simulations & T n ( r ) T n )Tj/T1_1 7.97 Tf6.6 0 Td(1 ( r ) log( T 0 n ( r ))=(log( T n ( r ))+ log( T n )Tj/T1_1 7.97 Tf6.6 0 Td(1 ( r ))) = 2 T 0 n T 0 n )Tj/T1_1 7.97 Tf6.6 0 Td(1 (log T 0 n )Tj/T1_0 11.955 Tf12 0 Td[(log T 0 n )Tj/T1_1 7.97 Tf6.6 0 Td(1 ) = log T 0 n < 0.1

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T =1600 10 3 r z = 1 H ( r )

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r r 600 150 6 w ,esc 700 20 300 50 53 w ,esc =51 ) 10 8 10 9 2.3.1DustOpacity n H 2 > 10 10 cm )Tj/T1_5 7.97 Tf6.6 0 Td(3

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R V =4 2.3.2GasOpacity T > 1600 10 4

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3000 3000 10 8 10 6 )Tj/C2_0 11.955 Tf10.44 -4.32 Td[<0045>4<0052>4<0058>4<0051>4<0047>4<0010>2<0049>-3<0055>2<0048>4<0048>]TJ-394.44 -24 Td[<0044>4<0045>4<0056>-2<0052>4<0055>-28<0053>4<0057>-3<004C>1<0052>4<0051>4<000F>-304<0048>4<004F>1<0048>4<0046>-2<0057>-3<0055>2<0052>4<0051>4<0010>2<004B>34<005C>-2<0047>4<0055>2<0052>4<004A>4<0048>4<0051>4<0012>-3<004B>4<0048>4<004F>1<004C>1<0058>4<0050>-321<0049>-3<0055>2<0048>4<0048>4<0010>2<0049>-3<0055>2<0048>4<0048>-287<0044>4<0045>4<0056>-2<0052>4<0055>-28<0053>4<0057>-3<004C>1<0052>4<0051>4<0011>-364<0029>29<0052>4<0055>-289<0056>-2<0046>-2<0044>4<0057>-3<0057>-3<0048>4<0055>-8<004C>1<0051>4<004A>4<000F>-284<0037>-1<004B>4<0052>4<00500053>4<0056>-2<0052>4<0051>]TJ0 -23.88 TD[<0056>-2<0046>-2<0044>4<0057>-3<0057>-3<0048>4<0055>-8<004C>1<0051>4<004A>-287<005A>-1<004C>1<0057>-3<004B>-277<0044>-277<0046>-2<0052>4<004F>1<004F>1<0048>4<0046>-2<0057>-3<004C>1<0059>18<0048>-277<0048>4<0049>-3<0049>27<0048>4<0046>-2<0057>-274<004C>1<0056>-283<0046>-2<0052>4<0051>4<0056>-2<004C>1<0047>4<0048>4<0055>2<0048>4<0047>-297<000B>]TJ0 0 1 rg252 0 Td[<0025>5<0052>4<0048>4<0055>2<0046>18<004E>18<0048>4<0055>-289<0014>4<001C>4<001B>4<001A>]TJ0 0 0 1 k77.28 0 Td[<000C>2<0011>-344<0029>29<0052>4<0055>-279<0055>2<0048>4<004A>4<004C>1<0052>4<0051>4<0056>-303<005A>-1<004C>1<0057>-3<004B>]TJ/T1_4 11.955 Tf99.36 0 Td(T < 3 000 8 10 )Tj/T1_2 7.97 Tf6.6 0 Td[(12 g = cm 3 2000 2 )Tj/C2_0 11.955 Tf10.44 -4.32 Td[<0044>4<0045>4<0056>-2<0052>4<0055>-28<0053>4<0057>-3<004C>1<0052>4<0051>-297<0044>4<0051>4<0047>]TJ-372.12 -23.88 Td[<0035>-1<0044>34<005C>-2<004F>1<0048>4<004C>1<004A>4<004B>-287<0056>-2<0046>-2<0044>4<0057>-3<0057>-3<0048>4<0055>-8<004C>1<0051>4<004A>-287<0052>4<0049>-284<002B>-282<0044>4<0051>4<0047>-287<002B>]TJ/T1_2 7.97 Tf162 -1.8 Td(2 6 10 )Tj/T1_2 7.97 Tf6.6 0 Td(8 10 )Tj/T1_2 7.97 Tf6.6 0 Td[(15 3 T

