THE FORMATION OF MASSIVE STARS. η Carina (NASA, ESA, N. Smith)

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1 THE FORMATION OF MASSIVE STARS η Carina (NASA, ESA, N. Smith)

2 THE FORMATION OF MASSIVE STARS Christopher F. McKee Institute for Astronomy November 2, 2011 with Andrew Cunningham Edith Falgarone Richard Klein Mark Krumholz Andrew Myers Stella Offner Jonathan Tan

3 MASSIVE STARS: Create most of the heavy elements

4 Cas A Supernova Remnant NASA/CXC/MIT/Umass Amherst/D. Stage ea

5 MASSIVE STARS: Create most of the heavy elements

6 MASSIVE STARS: Create most of the heavy elements Energize the interstellar medium (ISM) UV emission heats via photoelectric effect (~10 2 K) Ionizing luminosity creates ionized gas (~10 4 K) Stellar winds and supernovae create hot gas (~10 6 K)

7 T. Megeath

8 MASSIVE STARS: Create most of the heavy elements Energize the interstellar medium (ISM) UV emission heats via photoelectric effect (~10 2 K) Ionizing luminosity creates ionized gas (~10 4 K) Stellar winds and supernovae create hot gas (~10 6 K) Govern the evolution of galaxies -Radiation pressure drives outflows

9 M82 Red: IR (Spitzer) Orange: HII (Hubble) Blue: X-rays (Chandra)

10 MASSIVE STARS: Create most of the heavy elements Energize the interstellar medium (ISM) UV emission heats via photoelectric effect (~10 2 K) Ionizing luminosity creates ionized gas (~10 4 K) Stellar winds and supernovae create hot gas (~10 6 K) Regulate star formation Govern the evolution of galaxies -Radiation pressure drives outflows May have re-ionized the universe

11

12 WHY DO WE KNOW SO LITTLE ABOUT MASSIVE STAR FORMATION?

13 WHY DO WE KNOW SO LITTLE ABOUT MASSIVE STAR FORMATION? OBSERVATION: Highly obscured (A V ~ ) > ~ Far away (D 2 kpc) Crowded (10 4 stars pc -3 at the center of Orion)

14 WHY DO WE KNOW SO LITTLE ABOUT MASSIVE STAR FORMATION? OBSERVATION: Highly obscured (A V ~ ) > ~ Far away (D 2 kpc) Crowded (10 4 stars pc -3 at the center of Orion) THEORY: Wide range of length and time scales (like low-mass star formation) Radiation dynamically important (unlike low-mass star formation)

15 OUTLINE

16 *Basics OUTLINE -Part I: Star Formation in Isothermal Gas: Everything you ever wanted to know about star formation in three slides -Part II: Star Formation in Turbulent Gas

17 *Basics OUTLINE -Part I: Star Formation in Isothermal Gas: Everything you ever wanted to know about star formation in three slides -Part II: Star Formation in Turbulent Gas * Theoretical models of massive star formation

18 *Basics OUTLINE -Part I: Star Formation in Isothermal Gas: Everything you ever wanted to know about star formation in three slides -Part II: Star Formation in Turbulent Gas * Theoretical models of massive star formation * Challenges in massive star formation: -Radiation pressure -Ionizing radiation -Constancy of the IMF

19 *Basics OUTLINE -Part I: Star Formation in Isothermal Gas: Everything you ever wanted to know about star formation in three slides -Part II: Star Formation in Turbulent Gas * Theoretical models of massive star formation * Challenges in massive star formation: -Radiation pressure -Ionizing radiation -Constancy of the IMF * Observational predictions

20 Hierarchical Structure of Molecular Clouds Terminology: Clump -> star cluster (~ 10 3 M sun ) GMC (~ M sun ) Core -> star/binary (~ 1-10 M sun ) Structure self-similar from stellar mass to GMC mass

21 CHARACTERISTICS OF REGIONS OF HIGH-MASS STAR FORMATION High-mass star-forming clumps (Plume et al. 1997; Shirley et al. 2003) Sound speed c s ~ 0.3 km s -1 (Temperature ~ 30 K) Supersonically turbulent: σ ~ 2.5 km s -1 Radius ~ 0.5 pc Mass ~ 4000 M sun

