Feedback in Massive Star Formation - uni-tuebingen.dekuiper/... · Rolf Kuiper Early Phases of Star...

Feedback in Massive Star FormationRolf Kuiper1,2

H. Klahr3, H. Beuther3, C. Dullemond4, Th. Henning3

H. Yorke1, T. Hosokawa1, N. Turner1

1 - Jet Propulsion Laboratory, Pasadena, CA, USA2 - Leopoldina Fellow, German Academy of Science3 - Max Planck Institute for Astronomy, Heidelberg, Germany4 - Institute for Theoretical Astrophysics, Heidelberg University, Germany

Early Phases of Star Formation 2012Ringberg, Germany

July 5th 2012

Rolf Kuiper Early Phases of Star Formation July 5th 2012

•How to prevent the high-mass gas reservoir from fragmenting?

•Radiative feedback

•Magnetic fields

•Magnetic fields + Radiation

•Dynamics: Colliding flows, Triggering

•How to overcome the radiation pressure barrier?

How to form massive stars?

➡ You will get the answer in THIS TALK!

➡ Not the topic of this talk


•Static 1D: generalized Eddington limitMstar → 20 M⊙

Challenging the radiation pressure barrierL⇤M⇤

� 4⇡ G c

⇤

•Dynamic 1D: „Thermal dust emission stops the collapse on core scales.“ Kahn (1974); Yorke & Krügel (1977); Kuiper et al. (2010), ApJ 722

Mstar → 40 M⊙

•Dynamic 2D: „Flashlight effect“ / Anisotropy of the thermal radiation fieldYorke & Sonnhalter (2002)

Mstar → 43 M⊙

•Dynamic 3D: „3D radiative Rayleigh-Taylor instability“Krumholz et al. (2009)

Mstar → 41.5 M⊙ (primary) + 29.2 M⊙ (secondary)


•First comprehensive scan of the parameter space (45 simulations published)

Numerics

Tradeoffs:

•Focus on the inner core region: Proto-Star + Disk scale

•Long-term and parameter studies in 2D, selected scenarios in 3D

Highlights:

•Fast and accurate 3D Hybrid Radiation Transport (Kuiper et al. 2010, A&A)

•frequency-dependent ray-tracing for stellar radiative feedback

•fast and robust flux-limited diffusion for thermal dust emission

•Resolution down to 1.27 AU (~ 10 times higher than before)

•grid in spherical coordinates with logarithmically increasing resolution•Complete coverage of the accretion phase (105 ...106 yrs) for the first time

•quantitative conclusions on the SFE / feedback efficiency


Spatial Scales

0.1 pc

10,000 AU 700 AU 90 AU

350 AU5,000 AU

Toroid Accretion Disk Inner Dust-Free Region

Pre-stellar Core

Outflow Cavities

50 AU


Results:

•

- Cut-off of inner gas disk

- Longer free fall phases

Dust Sublimation Front

•

- Cut-off of inner dust disk

- Diminishes anisotropy of thermal radiation field

- Artificially high Radiation Pressure

Kuiper et al. (2010), ApJ 722‣Resolving the Dust Sublimation Front yields sustained Disk Accretion!

Rsink < Rdust

Rsink > Rdust

not to scale

0 20 40 60 80 10010-5

10-4

10-3

t @kyrD

M.*@M ü

yr-1 D

such as in Yorke & Sonnhalter (2002)

resolved Dust Sublimation radius


Radiation Pressure Barrier?

Kuiper et al. (2010), ApJ 722

0 20 40 60 80 100 12010-6

10-5

10-4

10-3

10-2

M* @MüD

M.*@M ü

yr-1 D

Mcore

= 60 M�

Mcore

= 120 M�

Mcore

= 240 M�

Mcore

= 480 M�




0 20 40 60 80 100 12010-6

10-5

10-4

10-3

10-2

M* @MüD

M.*@M ü

yr-1 D

0 20 40 60 80 100 12010-6

10-5

10-4

10-3

10-2

M* @MüD

M.*@M ü

yr-1 D

Mcore

= 60 M� Mcore

= 120 M�

Mcore

= 240 M�

Mcore

= 480 M�




0 20 40 60 80 100 12010-6

10-5

10-4

10-3

10-2

M* @MüD

M.*@M ü

yr-1 D

0 20 40 60 80 100 12010-6

10-5

10-4

10-3

10-2

M* @MüD

M.*@M ü

yr-1 D

Mcore

= 60 M� Mcore

= 120 M�

Mcore

= 240 M�

Mcore

= 480 M�

‣First simulations including Radiation Pressure Feedback and forming stars much higher than the Radiation Pressure Barrier!