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T 1 R = R 1 0 ( @ B = @ T ) = ext ( )d R 1 0 ( @ B = @ T )d P = R 1 0 abs ( ) B d R 1 0 B d P = Z 0 abs ( ) P @ B @ T d P P P R log 10 4 h = kT =0.001 2.4Results 2.4.1SEDs 2.4.1.1SEDsofthemodelseries 60

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30 =60 =30

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=60 =30 =60 r sub r sub 10 5 3000

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2.4.1.2SEDsoftheducialmodel < 2 30 0 0 30 51

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2.4.1.3Effectofdifferentmasssurfacedensity )Tj/T1_3 7.97 Tf6.6 0 Td(1 = 2 cl cl 6 0 30 30 60 60

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2.4.2Images 2.4.2.1Imagesoftheducialmodel 60 30 10 9 60

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30 60 30

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6 0 2.4.2.2Effectofdifferentsurfacedensity cl

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2.5DiscussionsandConclusions 60 M f 8 M f Gm m (1 = r )Tj/T1_2 11.955 Tf9.24 0 Td(1 = r co ) r co 5 r L acc / 0.2 L acc

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10 5

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60 30 60 10 2 )Tj/T1_1 11.955 Tf12.48 0 Td[(10 3 30

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M f M f / r )Tj/T1_4 7.97 Tf6.6 0 Td[(1.5 M f M f M f 1 = 3 m 49.333 M f H 0 = r =0.01 r d ,in = r sub M f 29 M f M f 1 = 3 m r d ,in = r sub M f 1 = 3 m r d ,in = r sub H 0 = r =0.1 M f r d ,in = r sub M f m H 0 = r =0.06 r d ,in = r

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c l 2 R core r ew t f 1.29 10 5 3.06 10 5 5.44 10 4 r sp 2.57 10 3 4.57 10 3 1.45 10 3 r d m M f 2.398 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 1.035 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 5.667 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 r R f T 1.22 10 4 1.25 10 4 1.74 10 4 T ,hotspot 1.42 10 4 1.37 10 4 2.62 10 4 L L f 2.81 10 3 2.82 10 3 2.84 10 3 L acc L f 4.90 10 3 2.25 10 3 2.36 10 4 H 0 = r

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q q q q rr q r n He =0.1 n H 0 r =2 r d r =4 r d

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boundaryofthecore( 1 : 1 8 10 4 AU) expansionwavefront( 1 : 02 10 4 AU) sonicpoint(2 : 54 10 3 AU) disk star star dis k outowcavitywall r d =449AU r sub =5.51AU diskscaleheight r d

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n He =0.1 n H r

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60

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3 0

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T

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F F

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c l 2 cl 2 cl 2 60 30

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6 0

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3 0

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3 0

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60 30

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60

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8 M f M c =60 M f 20

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3.1Models f w =_ m w = m =0.1 f =0.64 3 .1.1Disk

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 @ @ t + @ @$($ v $) =$ @ in @ t )Tj/T1_0 11.955 Tf12 0 Td($@ w @ t ($ ) $v$ $@ in ($ ) =@ t $@ w ($ ) =@ t m acc $m acc ($ ) )]TJ/T1_1 11.955 Tf28.56 0 Td(2 $v$ = @ @ t [ m d ( $) )Tj/T1_2 11.955 Tf12 0 Td(m i n ($ )+ m w ( $) ] +_ m @ m d ($ ) =@ t $@ m w =@ t @ m in =@ t$ m  d m = m acc ( r )= 2.4 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 M f )Tj/T1_4 7.97 Tf6.6 0 Td(1 $@ @ t ($ 2 n)+ @ @$($ v  2 n ) = 1 2 @ G T @$+$ j i n @ in @ t )Tj/T1_0 11.955 Tf12 0 Td($j w @ w @ t G T =2$ $2 ( d n = d$ ) j in ( $) j w ($ )

