From Massive Cores to Massive Stars

From Massive Cores to Massive Stars

Mark Krumholz

Princeton UniversityCollaborators:

Richard Klein, Christopher McKee (UC Berkeley)

Kaitlin Kratter, Christopher Matzner (U. Toronto)

Jonathan Tan (University of Florida)

Todd Thompson (Princeton University)

Mark Krumholz

Princeton UniversityCollaborators:

Richard Klein, Christopher McKee (UC Berkeley)

Kaitlin Kratter, Christopher Matzner (U. Toronto)

Jonathan Tan (University of Florida)

Todd Thompson (Princeton University)

From Stars to PlanetsUniversity of FloridaApril 11, 2007

From Stars to PlanetsUniversity of FloridaApril 11, 2007

Talk OutlineTalk Outline From core to star

Initial fragmentation Disk formation and

evolution Binary formation Radiation pressure and

feedback Competitive accretion

Final summary

From core to star Initial fragmentation Disk formation and

evolution Binary formation Radiation pressure and

feedback Competitive accretion

Final summaryMassive core (PdBI, contours) inside IRDC (Spitzer IRAC, colors), Beuther et al. (2007)

Massive core (PdBI, contours) inside IRDC (Spitzer IRAC, colors), Beuther et al. (2007)

The Core Mass Function(Motte, Andre, & Neri 1998, Johnstone et al. 2001, Reid & Wilson

2005, 2006, Lombardi et al. 2006, Charlie Lada’s talk)

The Core Mass Function(Motte, Andre, & Neri 1998, Johnstone et al. 2001, Reid & Wilson

2005, 2006, Lombardi et al. 2006, Charlie Lada’s talk)

The core MF is similar to the stellar IMF, but shifted to higher masses a factor of 2 – 4

Seen in many regions, many observational tracers

Correspondence suggests a 1 to 1, constant efficiency, core to star mapping

The core MF is similar to the stellar IMF, but shifted to higher masses a factor of 2 – 4

Seen in many regions, many observational tracers

Correspondence suggests a 1 to 1, constant efficiency, core to star mapping

Core mass function in Pipe Nebula (red) vs. stellar IMF (gray) (Alves, Lombardi, & Lada 2007)

Core mass function in Pipe Nebula (red) vs. stellar IMF (gray) (Alves, Lombardi, & Lada 2007)

From Core to StarFrom Core to Star

Stage 1: Initial Fragmentation(Krumholz, 2006, ApJL, 641, 45)

Stage 1: Initial Fragmentation(Krumholz, 2006, ApJL, 641, 45)

Massive cores are much larger than MJ (~ M), so one might expect them to fragment while collapsing (e.g. Dobbs et al.

2005) However, accretion can

produce > 100 L even when protostars are < 1 M

Massive cores are much larger than MJ (~ M), so one might expect them to fragment while collapsing (e.g. Dobbs et al.

2005) However, accretion can

produce > 100 L even when protostars are < 1 M

Temperature vs. radius in a massive core before star formation (red), and once protostar begins accreting (blue)

Temperature vs. radius in a massive core before star formation (red), and once protostar begins accreting (blue)

m* =0.05 M

m*=0.8 M

Radiation-Hydro SimulationsRadiation-Hydro Simulations To study this effect, do simulations Use the Orion code to solve equations of

hydrodynamics, gravity, radiation (in flux-limited diffusion approximation) on an adaptive mesh (Krumholz, Klein, & McKee 2007, ApJ, 656, 959, and KKM, 2007, ApJS, submitted, astro-ph/0611003)

To study this effect, do simulations Use the Orion code to solve equations of

hydrodynamics, gravity, radiation (in flux-limited diffusion approximation) on an adaptive mesh (Krumholz, Klein, & McKee 2007, ApJ, 656, 959, and KKM, 2007, ApJS, submitted, astro-ph/0611003)

Mass conservationMomentum conservationGas energy conservationRad. energy conservationSelf-gravity

Mass conservationMomentum conservationGas energy conservationRad. energy conservationSelf-gravity

Simulation of a Massive CoreSimulation of a Massive Core

Simulation of 100 M, 0.1 pc turbulent core LHS shows in whole core, RHS shows 2000 AU

region around most massive star

Simulation of 100 M, 0.1 pc turbulent core LHS shows in whole core, RHS shows 2000 AU

region around most massive star

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Massive Cores Fragment WeaklyMassive Cores Fragment Weakly With RT: 6 fragments,

most mass accretes onto single largest star through a massive disk

Without RT: 23 fragments, many stellar collisions, disk smaller and less massive

Conclusion: radiation inhibits fragmentation, qualitatively changes star formation process

