High Mass Star Formationby Gravitational Collapse

of Massive Cores

High Mass Star Formationby Gravitational Collapse

of Massive Cores

Mark Krumholz

Princeton UniversityCollaborators: Richard Klein, Christopher McKee, Stella

Offner (UC Berkeley), and Jonathan Tan (U. Florida)

Mark Krumholz

Princeton UniversityCollaborators: Richard Klein, Christopher McKee, Stella

Offner (UC Berkeley), and Jonathan Tan (U. Florida)

Image: O’Dell & Wong (1995)

Talk OutlineTalk Outline Initial conditions: massive clumps and

cores Three things we don’t understand about

assembling a massive star Fragmentation Competitive accretion Feedback and the problem of accretion

Prospects and problems for the future

Initial conditions: massive clumps and cores

Three things we don’t understand about assembling a massive star Fragmentation Competitive accretion Feedback and the problem of accretion

Prospects and problems for the future

Sites of Massive Star Formation(Plume et al. 1997; Shirley et al. 2003; Rathbone et al. 2005; Yonekura et al. 2005)Sites of Massive Star Formation

(Plume et al. 1997; Shirley et al. 2003; Rathbone et al. 2005; Yonekura et al. 2005)

Massive stars form in clumps observed in mm continuum or lines, or in IR absorption (IRDCs)

Clumps have very high pressure / surface density (~1 g cm-2)

Very turbulent, ~ 4 km s-1, off ordinary linewidth-size relation

Virial parameter vir ~ 1

Massive stars form in clumps observed in mm continuum or lines, or in IR absorption (IRDCs)

Clumps have very high pressure / surface density (~1 g cm-2)

Very turbulent, ~ 4 km s-1, off ordinary linewidth-size relation

Virial parameter vir ~ 1Spitzer/IRAC (left) and Spitzer/MIPS (right), Rathbone et al. (2005)Spitzer/IRAC (left) and Spitzer/MIPS (right), Rathbone et al. (2005)

Massive Cores in Clumps(Beuther & Shilke 2004, Sridharan et al. 2005, Beuther, Sridharan, & Saito 2005, Garay 2005)

Massive Cores in Clumps(Beuther & Shilke 2004, Sridharan et al. 2005, Beuther, Sridharan, & Saito 2005, Garay 2005)

Largest cores in clumps: M ~ 100 M, R ~ 0.1 pc, ~ 1 g cm-2, centrally condensed

Some examples show no MIR emission starless cores

Largest cores in clumps: M ~ 100 M, R ~ 0.1 pc, ~ 1 g cm-2, centrally condensed

Some examples show no MIR emission starless cores

Core in IRDC 18223-3, Spitzer/IRAC (color) and PdBI 93 GHz continuum (contours), Beuther, Sridharan, & Saito (2005)

Core in IRDC 18223-3, Spitzer/IRAC (color) and PdBI 93 GHz continuum (contours), Beuther, Sridharan, & Saito (2005)

Cores in IRDC 18454-0158, MSX 8 m (grayscale), 1.2 mm IRAM 30m (contours), Sridharan et al. (2005)

Cores in IRDC 18454-0158, MSX 8 m (grayscale), 1.2 mm IRAM 30m (contours), Sridharan et al. (2005)

Turbulent Core Model(McKee & Tan 2003)

Turbulent Core Model(McKee & Tan 2003)

Model cores as self-similar spheres at high pressure, column density

High pressure and density gives free-fall time ~105 yr fast accretion, 10–4 - 10–3 M / yr

Supported predominantly by turbulent motions

Model cores as self-similar spheres at high pressure, column density

High pressure and density gives free-fall time ~105 yr fast accretion, 10–4 - 10–3 M / yr

Supported predominantly by turbulent motions

Mass-radius relation for cores in NGC 7538, SCUBA, Reid & Wilson (2005)

Mass-radius relation for cores in NGC 7538, SCUBA, Reid & Wilson (2005)

The Core Population(Motte, Andre, & Neri 1998, Reid & Wilson 2005, 2006, Stanke et al. 2006)

The Core Population(Motte, Andre, & Neri 1998, Reid & Wilson 2005, 2006, Stanke et al. 2006)