‣Disk Accretion solves the Radiation Pressure Problem!


Visualization: 3D effects

1200

AU


Cavities:

•Driven by radiation pressure

•v ~ 100 km s-1

•no radiative Rayleigh-Taylor instability

Accretion Disk:

•Spiral arms

•Gravitational torques drive accretion

video available athttp://www.youtube.com/RolfKuiper

http://www.youtube.com/rolfKuiper




Angular momentum transport

Comparison:

• 2D and 3D collapse simulations

• Viscous Disks vs. Self-Gravity

‣Angular Momentum Transport in Massive Accretion Disks

The Astrophysical Journal, 732:20 (11pp), 2011 May 1 Kuiper et al.

0 2 4 6 8 10 120

5

10

15

20

25

t kyr

MM

00.0010.0030.010.030.10.31.0

2D,

0 2 4 6 8 10 120

5

10

15

20

25

t kyr

MM

00.0010.0030.010.030.10.31.0

2D, 3D, 0

Free fall epochDisk accretion

epoch

3D, 0

Disk accretion epoch8 9 10 11 1210 5

10 4

10 3

10 2

0 100 200 300 400 500 600

t kyr

M.M

yr1

Orbits 10 AU

Figure 2. Stellar mass M! (upper panel) and accretion rate M! (lower panel)as a function of time t or number of inner orbits during the collapse of a120 M" pre-stellar core. The angular momentum transport in the 2D axiallysymmetric run (lines with symbols) is driven by shear viscosity, calculated viaan !-parameterization prescription. The angular momentum transport in the 3Drun (solid line) is driven by gravitational torques in the self-gravitating disk. SeeFigure 6 for a visualization of the non-axisymmetric disk structure. To visualizein particular the details during the disk accretion epoch, the lower panel displaysthe section from 7.8 kyr up to 12.1 kyr; as in the 60 M" case, the accretion rateduring the free-fall epoch (t < 7.8 kyr) is constant.

mass growth and the accretion history for the 3D case as wellas several 2D cases with and without viscosity are presented inFigure 2. Due to the high computational costs of the radiative3D hydrodynamic simulations from the pre-stellar core-collapsescale down to the 1 AU scale of the accretion disk formation andevolution, we are currently not able to report on the long-termevolution of the pre-stellar core collapse. The 11.8 kyr of col-lapse evolution simulated correspond to 0.25 tff of the initialpre-stellar core. For comparison, in our previous 2D collapsesimulations in Kuiper et al. (2010a), in which ! = 0.3 was alsothe case, we followed the collapse over 10 tff until no mass wasleft in the computational domain; it was either accreted ontothe central star or expelled over the outer boundary at 0.1 pc byradiative forces.

Here, we focus on the formation of the disk and the evolutionof the main disk accretion phase, which is well resolvedin the 3D simulation as well. The disk accretion epoch inthe 120 M" run starts roughly at 7.8 kyr, and we follow theevolution up to 11.8 kyr. These 4 kyr correspond to 566 innerdisk orbits (at 10 AU) or 28 outer disk orbits (on average

roughly at 75 AU), respectively, based on a mean stellar massof M!(7.8–11.8 kyr) # 20 M".

Compared with the axially symmetric simulations of theviscous accretion disk, the angular momentum transport bygravitational torques due to the 3D non-axially symmetric diskmorphology results in a much more time-dependent accretionhistory (see lower panel of Figure 2) with successive accretionevents rather than a smooth accretion flow. On the other hand,the integral over the accretion history

! t

0 M(t) dt , the actualstellar mass M!(t), so far remains qualitatively quite similar andfinally yields a slightly higher total stellar mass (see upper panelof Figure 2).

4. DISCUSSION

4.1. From the Free-fall Phase to the Disk Accretion Epoch

A characteristic feature of the accretion histories (see thelower panel of Figure 1) is a sharp drop down at roughlyt = 8 kyr. This point in time marks the transition between theinitial “free-fall” phase and the disk formation epoch afterward.During the free-fall phase, the gas dynamics are dominated bygravitational drag toward the core center. During the courseof the collapse, high angular momentum gas from initiallylarger radii reaches the inner core. At a specific point intime, the resulting centrifugal force (with slight support bythermal pressure) completely balances the gravity at the innercomputational boundary (in the first grid cell adjacent to thecentral sink cell). Hence, the accretion rate drops down.

