From Massive Cores to Massive Stars Mark Krumholz Princeton University Collaborators: Richard Klein, Christopher McKee (UC Berkeley) Kaitlin Kratter, Christopher Matzner (U. Toronto) Jonathan Tan (University of Florida) Todd Thompson (Princeton University) Mark Krumholz Princeton University Collaborators: Richard Klein, Christopher McKee (UC Berkeley) Kaitlin Kratter, Christopher Matzner (U. Toronto) Jonathan Tan (University of Florida) Todd Thompson (Princeton University) From Stars to Planets University of Florida April 11, 2007 From Stars to Planets University of Florida April 11, 2007

Talk 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 summary 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 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)

From Core to Star

Stage 1: Initial Fragmentation (Krumholz, 2006, ApJL, 641, 45) Massive cores are much larger than M J (~ 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 M J (~ 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) m * =0.05 M  m * =0.8 M 

Radiation-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/ ) 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/ ) Mass conservation Momentum conservation Gas energy conservation Rad. energy conservation Self-gravity Mass conservation Momentum conservation Gas energy conservation Rad. energy conservation Self-gravity

Simulation 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

Massive 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 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) 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 ~ c s 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 ~ c s 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) Disks reach M disk ~ 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 M disk ~ 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 projection

Observing Massive Disks Integrated T B in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH 3 CN GHz (KKM 2007, ApJ, submitted) T B as a function of velocity in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH 3 CN GHz (KKM 2007, ApJ, submitted)

Stage 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: M 1 = 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)

Close Binaries (Krumholz & Thompson, 2007, ApJ, in press, astro-ph/ ) 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 rate Radius vs. mass for protostars as a function of accretion rate

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 Minimum semi-major axis for RLOF as a function of accretion rate WR20a

Stage 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?

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

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

Beaming by Disks and Bubbles 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! Density and radiation flux vectors from simulation

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 Gas temperature distributions with a 50 M  star, 50 M  envelope Radiation and gravitational forces with and without outflow

Stage 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)

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

Global Collapse and the 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 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!

Summary 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 B Give up and appeal to intelligent design…