22 CHARACTERISTICS OF REGIONS OF HIGH-MASS STAR FORMATION High-mass star-forming clumps (Plume et al. 1997; Shirley et al. 2003) Sound speed c s ~ 0.3 km s -1 (Temperature ~ 30 K) Supersonically turbulent: σ ~ 2.5 km s -1 Radius ~ 0.5 pc Mass ~ 4000 M sun Density ρ ~ g cm -3, n H ~ cm -3 Surface density Σ ~ 1 g cm -2 (A V ~200)

23 CHARACTERISTICS OF REGIONS OF HIGH-MASS STAR FORMATION High-mass star-forming clumps (Plume et al. 1997; Shirley et al. 2003) Sound speed c s ~ 0.3 km s -1 (Temperature ~ 30 K) Supersonically turbulent: σ ~ 2.5 km s -1 Radius ~ 0.5 pc Mass ~ 4000 M sun Density ρ ~ g cm -3, n H ~ cm -3 Surface density Σ ~ 1 g cm -2 (A V ~200) Compare typical Giant Molecular Cloud: Σ ~ 0.03 g cm -2 n H ~ 100 cm -3

24 Massive Cores inside Star-forming Clumps Largest cores in clumps: M ~ 100 M, R ~ 0.1 pc Some are starless now, but they are expected to form massive stars Core in IRDC , Spitzer/IRAC (color) and PdBI 93 GHz continuum (contours), Beuther et al. (2005, 2007)

25 Massive Cores inside Star-forming Clumps Largest cores in clumps: M ~ 100 M, R ~ 0.1 pc Some are starless now, but they are expected to form massive stars Cores have power-law density profiles, index k ρ 1.5 Core density profile in 3 wavelengths, Beuther et al. (2007) Core in IRDC , Spitzer/IRAC (color) and PdBI 93 GHz continuum (contours), Beuther et al. (2005, 2007)

26 BASICS: PART I Star Formation in Isothermal Gas Pioneers: Jeans, Bonnor, Ebert, Larson, Shu

27 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 1 Characteristic timescale set by self-gravity: d 2 R dt 2 ~ R t 2 ~ GM R 2 t 2 R3 GM ~ 1 Gρ

28 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 1 Characteristic timescale set by self-gravity: d 2 R dt 2 ~ R t 2 ~ GM R 2 t 2 R3 GM ~ 1 Gρ Free-fall time: t ff = (3π/32Gρ) 1/2 = 1.4 x 10 5 (10 5 cm -3 /n) 1/2 yr

29 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 2 Characteristic mass: Kinetic energy/mass ~ gravitational energy/mass c s 2 P/ρ GM/R M ~ Rc s 2/G

30 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 2 Characteristic mass: Kinetic energy/mass ~ gravitational energy/mass c s 2 P/ρ GM/R M ~ Rc s 2/G Radius: R ~ c s t ff ~ c s /(Gρ) 1/2

31 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 2 Characteristic mass: Kinetic energy/mass ~ gravitational energy/mass c s 2 P/ρ GM/R M ~ Rc s 2/G Radius: R ~ c s t ff ~ c s /(Gρ) 1/2 Mass ~ Rc s 2/G ~ c s 3t ff /G ~ c s 3/(G 3 ρ) 1/2

32 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 2 Characteristic mass: Kinetic energy/mass ~ gravitational energy/mass c s 2 P/ρ GM/R M ~ Rc s 2/G Radius: R ~ c s t ff ~ c s /(Gρ) 1/2 Mass ~ Rc s 2/G ~ c s 3t ff /G ~ c s 3/(G 3 ρ) 1/2 Bonnor-Ebert mass = maximum mass of stable isothermal sphere: M BE = 1.18 c thermal 3 /(G 3 ρ) 1/2 Gravity not important for masses M << M BE

33 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 3 Characteristic accretion rate: m * ~ mbe / t ff ~ c s 3/(G 3 ρ) 1/2 (Gρ) 1/2 ~ c s 3/G

34 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 3 Characteristic accretion rate: m * ~ mbe / t ff ~ c s 3/(G 3 ρ) 1/2 (Gρ) 1/2 ~ c s 3/G For a singular isothermal sphere (Shu 1977): m * = c 3 s / G = 1.5 x 10-6 (T/ 10 K) 3/2 M sun yr -1