From now on, the follow-up mass spiraling inward builds upa circumstellar disk. In other words, the so-called centrifugalradius is increasing in time and therefore a circumstellar diskgrows from the inside outward during the collapse. Furtheraccretion through these disks has to be attended by an efficientangular momentum transport.

4.2. Viscous Disks (2D)

Our simulation series in axial symmetry with varying valuesof the !-shear viscosity can be separated into two distinguish-able regimes. The runs with low viscosity (! ! 0.05) yieldthe formation of rings instead of an extended accretion disk.As stated by Yorke et al. (1995), these rings would break upin corresponding 3D studies, resulting in angular momentumtransport by tidal torques. Runs with higher ! viscosity yieldthe formation of long-living accretion disks. Compared to an-alytical estimates of the ! values of massive accretion disksconsidering typical high mass accretion rates in standard ac-cretion disk models (including the thin disk approximation),presented in Vaidya et al. (2009), our dynamic study also allowsthe formation of massive accretion disks with slightly larger !values.

During the long-term evolution of these viscous circumstellardisks, the accretion rate onto the central star decreases continu-ously. The long-term runs differ only about 16% in the resultingstellar mass after 105 yr of evolution, although the ! values ofthese runs vary up to a factor of 20. After 105 yr the star hasgrown up to 19.0, 19.1, 17.8, and 16.0 M" for ! = 1.0, 0.3, 0.1,and 0.05, respectively. If we infer from these simulations thatthe accretion rate is rather independent of !, the well-knownrelation for the accretion rate in analytical steady-state models

M! = 3"#! (15)

implies that the surface density ! is inversely proportional to thedynamic viscosity #, as expected from self-similar solutions for

5

Results:

• Gravitational torques(1 < QToomre < 2)

• Episodic accretion events

• Mean accretion rate in 3D ~ viscous disk evolution in 2D axial symmetry

‣Consistent 3D model of Massive Accretion Disks including

• Self-Gravity as main driver of accretion

• Radiation pressure feedback

• Anisotropic shielding of the radiation pressure


Stability of radiation-pressure-dominated cavities

Kuiper et al. (2012), A&A 537

Hybrid: Ray-Tracing + Flux-Limited Diffusion (RT+FLD)







gray Flux-Limited Diffusion (FLD)





R. Kuiper et al.: On the stability of radiation-pressure-dominated cavities 11

0 10 20 30 40 50 6010!1510!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

M" !M!"

a!cms!

2 "

GravityRay!TracingFLD 2FLD 1

Rcavity #2000 AU

0 10 20 30 40 50 6010!1510!1410!1310!1210!1110!1010!910!810!710!610!510!410!3

M" !M!"a!cms!

2 "

GravityRay!TracingFLD 2FLD 1

Rcavity #10000 AU

Fig. 8. Radiative and gravitational acceleration at a position Rcavity = 2000 AU (left panel) and Rcavity = 10000 AU (right panel) above the massiveproto-star as a function of the stellar mass M! for three di!erent radiation transport approaches: The label “FLD 1” denotes the FLD approximationwith the opacity description of Krumholz et al. (2007). The label “FLD 2” refers to the FLD approximation with the opacities used in Kuiper et al.(2010a, 2011) and in this paper. The label “Ray-Tracing” refers to the RT step as in the hybrid radiation transport scheme.

the infrared regime) is computed in the FLD solver step. Thecorresponding length scale is given by l! = (!!(") #cavity)"1 andtherefore depends on the frequency " of the photons as well ason the actual shell density #cavity. This absorption length scale l!is shown as a function of frequency " for di!erent densities # ofthe cavity shell in Fig. 2.

8. Comparisons8.1. Comparison with a 3D gray FLD simulation

Krumholz et al. (2009) presented a self-gravity radiation hydro-dynamics simulation of the collapse of a 100 M# pre-stellar core.The outer core radius was chosen to be 0.1 pc and the den-sity profile declines in proportion to r"1.5. The initial isother-mal temperature of the core is 20 K. The pre-stellar core is ini-tially in solid-body rotation without any turbulent motion. Themodel describes a so-called monolithic collapse scenario. Theapplied radiation transport method is the gray flux-limited fif-fusion approximation. These properties of this configuration arethe same as in our simulation run “C-FLD”. The equations aresolved on a 3D adaptive mesh refinement grid in cartesian coor-dinates. Densities above the Jeans density on the finest grid levelare represented by sink particles.