With RT: 6 fragments, most mass accretes onto single largest star through a massive disk

Without RT: 23 fragments, many stellar collisions, disk smaller and less massive

Conclusion: radiation inhibits fragmentation, qualitatively changes star formation process

Column density with (upper) and without (lower) RT, for identical times and initial conditions

Column density with (upper) and without (lower) RT, for identical times and initial conditions

Stage 2: Massive Disks(Kratter & Matzner 2006, Kratter, Matzner & Krumholz, 2007, in preparation)

Stage 2: Massive Disks(Kratter & Matzner 2006, Kratter, Matzner & Krumholz, 2007, in preparation)

Accretion rate onto star + disk is ~ 3 / G ~ 10–3 M / yr in a massive core

Maximum accretion rate through a stable disk via MRI or local GI is ~ cs

3 / G ~ 5 x 10–5 M / yr for a disk with T = 100 K

Conclusion: cores accrete faster than stable disks can process, so disks become massive and unstable. Depending on thermodynamics, they may fragment.

Accretion rate onto star + disk is ~ 3 / G ~ 10–3 M / yr in a massive core

Maximum accretion rate through a stable disk via MRI or local GI is ~ cs

3 / G ~ 5 x 10–5 M / yr for a disk with T = 100 K

Conclusion: cores accrete faster than stable disks can process, so disks become massive and unstable. Depending on thermodynamics, they may fragment.

Massive Disks in Simulations(KKM, 2007, ApJ, 656, 959)

Massive Disks in Simulations(KKM, 2007, ApJ, 656, 959)

Disks reach Mdisk ~ M* / 2, r ~ 1000 AU

Global GI creates strong m = 1 spiral pattern

Spiral waves drive rapid accretion; eff ~ 1

Radiation keeps disks azimuthally isothermal

Disks reach Q ~ 1, unstable to fragment formation

Disks reach Mdisk ~ M* / 2, r ~ 1000 AU

Global GI creates strong m = 1 spiral pattern

Spiral waves drive rapid accretion; eff ~ 1

Radiation keeps disks azimuthally isothermal

Disks reach Q ~ 1, unstable to fragment formation Surface density (upper) and Toomre

Q (lower); striping is from projectionSurface density (upper) and Toomre Q (lower); striping is from projection

Observing Massive DisksObserving Massive Disks

Integrated TB in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH3CN 220.7472 GHz (KKM 2007, ApJ, submitted)Integrated TB in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH3CN 220.7472 GHz (KKM 2007, ApJ, submitted)

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TB as a function of velocity in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH3CN 220.7472 GHz (KKM 2007, ApJ, submitted)TB as a function of velocity in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH3CN 220.7472 GHz (KKM 2007, ApJ, submitted)

Stage 3: Binary FormationStage 3: Binary Formation Most massive stars in

binaries (Preibisch et al. 2001)

Binaries often very close, a < 0.25 AU

Mass ratios near unity (“twins”) common (Pinsonneault & Stanek 2006, Bonanos 2007)

Most massive known binary is WR20a: M1 = 82.7 M, q = 0.99 ± 0.05 (Rauw et al. 2005)

Most massive stars in binaries (Preibisch et al. 2001)

Binaries often very close, a < 0.25 AU

Mass ratios near unity (“twins”) common (Pinsonneault & Stanek 2006, Bonanos 2007)

Most massive known binary is WR20a: M1 = 82.7 M, q = 0.99 ± 0.05 (Rauw et al. 2005)

Mass ratio for 26 detached elcipsing binaries in the SMC (Pinsonneault & Stanek 2006)

Mass ratio for 26 detached elcipsing binaries in the SMC (Pinsonneault & Stanek 2006)

Close Binaries(Krumholz & Thompson, 2007, ApJ, in press, astro-ph/0611822)

Close Binaries(Krumholz & Thompson, 2007, ApJ, in press, astro-ph/0611822)

Stars migrate through disk to within 10 AU of primary

Some likely merge, some form tight binaries, a < 1 AU

Protostars with masses 5 – 15 M reach radii ~ 0.1 AU due to deuterium shell burning

Stars migrate through disk to within 10 AU of primary

Some likely merge, some form tight binaries, a < 1 AU

Protostars with masses 5 – 15 M reach radii ~ 0.1 AU due to deuterium shell burning Radius vs. mass for protostars as a

function of accretion rateRadius vs. mass for protostars as afunction of accretion rate

Mass Transfer and “Twins”Mass Transfer and “Twins” Large radii likely

produce RLOF, mass transfer

Transfer is from more to less massive transfer unstable

System becomes isentropic contact binary, stabilizes at q 1, contracts to MS

Result: massive twin

Large radii likely produce RLOF, mass transfer

Transfer is from more to less massive transfer unstable

System becomes isentropic contact binary, stabilizes at q 1, contracts to MS

Result: massive twin

Minimum semi-major axis for RLOF as a function of accretion rateMinimum semi-major axis for RLOF as a function of accretion rate

WR20aWR20a

Stage 4: Radiation PressureStage 4: Radiation Pressure Massive protostars reach MS in a Kelvin

time:

This is shorter than the formation time accretion is opposed by huge radiation pressure on dust grains

Question: how can accretion continue to produce massive stars?