PAGE 73

n G T =0 d j dt = @ j @ t + v $@ j @$ = 1 (2 $) @ G T @$ + ( j i n )Tj/T1_1 11.955 Tf12 0 Td(j ) @ i n @ t + ( j )Tj/T1_1 11.955 Tf11.88 0 Td(j w ) @ w @ t j $2 n j @ G T =@$< 0 @ j =@ t / @ n =@ t f d = m d m = m d ( $d ) m = 1 = 3, m d ($ d ) @ w =@ t j w m w ( $d )= f w m =0.1_ m m in ($ d )=(1+ f w + f d )_ m @ in =@ t j in

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( $) @ ($ ) =@ t =1.37 G m m r = L a cc + L w + L d + E d G L acc = G m m = (2 r ) L w L d L acc L d E d L w L d L w =1.22 L d L acc 2.45 10 3 L f T ,acc =1.43 10 4 2.82 10 3 L f 3.1.1.1Thindisk

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4 T 4 c = (3 ) T c r = $d cos w ,esc sin 2 w ,esc cos w esc )Tj/T1_0 11.955 Tf12 0 Td[(cos$ d sin 2 w ,esc = = 2 w ,esc = 2 r $d$ d sin 2 w ,esc 10 4 T 1600

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_ m a cc @ m w =@ t @ m d =@ t m a cc m acc @ m in =@ t 3.1.1.2Effectofdiskthickness  d $d$ w ,max >$d sin 2 w ,esc$ d $d PAGE 77 z d ,max$> 400 3.1.2Outows p w / ( r sin w ) )Tj/T1_2 7.97 Tf6.6 0 Td(2

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$max ( z )$ = $d sin 2 w ,esc$ c ( z ) $c ( z )$ c ( z ) $0 z d ($ 0 ) $c 0 = r$ )Tj/T1_1 7.97 Tf6.6 0 Td(3 = 2 v K / $)Tj/T1_1 7.97 Tf6.6 0 Td(1 = 2 @ m w ($ ) @ t = 4 Z $max,0 r$ 0 v z d $0 / ln($ max,0 =$c 0 ), z z 0$ 0 j w = n $2 A PAGE 79$ A $A =$ 0 3 $A =$ 0 =5.48 e w e w n 2 $2 0 = j w n$ 2 0 )Tj/T1_4 11.955 Tf13.08 8.16 Td(3 2 = $A$ 0 2 )Tj/T1_4 11.955 Tf13.08 8.16 Td(3 2 = 28.5. 3.1.3DustandGasOpacities T sub =1600 m w

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$d$ d sin 2 w ,sec n H < 2 10 10 cm )Tj/T1_3 7.97 Tf6.6 0 Td(3 1400 10 4 3000 T < 3000 2 000 T T < 2000 2000

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3.1.4Simulations T = 5 1.5 10 6 4 T 4 P ( T ) + P gas r v + r ( u v ) = L N P l V P v P gas u L N V P l

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r R c < 100 T T 4 10 3 )Tj/T1_4 11.955 Tf12.72 0 Td[(10 4 n H > 10 5 cm )Tj/T1_2 7.97 Tf6.6 0 Td(3 r r r 20 =5 =50 53 Spitzer GTC Herschel SOFIA 30 60 10 8 5 10 8

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3.1.5ModelSeries cl =0.316 )Tj/T1_2 7.97 Tf6.6 0 Td(2 cl =3.16 )Tj/T1_2 7.97 Tf6.6 0 Td(2 )Tj/T1_2 7.97 Tf6.6 0 Td(1 = 2 cl 3 = 2 cl 2 cl 3 = 4 cl 3.2ResultsandDiscussion 3.2.1SEDs 60 30 60

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30 < 2

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< 1 6 0 5 R c 10 R c A V / $)Tj/T1_6 7.97 Tf6.6 0 Td(2 r )Tj/T1_6 7.97 Tf6.6 0 Td(2 5 R c$ 0 =2 R c =1.2 10 4 R c 3 10

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F 10 < 40 3 F

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c l 3 = 2 cl )Tj/T1_1 7.97 Tf6.6 0 Td(1 = 2 3 = 4 cl cl

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3.2.2Images 6 0 30 5 10 8 70 60 40 & 70 60 20 5 R c

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3 0 =1 = 1 30 =1 > 100 60 30 00 2 00 10 )Tj/T1_5 7.97 Tf6.6 0 Td(6 60 > 0 30