During the simulation, bipolar “radiation-filled bubbles” areblown into the environment of the forming massive star. To clar-ify our terminology, these “radiation-filled bubbles” correspondto the “radiation-pressure-dominated cavities” and the “bubblewall” is called a “cavity shell” in this paper. At an extent ofroughly from 1200 to 2000 AU (from Krumholz et al. (2009),Fig. 1 therein) the cavity shell is subject to a “radiative Rayleigh-Taylor instability”, meaning that the radiation pressure expandsthe optically thin region only at specific solid angles, while atother solid angles the concentrated mass load on top of the cav-ity shell is able to penetrate into the low-density region.

This mechanism of shell instability, the focus of radiationpressure onto solid angles with lower optical depth, and the col-lapse of condensed material from the infalling envelope at othersolid angles, precisely matches the outcome of our simulations,if the FLD approximation is used for the stellar radiation feed-back. After the epoch of instability – the caving-in of material– the continuing evolution of their simulation di!ers in terms ofmorphology from our simulations because of the evolving non-

axisymmetric structures. We comment further on this di!erenceafter the following paragraph on the RT + FLD simulations.

In our simulations using the frequency-dependent RT stepfor the stellar irradiation, the mass load on top of the cavityshell causes a dependence of the optical depth on the solid an-gle (owing to the decreasing centrifugal forces towards the pole).However, in these simulations, the caving-in of material at solidangles of high optical depth is prohibited; this is most likelycaused by the treatment of the direct stellar irradiation by meansof a RT approach preserving the natural isotropy of the irradi-ation up to the first absorption layer. Furthermore, the RT ap-proach accounts for the respective frequency-dependent absorp-tion coe"cients as demonstrated in the previous sections.

The cavity is a!ected by Rayleigh-Taylor-like instabilities,when the FLD approximation is used for the radiation transport.This implication is verified by the axial symmetric simulationsperformed herein as well as by the 3D simulation in Krumholzet al. (2009). Improving the radiation transport scheme by in-corporating a ray-tracing of the direct stellar irradiation correctsfor this behavior and leads to a stable cavity growth. This impli-cation is verified by the axial symmetric simulations performedherein as well as by the 3D simulation in Kuiper et al. (2011).The largest di!erences between the numerical treatment in thesimulation of Krumholz et al. (2009) and the simulations withsimilar initial conditions presented herein are twofold: the radi-ation transport approaches and our assumed axial symmetry. Asmentioned above, the simplification to axial symmetry increasesthe di"culty of a comparison of epochs after the occurrence ofthe instability, but the overall simulation results indicate that theoutcome, regardless of whether the instability occurs, does notdepend on the axial symmetric approach:

– The 2D simulations in the FLD approximation match theoutcome of the 3D simulation in the FLD approximation,namely the instability of the cavity.

– In the 2D simulations with the improved radiation transportscheme (ray-tracing + FLD), the cavity remains stable.

– In our 3D simulation (Kuiper et al. 2011), using a frequency-dependent RT step to account for stellar irradiation, the out-flow cavity contains strong non-axisymmetric features, butno instability is detected.



Analytically:

• gray FLD approximation strongly (1-2 orders of magnitude!)underestimates the opacity / radiative force in the cavity shell

In Massive Star Formation:

‣radiative Rayleigh-Taylor instability does NOT occur

‣radiation-pressure-dominated cavities remain stable!


Proto-stellar Outflows

preliminary






Results:Large-scales:

• Clearing of the bipolar regions (prior to the radiation pressure feedback)

• Alleviates the Flashlight effect

preliminary

R [AU]z

[AU

]

Numerical achievements:

• Adopt basic method from Cunningham et al. (2011), based on Matzner & McKee (2000)

• Studying the large-scale flow

• Resolving the scale height of the accretion disk!

‣Outflow - Disk interaction!