35 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 3 Characteristic accretion rate: m * ~ mbe / t ff ~ c s 3/(G 3 ρ) 1/2 (Gρ) 1/2 ~ c s 3/G For a singular isothermal sphere (Shu 1977): m * = c 3 s / G = 1.5 x 10-6 (T/ 10 K) 3/2 M sun yr -1 An isothermal gas at 10 K takes 6.5 x 10 5 yr to form a 1 M sun star 6.5 x 10 7 yr to form a 100 M sun star >> age of star (~ 3 Myr)

36 EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 3 Characteristic accretion rate: m * ~ mbe / t ff ~ c s 3/(G 3 ρ) 1/2 (Gρ) 1/2 ~ c s 3/G For a singular isothermal sphere (Shu 1977): m * = c 3 s / G = 1.5 x 10-6 (T/ 10 K) 3/2 M sun yr -1 An isothermal gas at 10 K takes 6.5 x 10 5 yr to form a 1 M sun star 6.5 x 10 7 yr to form a 100 M sun star NEED TO GENERALIZE THEORY >> age of star (~ 3 Myr)

37 BASICS: PART II Star Formation in Turbulent Gas Pioneers in observation: Larson, Falgarone, Solomon, Myers, Goodman Pioneers in theory: Gammie Ostriker & Stone, MacLow, Padoan & Nordlund, Vazquez-Semadeni

38 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale:

39 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale: Supersonic turbulence:

40 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale: Supersonic turbulence: Linewidth-size relations

41 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale: Supersonic turbulence: Linewidth-size relations Larson (1981) discovered the linewidth-size relation in the ISM

42 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale: Supersonic turbulence: Linewidth-size relations Larson (1981) discovered the linewidth-size relation in the ISM What drives the turbulence in molecular gas?

43 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale: Supersonic turbulence: Linewidth-size relations Larson (1981) discovered the linewidth-size relation in the ISM What drives the turbulence in molecular gas? Supernovae (Mac Low & Klessen 2004)

44 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale: Supersonic turbulence: Linewidth-size relations Larson (1981) discovered the linewidth-size relation in the ISM What drives the turbulence in molecular gas? Supernovae (Mac Low & Klessen 2004) Star formation (Norman & Silk 1980; McKee 1989; Matzner 2002; Nakamura & Li 2005)

45 LINEWIDTH-SIZE RELATION IN TURBULENT GAS Incompressible turbulence (Kolmogorov 1941) Energy cascade from driving scale to dissipation scale: Supersonic turbulence: Linewidth-size relations Larson (1981) discovered the linewidth-size relation in the ISM What drives the turbulence in molecular gas? Supernovae (Mac Low & Klessen 2004) Star formation (Norman & Silk 1980; McKee 1989; Matzner 2002; Nakamura & Li 2005) Self-gravity (Field et al. 2008), gravitational accretion (Klessen & Hennebelle 2010; Goldbaum, Krumholz, Matzner, & McKee 2011)

46 Turbulent Linewidth-Size Relation for Galactic Molecular Gas GMCs (Solomon et al; Dame & Thaddeus; May et al) High-latitude clouds (Falgarone, Perault et al) (Falgarone & McKee 2011?)

47 Turbulent Linewidth-Size Relation for Galactic Molecular Gas Δv NT = (1.4 ± 0.5 dex) L pc 1/2 km/s (Falgarone & McKee 2011?)

48 Linewidth-Size Relation including High-Mass Star-Forming Regions Infra-Red Dark Clouds (IRDCs) Rathborne et al (2007) Battersby et al (2010) High-mass star-forming regions lie above the turbulent linewidth-size relation

49 Turbulent linewidth-size relation for gravitationally unbound gas:

50 Turbulent linewidth-size relation for gravitationally unbound gas: Virialized linewidth-size relation for gravitationally bound gas:

51 Turbulent linewidth-size relation for gravitationally unbound gas: Virialized linewidth-size relation for gravitationally bound gas: for bound clouds with α vir ~ 1 (Heyer ea 2009)

52 Turbulent linewidth-size relation for gravitationally unbound gas: Virialized linewidth-size relation for gravitationally bound gas: Converting to FWHM, Δv=2.355 σ : for bound clouds with α vir ~ 1 (Heyer ea 2009)

53 Generalized Linewidth-Size Relation for Bound and Unbound Gas Turbulent linewidth-size relation (unbound) GMCs Virialized linewidth-size relation (bound) 2 (Falgarone & McKee 2011?)