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10 > 37 cl cl 3.3Summary M f M f

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10 30 & cl cl

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F

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ModelsOpacity Disk Outow T > 1 600 T < 1600 < T <

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M c M f cl 2 R c $d m M f 1.035 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 2.398 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 5.667 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 r R f T 1.25 10 4 1.22 10 4 1.74 10 4 T ,acc 1.37 10 4 1.42 10 4 2.62 10 4 L L f 2.82 10 3 2.81 10 3 2.84 10 3 L acc L f 1.13 10 3 2.45 10 3 1.18 10 4 L d L f 5.55 10 2 1.10 10 3 5.44 10 3 L bol L f 4.51 10 3 6.46 10 3 2.01 10 4 PAGE 95$ n He =0.1 n H

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n He =0.1 n H z T =1600

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60 30

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6 0

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F F

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cos view

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c l =0.316 )Tj/T1_1 7.97 Tf6.6 0 Td(2 cl =1 )Tj/T1_1 7.97 Tf6.6 0 Td(2 cl =3.16 )Tj/T1_1 7.97 Tf6.6 0 Td(2

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6 0 80 00 80 00 80 00 8 10 4

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3 0

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3 0

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= 1 30

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2 00 60 30

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60 40 00 40 00

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60 4 00 R c = 2 )Tj/T1_2 11.955 Tf9.24 0 Td(R c = 2

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cl =0.316 )Tj/T1_1 7.97 Tf6.6 0 Td(2 cl =1 )Tj/T1_1 7.97 Tf6.6 0 Td(2 cl =3.16 )Tj/T1_1 7.97 Tf6.6 0 Td(2 60 00 60 00

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4.1Models 4.1.1ProtostellarEvolution n n

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4.1.2EvolutionoftheOutowCavities 70 m ( t ) (1+ f d + f w f w ,esc ( t ))=cos w ,esc ( t )_ m d ,0 ( t ),

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_ m d 0 m d ,0 =9.2 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 M c 60 M f 3 = 4 3 = 4 c l m d ,0 M c 0 .5 M f yr )Tj/T1_4 7.97 Tf6.6 0 Td(1 w ,esc cos w ,esc m f d m f w m f w f w ,esc m f d =1 = 3 f w =0.1 f w ,esc ( t ) m ( t ) m d 0 ( t ) = cos w ,esc ( t ) 1+ f d + f w f w esc ( t ) w ,esc w esc v esc c g dM c d n v e sc = dp w ( t ) d n c g dp w ( t ) d n = p w ( t ) 4 P ( ) dM c d n = M c 4 Q ( )

PAGE 115

c os esc cos w ,sec P ( esc ) Q ( e sc ) = c g M c v esc p w Q ( )=1 P ( ) = 1 ln(2 = 0 )(1+ 2 0 )Tj/T1_0 11.955 Tf12 0 Td( 2 ) 0 0.01 1 + 2 0 )Tj/T1_0 11.955 Tf11.88 0 Td( 2 esc =1 = X X =5.28 c g ln(2 = 0 ) ln200 M c v e sc p w X c g = 5.04 M c =60 M f cl =1gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2 v esc = p 2 GM c = R c p w ( t ) p w t p w p w = Z $d r 2$ 0 v 0 v 1 d $=2 f w m$ A $0 r 2 Gm r 1 )Tj/T1_2 11.955 Tf12 0 Td(($ d = r ) )Tj/T1_3 7.97 Tf6.6 0 Td(1 = 2 ln( $d = r ) PAGE 116 v 1 p 2($ A =$0 ) v K ($ 0 ) $A =$ 0 = p 30 f w ,esc d m w d n = m w 4 M ( ) f w ,esc = R 1 esc M ( ) d M ( ) = P ( ) f w ,sec M ( ) / P ( ) 4.1.3ModelGroups 60 M f cl =1gcm )Tj/T1_6 7.97 Tf6.6 0 Td(2 =0.5 2 M f 4 M f 8 M f 16 M f 24 M f