Results:Small-scales:

• Decrease of the actual accretion rate

• Final stellar mass?preliminary

R [AU]

z [A

U]

Radiation Pressure+


Radiation Pressure

No Feedback


HII RegionsNumerical implementation:

• Ray-Tracing the stellar ionizing flux through the computational domain

• angular-dependent Stroemgren-Ansatz for the spatial extent of the HII region

‣no diffuse UV field

Preliminary Results:

• Ionizing voided bipolar region

• Large-scale pressure wave

• No influence on early disk accretion

preliminary


Gas disks

Results:

• inner dust-free gas disk yields anisotropy of the optical depth

‣ further shielding of the radiation pressure

‣even longer disk accretion epoch

preliminary

Numerical implementation:

• Rosseland and Planck mean opacities for hot gas in circumstellar disks by Helling et al. (2000) / Semenov et al. (2003)

Helling et al. (2000)

constant gas opacitygas = 0.01 cm2 g�1


Results:

• robust features / phases (of all runs):I. initiallyII. bloating phaseIII. transition to zero-age main sequenceIV. main sequence evolution

• diverse features on small timescales

‣ Proto-Star - Disk interaction

Lacc � L⇤

t 5 kyr

(Proto-) Stellar Evolution

I II III IV

o

0 5 10 15 20 25 30

100

101

102

M* @MüD

R*@R üD

I II III IV

o

0 5 10 15 20 25 30

10-4

10-3

M* @MüDM.*@M ü

yr-1 D

Kuiper & Yorke, in prep.


Kuiper & Yorke, in prep.

Results:

• robust features / phases (of all runs):I. initiallyII. bloating phaseIII. transition to zero-age main sequenceIV. main sequence evolution

• diverse features on small timescales

‣ Proto-Star - Disk interaction

• evolution on larger timescale similar to tracks assuming constant accretion

Lacc � L⇤1000 Rü

100 Rü

10 Rü

1 Rü0.1 Rü0.050.05

1122

33

44 551010

121215152020

104 10310-2

100

102

104

106

T* @KD

L *@L üD

constant accretion

core accretion

(Proto-) Stellar Evolution

t 5 kyr


SummaryRadiation Pressure Barrier:

• Disk accretion solves the problem!

The Astrophysical Journal, 732:20 (11pp), 2011 May 1 Kuiper et al.

0 2 4 6 8 10 120

5

10

15

20

25

t kyr

MM

00.0010.0030.010.030.10.31.0

2D,

0 2 4 6 8 10 120

5

10

15

20

25

t kyr

MM

00.0010.0030.010.030.10.31.0

2D, 3D, 0

Free fall epochDisk accretion

epoch

3D, 0

Disk accretion epoch8 9 10 11 1210 5

10 4

10 3

10 2

0 100 200 300 400 500 600

t kyr

M.M

yr1

Orbits 10 AU

Figure 2. Stellar mass M! (upper panel) and accretion rate M! (lower panel)as a function of time t or number of inner orbits during the collapse of a120 M" pre-stellar core. The angular momentum transport in the 2D axiallysymmetric run (lines with symbols) is driven by shear viscosity, calculated viaan !-parameterization prescription. The angular momentum transport in the 3Drun (solid line) is driven by gravitational torques in the self-gravitating disk. SeeFigure 6 for a visualization of the non-axisymmetric disk structure. To visualizein particular the details during the disk accretion epoch, the lower panel displaysthe section from 7.8 kyr up to 12.1 kyr; as in the 60 M" case, the accretion rateduring the free-fall epoch (t < 7.8 kyr) is constant.

mass growth and the accretion history for the 3D case as wellas several 2D cases with and without viscosity are presented inFigure 2. Due to the high computational costs of the radiative3D hydrodynamic simulations from the pre-stellar core-collapsescale down to the 1 AU scale of the accretion disk formation andevolution, we are currently not able to report on the long-termevolution of the pre-stellar core collapse. The 11.8 kyr of col-lapse evolution simulated correspond to 0.25 tff of the initialpre-stellar core. For comparison, in our previous 2D collapsesimulations in Kuiper et al. (2010a), in which ! = 0.3 was alsothe case, we followed the collapse over 10 tff until no mass wasleft in the computational domain; it was either accreted ontothe central star or expelled over the outer boundary at 0.1 pc byradiative forces.

Here, we focus on the formation of the disk and the evolutionof the main disk accretion phase, which is well resolvedin the 3D simulation as well. The disk accretion epoch inthe 120 M" run starts roughly at 7.8 kyr, and we follow theevolution up to 11.8 kyr. These 4 kyr correspond to 566 innerdisk orbits (at 10 AU) or 28 outer disk orbits (on average

roughly at 75 AU), respectively, based on a mean stellar massof M!(7.8–11.8 kyr) # 20 M".