Massive protostars reach MS in a Kelvin time:

This is shorter than the formation time accretion is opposed by huge radiation pressure on dust grains

Question: how can accretion continue to produce massive stars?

Radiation Pressure in 1D(Larson & Starrfield 1971; Kahn 1974;

Yorke & Krügel 1977; Wolfire & Cassinelli 1987)

Radiation Pressure in 1D(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,

In reality, accretion isn’t spherical. Investigate 3D behavior with Orion.

Simulations of Radiation Pressure (KKM, 2005, IAU 227)

Simulations of Radiation Pressure (KKM, 2005, IAU 227)

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Beaming by Disks and BubblesBeaming by Disks and Bubbles 2D and 3D simulations reveal flashlight effect:

disks and bubbles collimate radiation At higher masses, radiation RT instability possible

2D and 3D simulations reveal flashlight effect: disks and bubbles collimate radiation

At higher masses, radiation RT instability possible

Collimation allows accretion to high masses!

Collimation allows accretion to high masses!

Density and radiation flux vectors from simulationDensity and radiation flux vectors from simulation

Beaming by Outflows(Krumholz, McKee, & Klein, ApJL, 2005, 618, 33)

Beaming by Outflows(Krumholz, McKee, & Klein, ApJL, 2005, 618, 33)

Massive stars outflows launched inside dust destruction zone

Result: outflow cavities optically thin, radiation can leak out of them

Simulate with MC radiative transfer code

Find factor of ~10 reduction in radiation pressure force on accreting gas

Massive stars outflows launched inside dust destruction zone

Result: outflow cavities optically thin, radiation can leak out of them

Simulate with MC radiative transfer code

Find factor of ~10 reduction in radiation pressure force on accreting gas

Gas temperature distributions with a 50 M star, 50 M envelopeGas temperature distributions with a 50 M star, 50 M envelopeRadiation and gravitational forces with and without outflowRadiation and gravitational forces with and without outflow

Stage 5: Competitive AccretionStage 5: Competitive Accretion Once initial core is accreted, could a star

gain additional mass from gas that wasn’t bound to it originally via BH accretion?

If so, no core to star mapping exists

Once initial core is accreted, could a star gain additional mass from gas that wasn’t bound to it originally via BH accretion?

If so, no core to star mapping exists

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

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

Accretion in a Turbulent Medium

(Krumholz, McKee, & Klein, 2006, ApJ, 638, 369; 2005, Nature, 438, 332)

Accretion in a Turbulent Medium

(Krumholz, McKee, & Klein, 2006, ApJ, 638, 369; 2005, Nature, 438, 332)

Result: virialized turbulence negligible accretion Implication: CA significant only if turbulence decays,

cluster collapses to stars in ~1 crossing time

Result: virialized turbulence negligible accretion Implication: CA significant only if turbulence decays,

cluster collapses to stars in ~1 crossing time

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Global Collapse andthe Star Formation Rate

(Krumholz & Tan, 2007, ApJ, 654, 304)

Global Collapse andthe Star Formation Rate

(Krumholz & Tan, 2007, ApJ, 654, 304)

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

Global collapse gives

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

Global collapse givesRatio of free-fall time to depletion time vs. density in observed systems (red) and simulations where CA occurs (black)

Ratio of free-fall time to depletion time vs. density in observed systems (red) and simulations where CA occurs (black)

Observed SFRs much too low for CA to occur!Observed SFRs much too low for CA to occur!

SummarySummary Massive stars form from massive cores

Massive cores fragment only weakly. MC produce massive, unstable disks. Close massive binaries likely experience

mass transfer, which explains massive twins. Radiation pressure does not halt accretion. CA is not significant in typical clumps.

Mass and spatial distributions of massive stars are inherited from massive cores

However, every new bit of physics added has revealed something unexpected…

Massive stars form from massive cores Massive cores fragment only weakly. MC produce massive, unstable disks. Close massive binaries likely experience

mass transfer, which explains massive twins. Radiation pressure does not halt accretion. CA is not significant in typical clumps.

Mass and spatial distributions of massive stars are inherited from massive cores

However, 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…