54 Generalized Linewidth-Size Relation for Bound and Unbound Gas High latitude molecular clouds GMCs High-mass starforming regions 2 (Falgarone & McKee 2011)

55 Generalization of Theory of Low-Mass Star Formation in Isothermal Cores to High-Mass Star Formation in Turbulent Cores (McKee & Tan 2002, 2003)

56 Generalization of Theory of Low-Mass Star Formation in Isothermal Cores to High-Mass Star Formation in Turbulent Cores (McKee & Tan 2002, 2003) Accretion rate m ~ σ 3 * /G (formation time ~ free-fall time) However, for massive stars, σ is highly supersonic; it depends on scale and must be determined self-consistently.

57 Generalization of Theory of Low-Mass Star Formation in Isothermal Cores to High-Mass Star Formation in Turbulent Cores Accretion rate m ~ σ 3 * /G (formation time ~ free-fall time) However, for massive stars, σ is highly supersonic; it depends on scale and must be determined self-consistently. Virial equilibrium σ 2 ~ GM/R (McKee & Tan 2002, 2003)

58 Generalization of Theory of Low-Mass Star Formation in Isothermal Cores to High-Mass Star Formation in Turbulent Cores Accretion rate m ~ σ 3 * /G (formation time ~ free-fall time) However, for massive stars, σ is highly supersonic; it depends on scale and must be determined self-consistently. Virial equilibrium σ 2 ~ GM/R (McKee & Tan 2002, 2003) Surface density Σ = M/πR 2 m * G 1/2 (M Σ) 3/4 Accretion rate determined by core mass M and surface density Σ: High Σ high accretion rate

59 Generalization of Theory of Low-Mass Star Formation in Isothermal Cores to High-Mass Star Formation in Turbulent Cores Accretion rate m ~ σ 3 * /G (formation time ~ free-fall time) However, for massive stars, σ is highly supersonic; it depends on scale and must be determined self-consistently. Virial equilibrium σ 2 ~ GM/R (McKee & Tan 2002, 2003) Surface density Σ = M/πR 2 m * G 1/2 (M Σ) 3/4 Accretion rate determined by core mass M and surface density Σ: High Σ high accretion rate Turbulent cores are scale-free model as singular polytropic spheres (McLaughlin & Pudritz 1996, 1997)

60 Generalization of Theory of Low-Mass Star Formation in Isothermal Cores to High-Mass Star Formation in Turbulent Cores Accretion rate m ~ σ 3 * /G (formation time ~ free-fall time) However, for massive stars, σ is highly supersonic; it depends on scale and must be determined self-consistently. Virial equilibrium σ 2 ~ GM/R Surface density Σ = M/πR 2 m * G 1/2 (M Σ) 3/4 Accretion rate determined by core mass M and surface density Σ: High Σ high accretion rate Numerical evaluation massive stars form in about 10 5 yr: t *f = 1.3 x 10 5 (m *f /30 M sun ) 1/4 Σ 3/4 yr (McKee & Tan 2002, 2003) Turbulent cores are scale-free model as singular polytropic spheres (McLaughlin & Pudritz 1996, 1997)

61 THEORIES OF MASSIVE STAR FORMATION * Gravitational collapse of bound protostellar cores -Turbulent core model (McKee & Tan 2002, 2003) Extension of inside-out collapse model (Shu 1977) to massive stars -Direct numerical simulation (Krumholz et al. 2009; Cunningham et al. 2011)

62 THEORIES OF MASSIVE STAR FORMATION * Gravitational collapse of bound protostellar cores -Turbulent core model (McKee & Tan 2002, 2003) Extension of inside-out collapse model (Shu 1977) to massive stars -Direct numerical simulation (Krumholz et al. 2009; Cunningham et al. 2011) * Bondi-Hoyle accretion by many protostars from a common reservoir -Competitive accretion (Zinnecker 1982; Bonnell et al 1997) -Problems: Fails in a turbulent medium (Krumholz, McKee & Klein 2005) or if radiation pressure becomes important (Edgar & Clarke 2004) -Variant: Fragmentation-induced starvation (Peters et al. 2010)