Compared with the axially symmetric simulations of theviscous accretion disk, the angular momentum transport bygravitational torques due to the 3D non-axially symmetric diskmorphology results in a much more time-dependent accretionhistory (see lower panel of Figure 2) with successive accretionevents rather than a smooth accretion flow. On the other hand,the integral over the accretion history

! t

0 M(t) dt , the actualstellar mass M!(t), so far remains qualitatively quite similar andfinally yields a slightly higher total stellar mass (see upper panelof Figure 2).

4. DISCUSSION

4.1. From the Free-fall Phase to the Disk Accretion Epoch

A characteristic feature of the accretion histories (see thelower panel of Figure 1) is a sharp drop down at roughlyt = 8 kyr. This point in time marks the transition between theinitial “free-fall” phase and the disk formation epoch afterward.During the free-fall phase, the gas dynamics are dominated bygravitational drag toward the core center. During the courseof the collapse, high angular momentum gas from initiallylarger radii reaches the inner core. At a specific point intime, the resulting centrifugal force (with slight support bythermal pressure) completely balances the gravity at the innercomputational boundary (in the first grid cell adjacent to thecentral sink cell). Hence, the accretion rate drops down.

From now on, the follow-up mass spiraling inward builds upa circumstellar disk. In other words, the so-called centrifugalradius is increasing in time and therefore a circumstellar diskgrows from the inside outward during the collapse. Furtheraccretion through these disks has to be attended by an efficientangular momentum transport.

4.2. Viscous Disks (2D)

Our simulation series in axial symmetry with varying valuesof the !-shear viscosity can be separated into two distinguish-able regimes. The runs with low viscosity (! ! 0.05) yieldthe formation of rings instead of an extended accretion disk.As stated by Yorke et al. (1995), these rings would break upin corresponding 3D studies, resulting in angular momentumtransport by tidal torques. Runs with higher ! viscosity yieldthe formation of long-living accretion disks. Compared to an-alytical estimates of the ! values of massive accretion disksconsidering typical high mass accretion rates in standard ac-cretion disk models (including the thin disk approximation),presented in Vaidya et al. (2009), our dynamic study also allowsthe formation of massive accretion disks with slightly larger !values.

During the long-term evolution of these viscous circumstellardisks, the accretion rate onto the central star decreases continu-ously. The long-term runs differ only about 16% in the resultingstellar mass after 105 yr of evolution, although the ! values ofthese runs vary up to a factor of 20. After 105 yr the star hasgrown up to 19.0, 19.1, 17.8, and 16.0 M" for ! = 1.0, 0.3, 0.1,and 0.05, respectively. If we infer from these simulations thatthe accretion rate is rather independent of !, the well-knownrelation for the accretion rate in analytical steady-state models

M! = 3"#! (15)

implies that the surface density ! is inversely proportional to thedynamic viscosity #, as expected from self-similar solutions for

5

0 20 40 60 80 100 12010-6

10-5

10-4

10-3

10-2

M* @MüD

M.*@M ü

yr-1 D

Angular momentum transport:

• Self-Gravity drives accretionRadiation-pressure dominated cavities:

• Stable in 2D and 3D

• Gray Flux-Limited-Diffusion approximation artificially yields instability

0 20 40 60 80 10010-5

10-4

10-3

t @kyrD

M.*@M ü

yr-1 D

Resolving the Dust Sublimation Front:


Summary (preliminary studies)

Proto-stellar Outflows:

• clear bipolar regions

• diminish radiation pressure onto disk accretion flow

• diminish disk accretion rate

Ionization:

• fills voided bipolar regions

• large-scale pressure wave

Gas disks:

• amplify anisotropy of radiation field

• diminish radiation pressure feedback

Thanks for y

our atte

ntion!