Core MF is just a shifted stellar IMF

Cores mass segregated, just like star clusters

Core MF is just a shifted stellar IMF

Cores mass segregated, just like star clusters

Core mass function in M17 from SCUBA, Reid & Wilson (2006)Core mass function in M17 from SCUBA, Reid & Wilson (2006)

Core mass function for inner (red) and outer (blue) parts of Oph, Stanke et al. (2006)

Core mass function for inner (red) and outer (blue) parts of Oph, Stanke et al. (2006)

Assembling a Massive StarAssembling a Massive Star

Problem 1: FragmentationProblem 1: Fragmentation Cores follow the stellar IMF and are mass

segregated, just like stars. It is appealing to explain properties of

massive stars in terms of massive cores …but if massive cores fragment to many

stars, there is no direct core-star mapping, MF agreement is just a coincidence.

Do massive cores fragment?

Cores follow the stellar IMF and are mass segregated, just like stars.

It is appealing to explain properties of massive stars in terms of massive cores

…but if massive cores fragment to many stars, there is no direct core-star mapping, MF agreement is just a coincidence.

Do massive cores fragment?

Fragmentation and Heating(Krumholz, 2006, ApJL, 641, 45)

Fragmentation and Heating(Krumholz, 2006, ApJL, 641, 45)

Cores initially cold (10-20 K), mass is many thermal Jeans masses

Pure hydro simulations find many small fragments, no massive stars (Dobbs, Bonnell, & Clark 2005)

However, accretion luminosity can be 100 L even onto 0.1 M stars

Analytic RT models show this inhibits fragmentation

Cores initially cold (10-20 K), mass is many thermal Jeans masses

Pure hydro simulations find many small fragments, no massive stars (Dobbs, Bonnell, & Clark 2005)

However, accretion luminosity can be 100 L even onto 0.1 M stars

Analytic RT models show this inhibits fragmentation

Temperature and min. fragment mass for RT (blue) and a barotropic EOS (red) in a 50 M, 1 g cm-2 core

Temperature and min. fragment mass for RT (blue) and a barotropic EOS (red) in a 50 M, 1 g cm-2 core

m* =0.8 M

m

* =0.05 M

Barotropic EOS, no RT

RT calculation

Radiation-Hydro SimulationsRadiation-Hydro Simulations

Start with McKee & Tan core: r –1.5, turbulent with vir ≈ 1, flat bottom ( const in center)

Result: most mass goes into a single object

Start with McKee & Tan core: r –1.5, turbulent with vir ≈ 1, flat bottom ( const in center)

Result: most mass goes into a single object

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Massive Cores Fragment WeaklyMassive Cores Fragment Weakly

Radiation critical even at early times due to large Lacc

The barotropic approximation severely the under-estimates true temperature too many fragments

Radiation critical even at early times due to large Lacc

The barotropic approximation severely the under-estimates true temperature too many fragments

Weak fragmentation all core mass falls onto a few stars, stellar IMF should resemble core MF

Weak fragmentation all core mass falls onto a few stars, stellar IMF should resemble core MF

Ratio of temperature computed with radiation to temperature computed with barotropic approximation when m* ≈ 4 M

Ratio of temperature computed with radiation to temperature computed with barotropic approximation when m* ≈ 4 M

Problem 2: Competitive Accretion

Problem 2: Competitive Accretion

Since massive cores don’t fragment strongly, this suggests a direct core to star mapping

…but could stars accrete significant mass from outside their parent cores?

If so, then this competitive accretion of outside gas determines stellar properties, not the properties of cores.

Since massive cores don’t fragment strongly, this suggests a direct core to star mapping

…but could stars accrete significant mass from outside their parent cores?

If so, then this competitive accretion of outside gas determines stellar properties, not the properties of cores.

Could Stars Gain Extra Mass?Could Stars Gain Extra Mass? Core is dense, bound, coherent in velocity

(e.g. Goodman et al. 1998). After it is gone, accretion could occur from uncorrelated clump gas.

Let , where is accretion rate after parent core is gone. Is ?

Core is dense, bound, coherent in velocity (e.g. Goodman et al. 1998). After it is gone, accretion could occur from uncorrelated clump gas.

Let , where is accretion rate after parent core is gone. Is ?