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45 m =0.5_ m d ,0 m d ,0 M f ( t f )=37 M f = 60 M f =0.62 (1 = 3) m m d ,0 $d / m 1 = (3 )Tj/T1_3 7.97 Tf6.6 0 Td(k ) d ,0 PAGE 118 m =0.1 M f m 0.05 M f L acc = G m m = 2 r 4 .2ResultsofRadiationTransferModeling 100 40 PAGE 119 100 20 m =2 M f 70 160 PAGE 120 40 4.3Summary M c =60 M f cl =1gcm )Tj/T1_7 7.97 Tf6.6 0 Td(2 37 M f & 0.6 40 PAGE 121 M c =60 M f cl =1gcm )Tj/T1_4 7.97 Tf6.6 0 Td(2 R c =0.057 m M f$ d m M f 1.2 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 1.7 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 2.4 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 3.4 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 4.1 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 r R f T ,acc 1.1 10 4 1.5 10 4 1.4 10 4 3.1 10 4 4.0 10 4 L ,acc L f 5.6 10 2 2.0 10 3 5.3 10 3 3.7 10 4 9.6 10 4 m M f $d m M f 1.2 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 1.7 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 2.4 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 3.4 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 4.1 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 r R f T ,acc 1.5 10 4 1.4 10 4 1.2 10 4 3.7 10 4 4.1 10 4 L ,acc L f 8.9 10 2 1.6 10 3 1.0 10 4 6.6 10 4 1.1 10 5 m M f$ d m M f 1.4 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 2.0 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 2.8 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 3.8 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 4.1 10 )Tj/T1_4 7.97 Tf6.6 0 Td(4 r R f T ,acc 1.8 10 4 1.3 10 4 1.1 10 4 3.6 10 4 4.1 10 4 L ,acc L f 1.2 10 3 1.7 10 3 1.2 10 4 7.5 10 4 1.1 10 5

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M f M f

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60 m =2 M f 4 M f 8 M f 16 M f 24 M f

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m =2 M f 4 M f 8 M f 16 M f 24 M f 60

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m =2 M f 4 M f 8 M f 16 M f 24 M f 60

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60

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3.3 10 4 L f 20 )Tj/T1_1 11.955 Tf12.48 0 Td[(34 M f 35 )Tj/T1_1 11.955 Tf11.4 0 Td[(50 cl 0.4 )Tj/T1_1 11.955 Tf11.4 0 Td[(1gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2 (0.7 )Tj/T1_1 11.955 Tf12.36 0 Td[(2.2) 10 5 L f 5.1Introduction

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Outow-ConnedHIIRegion 500 M f 3800 M f 5 .2ObservationsandDataReduction 00 20%

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1 = 0.15 00 2 00 0.2 00 00 00 2 00 00 00 00

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5.3Results 4 5.3.1SEDandProtostellarModelGlobalParameters 40 00 50 00

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0 0 40 00 50 00 6.5 0 3 0 2.37 10 3 4.35 10 3 27 00 18 00 25 00 3.8 00 22 00 12 00 M c = 240 M f m =34 M f cl =1gcm )Tj/T1_4 7.97 Tf6.6 0 Td(2 R c =0.11 10 R c

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c l 1gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 10 R c 4.8 10 3 M f 5.1 10 )Tj/T1_1 7.97 Tf6.6 0 Td(4 M f yr )Tj/T1_1 7.97 Tf6.6 0 Td(1 2.2 10 5 L f w esc =51 view =58 3.6 10 4 L f A V =8 50 00 3.3 10 4 L f cl m view

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cl view 20 )Tj/T1_0 11.955 Tf15.12 0 Td[(34 M f cl 0.4 )Tj/T1_0 11.955 Tf15 0 Td[(1gcm )Tj/T1_1 7.97 Tf6.6 0 Td(2 5.3.2ResolvedIntensityProlesalongtheOutowAxis 6 00

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A V =15 10 )Tj/T1_2 11.955 Tf15.12 0 Td[(40 cl cl 0.4gcm )Tj/T1_5 7.97 Tf6.6 0 Td(2 5.4DiscussionsandConclusions

