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Theory of Massive Star Formation

Theory of Massive Star Formation. Mark Krumholz UC Santa Cruz Collaborators: Richard Klein, Chris McKee, Andrew Myers (UC Berkeley) Stella Offner, Kaitlin Kratter (CfA) Chris Matzner (Toronto) Mike Fall (STScI) Andrew Cunningham (LLNL). Great Barriers to High Mass Star Formation

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Theory of Massive Star Formation

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  1. Theory of Massive Star Formation Mark Krumholz UC Santa Cruz Collaborators: Richard Klein, Chris McKee, Andrew Myers (UC Berkeley) Stella Offner, Kaitlin Kratter (CfA) Chris Matzner (Toronto) Mike Fall (STScI) Andrew Cunningham (LLNL) Great Barriers to High Mass Star Formation Townsville, Australia September 17, 2010

  2. Talk Outline • Fragmentation and the origin of massive stars • Disks and binaries (deferred to Kaitlin Kratter’s talk) • The radiation pressure (non-) problem (see also talk by Rolf Kuiper) • Star formation efficiency and bound clusters

  3. Fragmentation

  4. The Importance of Fragmentation • Observations hint that in some regions fragmentation stops at masses ~10-50 M (eg. talk by Bontemps) • Implies at least intermediate mass stars sometimes form by direct collapse, albeit in cores that are growing as they collapse • Need to stop fragmentation to make massive stars

  5. Why Non-Isothermality Matters • MJT3/2–1/2, but T ~ constant and  varies hugely  isothermal gas is scale free • All dimensionless numbers invariant under x, Lx–1/2L, Bx1/2B, but Mx–1/2M

  6. Radiation Limits Fragmentation(Krumholz+ 2006, 2007, 2008, 2010; Bate 2009; Offner+ 2009; Urban+ 2010) Radiation No radiation Comparison of otherwise-identical simulations with (top) and without (bottom) radiative transfer (left: Krumholz+ 2007; middle: Bate 2009; right: Urban+ 2010)

  7. What is Required to Halt Fragmentation(Krumholz & McKee 2008) • Halting fragmentation requires that a cloud be heated throughout • This requires a light to mass ratio halt() • Accretion produces a maximum luminosity / unit mass acc(,Mc) • Result: a threshold  for massive SF!

  8. Radiation-Hydro Simulations • To study this effect, do simulations • Use the Orion code adaptive mesh refinement code, including (Krumholz, Klein, & McKee 2007a, 2007b) • Hydrodynamics • Gravity • Radiation (gray FLD) • Radiating sink particles Mass conservation Momentum conservation Gas energy conservation Rad. energy conservation Self-gravity

  9. Simulation of a Massive Core • Column density from simulation of a core with M = 100 M,  = 0.7 g cm–2, R = 0.1 pc,  = 1.7 km s–1 • Left: whole core; right: central (2000 AU)2

  10. 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 • Conclusion: radiation inhibits fragmentation Column density with (upper) and without (lower) RT, for identical times and initial conditions

  11. Simulation with Varying (Krumholz, Cunningham, Klein, & McKee, 2010) Simulate 100 M clouds with identical initial structure, differing surface density, for same # of dynamical times. Large-scale structure is homologous, no variation with surface density. On small scales clouds are highly non-homologous. Low column density clouds fragment much more.

  12. MJ = 10 M MJ = 10 M MJ = 10 M MJ = 1 M MJ = 1 M MJ = 1 M MJ = 0.1 M MJ = 0.1 M MJ = 0.1 M Gas Temperature Evolution t = 0.1 tff t = 0.6 tff Gas temperatures in the three runs are very different even at time when total stellar mass is < 0.5 M This effect is self-reinforcing: higher T produces more massive stars, leading to higher T, etc… NB: this effect does not depend on raising the thermal Jeans mass to ~50 M!

  13. Fragmentation History Total stellar mass unaffected by radiation, but distribution of stellar masses is

  14. A Hint: Threshold May be Different as a Function of Z(Myers+ 2010, in preparation) Z = 0.2 Z Z = 0.05 Z

  15. Radiation Pressure

  16. Radiation Pressure and Accretion(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

  17. Simulations of Radiation Pressure(Krumholz, Klein, McKee, Offner, & Cunningham 2009) System mass at end of run: 70 M!

  18. Radiation Beaming • RT instability allows accretion! • Radiation leaves through transparent chimneys, mass accretes through opaque fingers

  19. Including Outflows(Krumholz+ 2005; Cunningham+ 2010, in preparation)

  20. Clusters and Feedback

  21. Unbound Clusters Cluster age distribution in the LMC (Chandar+ 2010)

  22. Cluster Formation Efficiency • Turbulence, B fields, accretion slow star formation, but given enough time the SF efficiency always goes to ~1 • … but most star formation does not produce bound clusters • Thus either (1) most clouds are unbound or (2) something shuts off star formation and removes most of the gas mass, allowing the stars to escape

  23. Feedback in High , Proto-Cluster Gas Clouds • For massive proto-clusters, ionized gas pressure is ineffective • Ex.: R136, M = 5 x 104 M, R = 1 pc, vesc = 20 km s–1 2 cII • SNe are too late • For R136, tcr ~ 50 kyr • Only possibilities: hot gas from winds, radiation pressure 30 Doradus HII region in IR (red), H (green), x-ray (blue) (Townsley+ 2006)

  24. When is Radiation Pressure Important in HII Regions?(Krumholz & Matzner 2009) • RP force >> gas pressure force when • RP-driven expansion stalls at radius • Ex. R136: n2 ~ 103, S49 ~ 102 ~ 100, rst ~ 1 pc RP strong RP weak Importance of RP in clusters in M82 (blue), Antennae (red), Orion (brown), Arches (green)

  25. Why Does RP Matter for Clusters?(Murray+ 2010; Fall+ 2010) • In a massive core, radiation momentum not significant, and RT prevents energy driven flow • Protocluster clump more loosely bound – momentum alone able to unbind it Simulation of radiation-driven shell (Murray+ 2010)

  26. Star Formation Efficiency from Radiation Pressure(Fall, Krumholz, & Matzner 2010) • Rough SFE estimate: as SF proceeds and SFE rises, n2 drops, rst rises • When rst > Rcl, mass is ejected • Result: • NB: depends on M only through  SFE vs. , computed using RP feedback

  27. Implications for Cluster MF(Fall, Krumholz, & Matzner 2010) • Protoclusters have  ~ 0.2 - 1 g cm–2 independent of M  SFE independent of M • For observed , SFE ~ 0.2 - 0.4  most but not all clusters dissolve at all M • Cluster MF ~ same as cloud MF, in agree-ment with observations Cluster-forming clumps: CS emission (Shirley+ 2003, black), dust (Faundez+ 2004, blue), C17O (Fontani+ 2005, red)

  28. Summary • Non-isothermal fragmentation due to radiative feedback explains when / where massive stars form • No radiation pressure problem for individual stars • On cluster scales, radiation pressure produces SFE ~ 0.3 independent of mass; explains observed cluster mass function

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