Simulation of star cluster formation, Bonnell, Vine, & Bate (2004)

Simulation of star cluster formation, Bonnell, Vine, & Bate (2004)

1 M

The Competitive Accretion RateThe Competitive Accretion Rate Stars can accrete by capturing unbound

gas (Bondi-Hoyle) or capturing other cores Analytically compute fm from captures:

(Krumholz, McKee, & Klein, 2005, Nature, 438, 332)

where co = core mass fraction ~ 0.1, u = ratio of core escape velocity to clump velocity dispersion,

This gives fm in terms of star mass M*, clump mass M, virial ratio vir = KE / PE

Stars can accrete by capturing unbound gas (Bondi-Hoyle) or capturing other cores

Analytically compute fm from captures: (Krumholz, McKee, & Klein, 2005, Nature, 438, 332)

where co = core mass fraction ~ 0.1, u = ratio of core escape velocity to clump velocity dispersion,

This gives fm in terms of star mass M*, clump mass M, virial ratio vir = KE / PE

Turbulent BH Accretion(Krumholz, McKee, & Klein, 2005, 618, 757 and 2006, ApJ, 638, 369)

Turbulent BH Accretion(Krumholz, McKee, & Klein, 2005, 618, 757 and 2006, ApJ, 638, 369)

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For fm due to gas accretion, use simulations to develop model for Bondi-Hoyle accretion in a turbulent mediumFor fm due to gas accretion, use simulations to develop model for Bondi-Hoyle accretion in a turbulent medium

The Turbulent BH Accretion RateThe Turbulent BH Accretion Rate Simulations show

accretion rate very well fit by

with BH a known function of Mach number, region size

From this, compute mass gained by accreting unbound gas:

Simulations show accretion rate very well fit by

with BH a known function of Mach number, region size

From this, compute mass gained by accreting unbound gas:

Accretion rate distribution from model (solid line) and simulation (histogram), Krumholz, McKee, & Klein, 2006, ApJ, 638, 369

Accretion rate distribution from model (solid line) and simulation (histogram), Krumholz, McKee, & Klein, 2006, ApJ, 638, 369

Is There Competitive Accretion?(Krumholz, McKee, & Klein, 2005, Nature, 438, 332)

Is There Competitive Accretion?(Krumholz, McKee, & Klein, 2005, Nature, 438, 332)

Combining fm due to captures and BH accretion shows for 0.5 M stars in clumps with

Entire clumps have M ~ 1000 M, vir ≈ 1 no competitive accretion

If clumps undergo global collapse, stagnation points form with low mass, velocities where stars stay after accreting cores (Bonnell & Bate 2006), (although these may not fragment at all)

CA can occur only if clumps are collapsing

Combining fm due to captures and BH accretion shows for 0.5 M stars in clumps with

Entire clumps have M ~ 1000 M, vir ≈ 1 no competitive accretion

If clumps undergo global collapse, stagnation points form with low mass, velocities where stars stay after accreting cores (Bonnell & Bate 2006), (although these may not fragment at all)

CA can occur only if clumps are collapsing

Global Collapse in Gas Clumps and Star Clusters

Global Collapse in Gas Clumps and Star Clusters

Most clumps don’t show infall in their line profiles (Garay 2005)

Age spreads in star clusters should be ~ tcr (~ 2 tff) if global collapse occurs, but they are usually 3 – 5 tcr (Tan, Krumholz, & McKee,

2006, ApJL, 641, 121)

Most clumps don’t show infall in their line profiles (Garay 2005)

Age spreads in star clusters should be ~ tcr (~ 2 tff) if global collapse occurs, but they are usually 3 – 5 tcr (Tan, Krumholz, & McKee,

2006, ApJL, 641, 121)

tcr ≈ 0.6 Myrtcr ≈ 0.6 Myr

Stellar age distribution in IC 348, Palla & Stahler (2000)Stellar age distribution in IC 348, Palla & Stahler (2000)

Inconsistent with global collapse, CAInconsistent with global collapse, CA

Global Collapse andthe Star Formation Rate

(Krumholz & Tan, 2006, ApJ, submitted)

Global Collapse andthe Star Formation Rate

(Krumholz & Tan, 2006, ApJ, submitted)

If clumps collapse, mass forms stars in ~tcr. This gives a SFR.