(Proto-)Stellar Evolution:

• Strong bloating phase

• Proto-Star - Disk interaction

1000 Rü

100 Rü

10 Rü

1 Rü0.1 Rü0.050.05

1122

33

44 551010

121215152020

104 10310-2

100

102

104

106

T* @KD

L *@L üD


Anisotropy of the thermal radiation field

not to scalenot to scale

Spherical Infall Accretion Disk



Kuiper et al. (2012), A&A 5372000 AU

Cavity morphology:

• frequency-dependent RT: pre-acceleration of layers on top of the cavity shell

RT + FLDFLD




gray FLD15

00 A

U

We halted the simulation at 57,000 years, aftera ~20,000-year period when there was no furtherqualitative change in the evolution (Fig. 1E). Atthis point the system was a binary with a totalmass of 70.7M⊙ and a time-averaged total lumi-nosity of ~5 ! 105 L⊙. The two stars had massesof 41.5 M⊙ and 29.2 M⊙ and were 1590 AUapart. Neglecting the effects of the gas, thesemimajor axis of the orbit was 1280 AU(eccentricity 0.25), but because this neglects thegas, it may be an overestimate. Orbits like this aretypical of young O stars, at least 40% of whichare visual binaries with separations of ~1000 AU(12). These are not the final system parameters,because the envelope and the disk still contained28.3 M⊙ of gas and the accretion rate had notdiminished. However, the qualitative nature ofthe final system was well established.

We compared our result to two-dimensionalsimulations. The largest star that formed in anytwo-dimensional simulation with gray radiativetransfer had a mass of 22.9M⊙. If the simulationincluded a multifrequency treatment of the radia-tion, which we omitted because of its computa-tional cost (23), themaximummass of the star thatformed was 42.9M⊙ (7). In these two-dimensionalsimulations, the initial phases of collapse, diskformation, and growth of a polar bubble werequite similar to ours, although the disk lackednonaxisymmetric structure. In both cases therewas a “flashlight effect” (7, 26) in which the diskbeamed radiation preferentially in the polardirection. In two dimensions, however, as thestar’s mass grew, radiation halted accretion overan ever larger fraction of the solid angle aroundthe star. This eventually stopped infall onto thedisk. Some of the gas remaining in the diskcontinued to accrete onto the star, but at adiminishing rate, and eventually the disk densitybecame low enough for stellar radiation to blowit away.

This never happened in our simulation. Instead,when the luminosity became large enough that ourbubbles no longer delivered mass to the disk ef-ficiently, they became asymmetric and clumpy. Insome places radiation blew out sections of thebubble wall, whereas in others dense filaments ofgas fell toward the stars (Fig. 3). The structure ofdense fingers of heavy, downward-moving fluidalternating with chimneys of outgoing radiationis analogous to that of a classical Rayleigh-Taylorinstability, with radiation taking the place of thelight fluid. Radiation forces away from the starare stronger than gravity when averaged over 4psr, producing velocities and net forces that havean outward direction over most of the solid angle.Much of the mass is concentrated into the densefingers, and because radiation flows around ratherthan through these structures, within them thevelocity and the net force have an inward direc-tion. However, this did not remove the angularmomentum of the gas, so it continued to fall ontothe disk rather than directly onto the stars. Thegrowth of clumps in the disk that form secondarystars is a natural side effect of this process, but

radiation may be just accelerating a process thatis caused by gravity. At least 40%of the accretinggas reached the disk through this Rayleigh-Taylormechanism; gas falling onto the outer disk di-rectly accounted for ~25% of the accretion, andgas reaching the disk by traveling along the

bubbles’ outer walls contributed the remaining~35% (23).

Continued disk feeding is what made thethree-dimensional results different from earliertwo-dimensional ones. At 34,000 and 41,700years (Fig. 1, C and D), bracketing the onset of

Fig. 1. Snapshots of the sim-ulation at (A) 17,500 years,(B) 25,000 years, (C) 34,000years, (D) 41,700 years, and(E) 55,900 years. In eachpanel, the left image showscolumn density perpendic-ular to the rotation axis in a(3000 AU)2 region; the rightimage shows volume densityin a (3000 AU)2 slice alongthe rotation axis. The colorscales are logarithmic (blackat the minimum, red at themaximum), from 100 to102.5 g cm!2 on the left and10!18 to 10!14 g cm!3 on theright. Plus signs indicate theprojected positions of stars.See figs. S1 to S3 and movieS1 for additional images.

A

B

C

D

E

www.sciencemag.org SCIENCE VOL 323 6 FEBRUARY 2009 755

REPORTS

on

Oct

ober

8, 2

009

www.

scie

ncem

ag.o

rgDo

wnlo

aded

from

Krumholz et al. (2009), Science

1500

AU

not the same color coding!


