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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
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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)
QuickTime™ and aYUV420 codec decompressor
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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…