Compare to observed SFR in dense gas (e.g. Gao & Solomon 2004, Wu et al. 2005)

Global collapse gives

If clumps collapse, mass forms stars in ~tcr. This gives a SFR.

Compare to observed SFR in dense gas (e.g. Gao & Solomon 2004, Wu et al. 2005)

Global collapse gives

Ratio of free-fall time to depletion time in observed systems (black), simulations (red), and from a theoretical model (blue), as a function of mean density

Ratio of free-fall time to depletion time in observed systems (black), simulations (red), and from a theoretical model (blue), as a function of mean density

Inconsistent with GC, CAInconsistent with GC, CA

Simulations with FeedbackSimulations with FeedbackFeedback (e.g. outflows) prevents global collapse, does not show stagnation points or CA

Feedback (e.g. outflows) prevents global collapse, does not show stagnation points or CA

Column density (below) and kinetic energy versus time (right) in a simulation of star cluster formation, Li & Nakamura (2006)

Column density (below) and kinetic energy versus time (right) in a simulation of star cluster formation, Li & Nakamura (2006)

Problem 3: Feedback and the Problem of Accretion

Problem 3: Feedback and the Problem of Accretion

If feedback prevents most of the mass in a large core from reaching the protostar, then the core MF can’t produce the stellar IMF

A protostar reaches the MS in a Kelvin time:

This is shorter than the formation time star reaches MS while still accreting

If feedback prevents most of the mass in a large core from reaching the protostar, then the core MF can’t produce the stellar IMF

A protostar reaches the MS in a Kelvin time:

This is shorter than the formation time star reaches MS while still accreting

Radiation Pressure(Larson & Starrfield 1971; Kahn 1974;

Yorke & Krügel 1977; Wolfire & Cassinelli 1987)

Radiation Pressure(Larson & Starrfield 1971; Kahn 1974;

Yorke & Krügel 1977; Wolfire & Cassinelli 1987) Dust absorbs UV &

visible, re-radiates IR Dust sublimes at T ~

1200 K, r ~ 30 AU Radiation > gravity for

For 50 M ZAMS star,

Dust absorbs UV & visible, re-radiates IR

Dust sublimes at T ~ 1200 K, r ~ 30 AU

Radiation > gravity for

For 50 M ZAMS star,

Massive stars approach their Eddington limits while forming

Ideas to Break the Radiation Pressure Barrier

Ideas to Break the Radiation Pressure Barrier

3D radiation hydro-dynamic effects may be important, so do detailed simulations to study them

Massive protostars have outflows, just like low mass stars; consider their effects

3D radiation hydro-dynamic effects may be important, so do detailed simulations to study them

Massive protostars have outflows, just like low mass stars; consider their effects

!!

Radiation-Hydro SimulationsRadiation-Hydro Simulations

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Radiation Beaming by Gas(Yorke & Sonnhalter 2002; Krumholz, Klein, & McKee 2005)

Radiation Beaming by Gas(Yorke & Sonnhalter 2002; Krumholz, Klein, & McKee 2005)

Do radiation-hydrodynamic simulations of massive cores in 2D or 3D

Flashlight effect: gas collimates radiation

Do radiation-hydrodynamic simulations of massive cores in 2D or 3D

Flashlight effect: gas collimates radiation

Collimation allows accretion to high masses!

Collimation allows accretion to high masses!

Density and radiation flux vectors from simulation, Krumholz, Klein, & McKee 2005

Density and radiation flux vectors from simulation, Krumholz, Klein, & McKee 2005

Have Radiation Bubbles Been Detected Already?

Have Radiation Bubbles Been Detected Already?