PAGE 136

m 22 )Tj/T1_0 11.955 Tf12.36 0 Td[(34 M f L bol (0.7 )Tj/T1_0 11.955 Tf12.36 0 Td[(2.2) 10 5 L f cl 0.4 )Tj/T1_0 11.955 Tf12.24 0 Td[(1gcm )Tj/T1_4 7.97 Tf6.6 0 Td(2 1 10 5 L f 0.1 M f yr )Tj/T1_4 7.97 Tf6.6 0 Td(1 kms )Tj/T1_4 7.97 Tf6.6 0 Td(1 0.003 M f yr )Tj/T1_4 7.97 Tf6.6 0 Td(1 kms )Tj/T1_4 7.97 Tf6.6 0 Td(1

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M c M f cl gcm )Tj/T1_4 7.97 Tf6.6 0 Td(2 m M f w ,esc view A V L bol L f 2.2 10 5 1.2 10 5 9.0 10 4 6.6 10 4

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6 0 00 60 00

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6 .1ConstructionofaSystematicModelGrid M c =60 M f cl =1gcm )Tj/T1_5 7.97 Tf6.6 0 Td(2 M c cl f rot f d f w 6.2RadiationTransferofMolecularLinesandObservationalTest

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30 M f 240 M f 5 r > 20 A V > ALMA IRAM

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N RO 6.3ApplicationtoLow-massStarFormationinaHighPressureEnvironment 2 M f 1 M f 0.2 M f 0.4 M f 0.6 M f H 2 O NH 3 CH 3 OH

PAGE 147

30 M f 240 M f ALMA 00 00

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30 M f 240 M f ALMA

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2 M f cl =0.1gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2 cl =1gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2 m =0.2 M f 0.4 M f 0.6 M f

PAGE 150

M f M f gcm )Tj/T1_3 7.97 Tf6.6 0 Td(2

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F M c = 60 M f cl = 1gcm )Tj/T1_6 7.97 Tf6.6 0 Td(2 37 M f & 0.6

PAGE 153

 @ @ t + @ @$($ v $) +$ @ w @ t )Tj/T1_0 11.955 Tf11.88 0 Td($@ i n @ t = 0,$ @ @ t ( $2 n)+ @ @$ ( $v$ $2 n ) )Tj/T1_1 11.955 Tf16.68 8.04 Td(1 2 @ G T @$ + $j w @ w @ t )Tj/T1_0 11.955 Tf12 0 Td($ j i n @ in @ t = 0, @ =@ t $@ w =@ t @ in =@ t$ v $G T =2$ $2 ( d n = d$ ) j w j in n r m acc ( $) )]TJ/T1_1 11.955 Tf21.84 0 Td(2$ v $= @ @ t [ m d ($ ) + m w ( $) )Tj/T1_2 11.955 Tf12 0 Td(m in ($ ) ] +_ m ( )Tj/T1_1 11.955 Tf9.24 0 Td(2 $)( )$ 2 @ n @$= ($ 2 n)_ m acc )Tj/T1_1 11.955 Tf15.12 0 Td(_ m ( r 2 n ) )Tj/T1_0 11.955 Tf15 8.16 Td(@ @ t [ J d ( $) + J w ($ ) )Tj/T1_2 11.955 Tf11.88 0 Td(J in ( $) ] @ m d ($ ) @ t = Z $r 2$ 0 @ @ t d $0 @ m w ($ ) @ t = Z  2 $0 @ w @ t d$ 0 @ m in ( $) @ t = Z$ r 2 $0 @ in @ t d$ 0 @ J w ( $) @ t = Z$ r 2 $0 j w @ w @ t d$ 0 @ J in ( $) @ t = Z$ r 2 $0 j in @ in @ t d$ 0

