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) Hubble Fellows Symposium April 4, 2007

Talk Outline What are massive cores? From core to star Final summary Fragmentation Disk Formation and Evolution Binary formation Radiation pressure and feedback Final summary

Sites of Massive Star Formation (Plume et al. 1997; Shirley et al 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 gas clumps seen in mm continuum or lines, or in IR absorption (IRDCs) Typical properties: M ~ 103 - 104 M R ~ 1 pc  ~ 1 g cm–2  ~ few km s-1 Properties very similar to young rich clusters Appear virialized pc pc Spitzer/IRAC (left) and Spitzer/MIPS (right), Rathbone et al. (2005)

Massive Cores in Clumps Largest cores in clumps: M ~ 100 M, R ~ 0.1 pc, centrally condensed Question: are these the progenitors of massive stars? Cores in IRDC 18454-0158, MSX 8 m (grayscale), 1.2 mm IRAM 30m (contours), Sridharan et al. (2005) Core in IRDC 18223-3, Spitzer/IRAC (color) and PdBI 93 GHz continuum (contours), Beuther et al. (2005, 2007)

The Core Mass Function (Motte, Andre, & Neri 1998, Johnstone et al The Core Mass Function (Motte, Andre, & Neri 1998, Johnstone et al. 2001, Reid & Wilson 2005, 2006, Lombardi et al. 2006) The core MF is similar to the stellar IMF, but shifted to higher masses a factor of 2 – 4 Correspondence suggests a 1 to 1 mapping from core  star with roughly constant efficiency Caveat: blending in distant, massive regions Core mass function in Pipe Nebula (red) vs. stellar IMF (gray) (Alves, Lombardi, & Lada 2007)

Massive Star Clustering Fraction of stars vs. radius for stars of different masses in the ONC (Hillenbrand & Hartmann 1998) < 5 M Most (all?) massive stars are born in clusters Massive stars in young clusters are strongly mass-segregated, but lower mass stars are not (Hillenbrand & Hartmann 1998, Huff & Stahler 2006)

The Clustering of Cores (Elmegreen et al. 2001, Stanke et al. 2006) Cores in clumps are also mass segregated Mass function below ~ 5 M is the same everywhere; more massive cores only found near center Similar to stellar mass segregation, also suggests core  star mapping Core mass function for inner (red) and outer (blue) parts of  Oph, Stanke et al. (2006)

From Core to Star

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 m*=0.05 M m*=0.8 M Temperature vs. radius in a massive core before star formation (red), and once protostar begins accreting (blue)

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 2007a, ApJ, 656, 959, and KKM, 2007b, ApJS, submitted, astro-ph/0611003) 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

Massive Cores Fragment Weakly With RT: 6 fragments, most mass accretes onto single largest star through a massive disk Without RT: 23 fragments, stars gain mass by collisions, disk less massive, disrupted by collisions and N-body interactions Conclusion: radiation inhibits fragmentation 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 ~ cs3 / 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 2007a) 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 radially isothermal Disks reach Q ~ 1, unstable to fragment formation Surface density (upper) and Toomre Q (lower); striping is from projection

Observing Massive Disks Integrated TB in simulated 1000 s / pointing ALMA observation of disk at 0.5 kpc in CH3CN 220.7472 GHz (KKM 2007c, 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: 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)

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

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 have outflows launched from dust destruction zone Outflow velocity ~103 km s–1  no time for grains to re-grow until gas is far from star Result: outflow cavities optically thin, radiation can leak out of them Simulate with MC radiative transfer code Gas temperature distributions with a 50 M star, 50 M envelope

Outflows Help Accretion Simulations show that this effect can produce an order-of-magnitude reduction in radiation force This can move the system from radiation being stronger than gravity to weaker than gravity Radiation and gravity forces vs. radius for a 50 M star and a typical outflow cavity geometry

Summary Massive stars form from massive cores Massive cores fragment only weakly They produce disks that are massive and unstable. This is probably observable. Close massive binaries likely experience mass transfer, which explains massive twins Radiation pressure does not halt accretion Mass and spatial distributions of massive stars are inherited from massive cores However, every new bit of physics added has revealed something unexpected…

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