Density, temperature in bubble walls good for maser emission

Observations show circles of maser spots

These may be direct evidence of radiation bubbles – no obvious alternative means of producing them

Density, temperature in bubble walls good for maser emission

Observations show circles of maser spots

These may be direct evidence of radiation bubbles – no obvious alternative means of producing them

Cepheus A HW 2, H20 Masers, VLA, Torrelles et al. 2001Cepheus A HW 2, H20 Masers, VLA, Torrelles et al. 2001

Massive Star Outflows(Richer et al. 2000; Beuther et al. 2002, 2003, 2004)

Massive Star Outflows(Richer et al. 2000; Beuther et al. 2002, 2003, 2004)

Observations show massive stellar outflows are well-collimated

Force required to drive outflows is ~10 – 103 L/c outflows probably hydro-magnetic

Observations show massive stellar outflows are well-collimated

Force required to drive outflows is ~10 – 103 L/c outflows probably hydro-magnetic

IRAS 19217+1631, SMA, Beuther et al. 2004IRAS 19217+1631, SMA, Beuther et al. 2004

Outflows Help Accretion(Krumholz, McKee, & Klein, ApJL, 2005, 618, 33)

Outflows Help Accretion(Krumholz, McKee, & Klein, ApJL, 2005, 618, 33)

Outflow cavities are nearly dust free very low optical depth

Dense envelope channels radiation into cavity: enhanced flashlight effect

Result: order-of-magnitude reduction in radiation force

Outflow cavities are nearly dust free very low optical depth

Dense envelope channels radiation into cavity: enhanced flashlight effect

Result: order-of-magnitude reduction in radiation force

Radiation and gravity forces vs. distance in simple model for a massive core with an outflow cavity

Radiation and gravity forces vs. distance in simple model for a massive core with an outflow cavity

Problems for the FutureProblems for the Future

Magnetic Fields(Crutcher 1999, 2005; Lai et al. 2001, 2002;Bourke et al. 2001; Matthews et al. 2005)

Magnetic Fields(Crutcher 1999, 2005; Lai et al. 2001, 2002;Bourke et al. 2001; Matthews et al. 2005)

Preliminary data M/M ~ 1 – 2

Large systematic uncertainties: geometry, resolution, source of signal

Different techniques disagree strongly

No MHD simulations to date; only cartoon models

Preliminary data M/M ~ 1 – 2

Large systematic uncertainties: geometry, resolution, source of signal

Different techniques disagree strongly

No MHD simulations to date; only cartoon models

Polarization vectors in MMS 6 (OMC), BIMA1.3 mm, Matthews et al. 2005

Polarization vectors in MMS 6 (OMC), BIMA1.3 mm, Matthews et al. 2005

Better Physics in SimulationsBetter Physics in Simulations Include outflows / winds in simulations of

both core and cluster formation Do radiative transfer on the cluster scale Better RT: beyond flux-limited diffusion,

3D multifrequency, ionization evolution Every new piece of physics has revealed a

qualitatively new and unexpected behavior

Include outflows / winds in simulations of both core and cluster formation

Do radiative transfer on the cluster scale Better RT: beyond flux-limited diffusion,

3D multifrequency, ionization evolution Every new piece of physics has revealed a

qualitatively new and unexpected behavior

We’ve probably learned all we can from hydro + gravity simulations

We’ve probably learned all we can from hydro + gravity simulations

Simulation-Observation CouplingSimulation-Observation Coupling Get better initial

conditions, e.g. density, velocity profiles of starless cores

Post-process simulations to predict observables, e.g. morphology, SEDs

Focus on observables for systems that are still forming stars: cluster properties not definitive

Get better initial conditions, e.g. density, velocity profiles of starless cores

Post-process simulations to predict observables, e.g. morphology, SEDs

Focus on observables for systems that are still forming stars: cluster properties not definitive

Simulated observation of radiation bubble viewed edge-on in a tracer of warm (>100 K) gas

Simulated observation of radiation bubble viewed edge-on in a tracer of warm (>100 K) gas

SummarySummary Massive stars form from massive cores

Massive cores fragment only weakly Stars don’t gain much mass from outside their

natal cores Radiation feedback cannot significantly inhibit

accretion from cores onto stars Many properties of massive stars are

inherited from their gas phase precursors However, our simulations are still simple,

and every new bit of physics added has revealed something unexpected…

Massive stars form from massive cores Massive cores fragment only weakly Stars don’t gain much mass from outside their

natal cores Radiation feedback cannot significantly inhibit

accretion from cores onto stars Many properties of massive stars are

inherited from their gas phase precursors However, our simulations are still simple,

and every new bit of physics added has revealed something unexpected…

Plan BPlan B

Give up and appeal to intelligent design…Give up and appeal to intelligent design…