PAGE 154

@ J d ( $) @ t = Z$ r 2 $0 @ @ t ($ 0 2 n) d $0 = Z$ r 2 $0 @ @ t ($ 0 2 n ) d $0 + Z$ r 2 $0$ 0 2 @ n @ t d $0 = m acc ($ ) )Tj/T1_3 11.955 Tf15.24 0 Td(_ m m m + m d ( $) 1 2 r$ 1 2 )Tj/T1_0 11.955 Tf13.2 8.16 Td(@ [ J d ( $) + J w ($ ) )Tj/T1_1 11.955 Tf11.88 0 Td(J in ( $) ] =@ t p G ( m + m d ($ ) ) $# 3 )Tj/T1_3 11.955 Tf24.12 8.16 Td(2 2$ 2 m + m d ( $) R = m 3 1 )Tj/T1_4 11.955 Tf12 13.2 Td( r$ 1 = 2 1. = = H 2. H = c s = n 3. c 2 s = P = 4. P = k m p T c + 4 3 c T 4 c 5 4 3 T 4 c = 1 2 ( $n 0 ) 2 6. = ( T c ) 7. = c s H 9 > > > > > > > > > > > > > > > > > = > > > > > > > > > > > > > > > > > ; m d = f d m m d ($ d )= f d m m w ( $d )= f w m m in ($ d )=(1+ f d + f w )_ m @ w =@ t @ in =@ t j w j in t @ ( $) =@ t ($ ) T c H @ = @ t =0 ( $) t t + dt PAGE 155 @ ($ ) =@ t $d m d ($ d )= Z $d r 2 @ ($ ) @ t $d$ + 2 ( $d )$ d $d = @ m d ($ ) @ t f f f $=$ d + 2 ( $d )$ d $d$ d / m d ( $d ) 1 = (3 )Tj/T1_3 7.97 Tf6.6 0 Td(k )$ d =$d = 1 = (3 )Tj/T1_2 11.955 Tf12 0 Td(k )[_ m d ($ d ) = m d ( $d )] @ m d ($ ) @ t f f f $=$ d = m d ( $d ) 1 )Tj/T1_1 11.955 Tf25.8 8.04 Td(2 3 )Tj/T1_2 11.955 Tf12 0 Td(k ($ d ) = m d ( $d ) = ($ 2 d ) $d ($ d ) = & 1 @ m d ( $) =@ t f f$ = $d < 0$ d

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v z v K v z 0 v z 0 = v K z $r sin$ 0  c 0 $max,0 z d ($ 0 ) $0 z d ($ 0 ) z 0 ( $0 )= z )Tj/T1_0 11.955 Tf12.12 0 Td(z d ($ 0 ) $c [ z 0 ($ c 0 ) ] $max [ z 0 ($ max,0 )]

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x 0 $0$ c 0 v K = v Kc x )Tj/T1_1 7.97 Tf6.6 0 Td(1 = 2 0 v z 0 = v zc 0 x )Tj/T1_1 7.97 Tf6.6 0 Td(1 = 2 0 v Kc =( Gm =$c 0 ) 1 = 2 v zc 0 0 ($ 0 ) $0 0 ($ 0 ) 0 ( $0 )= c 0$ 0 $c 0 )Tj/T1_4 7.97 Tf6.6 0 Td(q c 0 x )Tj/T1_4 7.97 Tf6.6 0 Td(q 0 c 0 d$ c 0 d m w =4 $0 0 v z 0 d$ 0 =4 $2 c 0 c 0 v zc 0 x 1 2 )Tj/T1_4 7.97 Tf6.6 0 Td(q 0 d x 0 m w =4$ 2 c 0 c 0 v zc 0 I w ( x max,0 )ln x max,0 I w 1 ln x m ax,0 0 @ x 3 2 )Tj/T1_4 7.97 Tf6.6 0 Td(q m ax,0 )Tj/T1_5 11.955 Tf11.88 0 Td(1 3 2 )Tj/T1_0 11.955 Tf11.88 0 Td(q 1 A q = 3 2 I w =1 d $z 0 d m w =4$ v z d $PAGE 158 V ($ 0 z 0 ) v z ( $0 z 0 ) v K ($ 0 ) @ ln $0 @ ln$ f f f f z 0 z 0 c 0 = m w 4 v K c I w ln x max,0 x 2 )Tj/T1_6 7.97 Tf6.6 0 Td(q 0 V $2 = 1 x 0$ / $)Tj/T1_3 7.97 Tf6.6 0 Td(2 x 0 1 B .1ApproximateStreamlines R ($ 0 z 0 ) $($ 0 z 0 ) $0 Z ($ 0 z 0 ) z 0 $0 R c ( Z )=$ c ( Z ) =$c 0 R max ( Z )=$ max ( Z ) =$max,0$ ( $0 Z )=$ c ( Z ) 1 )Tj/T1_10 7.97 Tf6.6 0 Td( $max ( Z ) PAGE 159 Z = 0 = ln x 0 ln x m ax,0 x 0 =1$ = $c x 0 = x max,0$ = $max ansatz$ c 0 $max,0 R ( Z )= R c ( Z ) 1 )Tj/T1_7 7.97 Tf6.6 0 Td( R max ( Z ) Z z 0 ch = m w 4$ 2 c 0 v Kc I w ln x max,0 = 4.3 10 )Tj/T1_3 7.97 Tf6.6 0 Td[(11 I w ln x max,0 10 12 R 3 = 2 M f m 1 = 2 m w 10 )Tj/T1_3 7.97 Tf6.6 0 Td(4 M f )Tj/T1_3 7.97 Tf6.6 0 Td(1 )Tj/T1_3 7.97 Tf6.6 0 Td(3 ( $0 z 0 ) = ch V ( Z ) R 2 ( x 0 z 0 ) x q 0 )Tj/T1_3 7.97 Tf6.6 0 Td(1 = )Tj/T1_1 11.955 Tf9.24 0 Td(( 1 )Tj/T1_2 11.955 Tf11.88 0 Td( ) @ ln$ c @ ln Z )Tj/T1_2 11.955 Tf12 0 Td( @$max @ ln Z +ln$ max $c @ @ ln$ 0 = )Tj/T1_1 11.955 Tf9.24 0 Td[((1 )Tj/T1_2 11.955 Tf11.88 0 Td( ) d ln R c ( Z ) d ln Z )Tj/T1_2 11.955 Tf12 0 Td( d ln R max ( Z ) d ln Z +1+ ln[ R max ( Z ) = R c ( Z )] ln x m ax,0 z 0 R Z R c ( Z )= R max ( Z )