We halted the simulation at 57,000 years, aftera ~20,000-year period when there was no furtherqualitative change in the evolution (Fig. 1E). Atthis point the system was a binary with a totalmass of 70.7M⊙ and a time-averaged total lumi-nosity of ~5 ! 105 L⊙. The two stars had massesof 41.5 M⊙ and 29.2 M⊙ and were 1590 AUapart. Neglecting the effects of the gas, thesemimajor axis of the orbit was 1280 AU(eccentricity 0.25), but because this neglects thegas, it may be an overestimate. Orbits like this aretypical of young O stars, at least 40% of whichare visual binaries with separations of ~1000 AU(12). These are not the final system parameters,because the envelope and the disk still contained28.3 M⊙ of gas and the accretion rate had notdiminished. However, the qualitative nature ofthe final system was well established.

We compared our result to two-dimensionalsimulations. The largest star that formed in anytwo-dimensional simulation with gray radiativetransfer had a mass of 22.9M⊙. If the simulationincluded a multifrequency treatment of the radia-tion, which we omitted because of its computa-tional cost (23), themaximummass of the star thatformed was 42.9M⊙ (7). In these two-dimensionalsimulations, the initial phases of collapse, diskformation, and growth of a polar bubble werequite similar to ours, although the disk lackednonaxisymmetric structure. In both cases therewas a “flashlight effect” (7, 26) in which the diskbeamed radiation preferentially in the polardirection. In two dimensions, however, as thestar’s mass grew, radiation halted accretion overan ever larger fraction of the solid angle aroundthe star. This eventually stopped infall onto thedisk. Some of the gas remaining in the diskcontinued to accrete onto the star, but at adiminishing rate, and eventually the disk densitybecame low enough for stellar radiation to blowit away.

This never happened in our simulation. Instead,when the luminosity became large enough that ourbubbles no longer delivered mass to the disk ef-ficiently, they became asymmetric and clumpy. Insome places radiation blew out sections of thebubble wall, whereas in others dense filaments ofgas fell toward the stars (Fig. 3). The structure ofdense fingers of heavy, downward-moving fluidalternating with chimneys of outgoing radiationis analogous to that of a classical Rayleigh-Taylorinstability, with radiation taking the place of thelight fluid. Radiation forces away from the starare stronger than gravity when averaged over 4psr, producing velocities and net forces that havean outward direction over most of the solid angle.Much of the mass is concentrated into the densefingers, and because radiation flows around ratherthan through these structures, within them thevelocity and the net force have an inward direc-tion. However, this did not remove the angularmomentum of the gas, so it continued to fall ontothe disk rather than directly onto the stars. Thegrowth of clumps in the disk that form secondarystars is a natural side effect of this process, but

radiation may be just accelerating a process thatis caused by gravity. At least 40%of the accretinggas reached the disk through this Rayleigh-Taylormechanism; gas falling onto the outer disk di-rectly accounted for ~25% of the accretion, andgas reaching the disk by traveling along the

bubbles’ outer walls contributed the remaining~35% (23).

Continued disk feeding is what made thethree-dimensional results different from earliertwo-dimensional ones. At 34,000 and 41,700years (Fig. 1, C and D), bracketing the onset of

Fig. 1. Snapshots of the sim-ulation at (A) 17,500 years,(B) 25,000 years, (C) 34,000years, (D) 41,700 years, and(E) 55,900 years. In eachpanel, the left image showscolumn density perpendic-ular to the rotation axis in a(3000 AU)2 region; the rightimage shows volume densityin a (3000 AU)2 slice alongthe rotation axis. The colorscales are logarithmic (blackat the minimum, red at themaximum), from 100 to102.5 g cm!2 on the left and10!18 to 10!14 g cm!3 on theright. Plus signs indicate theprojected positions of stars.See figs. S1 to S3 and movieS1 for additional images.

A

B

C

D

E

www.sciencemag.org SCIENCE VOL 323 6 FEBRUARY 2009 755

REPORTS

on

Oct

ober

8, 2

009

www.

scie

ncem

ag.o

rgDo

wnlo

aded

from



gray FLD15

00 A

U

Krumholz et al. (2009), Science

1500

AU

not the same color coding!

Feedback in Massive Star Formation - uni-tuebingen.dekuiper/... · Rolf Kuiper Early Phases of Star...

Documents

Transcript of Feedback in Massive Star Formation - uni-tuebingen.dekuiper/... · Rolf Kuiper Early Phases of Star...