1. High Mass Star Formation by Gravitational Collapse of Massive Cores Mark Krumholz Princeton University Collaborators: Richard Klein, Christopher McKee, Stella Offner (UC Berkeley), and Jonathan Tan (U. Florida) Mark Krumholz Princeton University Collaborators: Richard Klein, Christopher McKee, Stella Offner (UC Berkeley), and Jonathan Tan (U. Florida) Image: O’Dell & Wong (1995)

2. Talk 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

3. 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 Spitzer/IRAC (left) and Spitzer/MIPS (right), Rathbone et al. (2005)

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

5. 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 ~10 5 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 ~10 5 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)

6. 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 for inner (red) and outer (blue) parts of  Oph, Stanke et al. (2006)

7. Assembling a Massive Star

8. Problem 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?

9. 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 m * =0.8 M  m * =0.05 M  Barotropic EOS, no RT RT calculation

10. Radiation-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

11. Massive Cores Fragment Weakly Radiation critical even at early times due to large L acc 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 Ratio of temperature computed with radiation to temperature computed with barotropic approximation when m * ≈ 4 M 

12. 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.

13. 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) 1 M 

14. The Competitive Accretion Rate Stars can accrete by capturing unbound gas (Bondi-Hoyle) or capturing other cores Analytically compute f m 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 f m 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 f m 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 f m in terms of star mass M *, clump mass M, virial ratio  vir = KE / PE

15. Turbulent BH Accretion (Krumholz, McKee, & Klein, 2005, 618, 757 and 2006, ApJ, 638, 369) For f m due to gas accretion, use simulations to develop model for Bondi-Hoyle accretion in a turbulent medium

16. The 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

17. Is There Competitive Accretion? (Krumholz, McKee, & Klein, 2005, Nature, 438, 332) Combining f m 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 f m 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

18. 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 ~ t cr (~ 2 t ff ) if global collapse occurs, but they are usually 3 – 5 t cr (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 ~ t cr (~ 2 t ff ) if global collapse occurs, but they are usually 3 – 5 t cr (Tan, Krumholz, & McKee, 2006, ApJL, 641, 121) t cr ≈ 0.6 Myr Stellar age distribution in IC 348, Palla & Stahler (2000) Inconsistent with global collapse, CA

19. Global Collapse and the Star Formation Rate (Krumholz & Tan, 2006, ApJ, submitted) If clumps collapse, mass forms stars in ~t cr. 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 Inconsistent with GC, CA

20. Simulations with Feedback 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)

21. 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

22. 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,  Massive stars approach their Eddington limits while forming

23. 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 ! !

24. Radiation-Hydro Simulations

25. 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 Collimation allows accretion to high masses! Density and radiation flux vectors from simulation, Krumholz, Klein, & McKee 2005

26. 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, H 2 0 Masers, VLA, Torrelles et al. 2001

27. 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 – 10 3 L/c  outflows probably hydro- magnetic Observations show massive stellar outflows are well- collimated Force required to drive outflows is ~10 – 10 3 L/c  outflows probably hydro- magnetic IRAS 19217+1631, SMA, Beuther et al. 2004

28. 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

29. Problems for the Future

30. 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

31. Better 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

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

33. Summary 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…

34. Plan B Give up and appeal to intelligent design…