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)Tj/T1_2 7.97 Tf6.6 0 Td(1 = 1 )Tj/T1_5 11.955 Tf13.2 8.16 Td(d ln R d ln Z B.2BP-likeWinds $)Tj/T1_7 7.97 Tf6.6 0 Td(q 0 q = 3 2 I w =1 R 1+14ln(1+0.07 Z ), Z 1246 Z V ( Z ) l n(1.01+5 Z 0.8 ), Z Z =0 Z R 1+4.67ln(1+0.36 Z +3.4 10 )Tj/T1_2 7.97 Tf6.6 0 Td(4 Z 3 ); dR = dZ Z =0 PAGE 161$ d 0 ( r ) r $d = 0 ( 1 )Tj/T1_0 11.955 Tf12 0 Td( 2 0 ) 0 )Tj/T1_0 11.955 Tf12 0 Td( =cos 0 =cos 0 w ,esc$ max,0 z d ,max 0 = w ,esc z d ,max $max,0 =$ 2 d (1 )Tj/T1_0 11.955 Tf12 0 Td( 2 0 ) 2 + z 2 d ,max (1 )Tj/T1_0 11.955 Tf11.88 0 Td( 2 0 ) = 2 0 +2 $d z d ,max (1 )Tj/T1_0 11.955 Tf12 0 Td( 2 0 ) = 0 1 = 2 R max = Z 2 max 1 )Tj/T1_0 11.955 Tf11.88 0 Td( 2 0 2 0 + 2 Z max$ d $m ax,0 1 )Tj/T1_0 11.955 Tf12 0 Td( 2 0 0 + 2 Z max z d ,max$ m ax,0 1 )Tj/T1_0 11.955 Tf12 0 Td( 2 0 2 0 + 1 1 = 2 Z max = z 0 =$max,0 =( z )Tj/T1_4 11.955 Tf12.12 0 Td(z d ,max ) =$ max,0 $max,0$ d (1 )Tj/T1_0 11.955 Tf12.84 0 Td( 2 0 ) $d$ max,0 $d z d max =$ d 0 1 1 )Tj/T1_0 11.955 Tf11.88 0 Td( 2 0 + 2 0 1 = 2 )Tj/T1_3 11.955 Tf12 0 Td(1 # R max = Z 2 max 1 )Tj/T1_0 11.955 Tf11.88 0 Td( 2 0 2 0 + 2 Z max 1 )Tj/T1_0 11.955 Tf12 0 Td( 2 0 0 + 2 Z max z d ,max \$ d 1 )Tj/T1_0 11.955 Tf11.88 0 Td( 2 0 2 0 + 1 1 = 2

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w esc 60 x max,0 1 x max,0