63 THEORIES OF MASSIVE STAR FORMATION * Gravitational collapse of bound protostellar cores -Turbulent core model (McKee & Tan 2002, 2003) Extension of inside-out collapse model (Shu 1977) to massive stars -Direct numerical simulation (Krumholz et al. 2009; Cunningham et al. 2011) * Bondi-Hoyle accretion by many protostars from a common reservoir -Competitive accretion (Zinnecker 1982; Bonnell et al 1997) -Problems: Fails in a turbulent medium (Krumholz, McKee & Klein 2005) or if radiation pressure becomes important (Edgar & Clarke 2004) -Variant: Fragmentation-induced starvation (Peters et al. 2010) * Stellar coalescence (Bonnell, Bate & Zinnecker 1998) -Massive stars form as a result of physical collisions of low-mass stars, naturally overcoming radiation pressure problem -Requires stellar densities much higher than observed

64 CHALLENGES IN MASSIVE STAR FORMATION Larson & Starrfield (1971)

65 CHALLENGES IN MASSIVE STAR FORMATION Larson & Starrfield (1971) * Formation time exceeds stellar lifetime for m * > 60 M sun Possible solution: increase T higher ρ, shorter free-fall time

66 CHALLENGES IN MASSIVE STAR FORMATION Larson & Starrfield (1971) * Formation time exceeds stellar lifetime for m * > 60 M sun Possible solution: increase T higher ρ, shorter free-fall time * Radiation pressure on dust (a fundamental problem)

67 CHALLENGES IN MASSIVE STAR FORMATION Larson & Starrfield (1971) * Formation time exceeds stellar lifetime for m * > 60 M sun Possible solution: increase T higher ρ, shorter free-fall time * Radiation pressure on dust (a fundamental problem) (1) UV radiation on inner dust shell > gravity for m * > 20 M sun Possible solution: mass build-up in shell, instability

68 CHALLENGES IN MASSIVE STAR FORMATION Larson & Starrfield (1971) * Formation time exceeds stellar lifetime for m * > 60 M sun Possible solution: increase T higher ρ, shorter free-fall time * Radiation pressure on dust (a fundamental problem) (1) UV radiation on inner dust shell > gravity for m * > 20 M sun Possible solution: mass build-up in shell, instability (2) IR radiation from dust shell > gravity for m * > 25 M sun (Current values for opacity, stellar luminosity m *crit = 17 M sun )

69 CHALLENGES IN MASSIVE STAR FORMATION Larson & Starrfield (1971) * Formation time exceeds stellar lifetime for m * > 60 M sun Possible solution: increase T higher ρ, shorter free-fall time * Radiation pressure on dust (a fundamental problem) (1) UV radiation on inner dust shell > gravity for m * > 20 M sun Possible solution: mass build-up in shell, instability (2) IR radiation from dust shell > gravity for m * > 25 M sun (Current values for opacity, stellar luminosity m *crit = 17 M sun ) * Formation time > time to reach main sequence HII region Ionizes natal cloud for m * > 25 M sun Possible solution: increase cloud density by lower star formation efficiency, higher T, turbulence

70 THE RADIATION PRESSURE PROBLEM 1. UV radiation at the dust destruction front near the protostar Wolfire & Cassinelli (1987) Require momentum in accretion flow at dust destruction radius to exceed momentum in radiation field:

71 THE RADIATION PRESSURE PROBLEM 1. UV radiation at the dust destruction front near the protostar Wolfire & Cassinelli (1987) Satisfied by Turbulent Core model: for 30 M sun star

72 THE RADIATION PRESSURE PROBLEM 2. IR RADIATION ON DUST Eddington luminosity L edd : radiative force balances gravity at L Edd = 4πGMc/(σ/µ) Maximum IR cross section per unit mass for dust in massive protostellar envelopes: σ/µ 8 cm 2 g -1 L Edd = 1600 (M/M sun ) L sun

73 THE RADIATION PRESSURE PROBLEM 2. IR RADIATION ON DUST Eddington luminosity L edd : radiative force balances gravity at L Edd = 4πGMc/(σ/µ) Maximum IR cross section per unit mass for dust in massive protostellar envelopes: σ/µ 8 cm 2 g -1 L Edd = 1600 (M/M sun ) L sun Predict growth of protostar stops for L > L Edd stars cannot grow past ~17 M sun

74 THE RADIATION PRESSURE PROBLEM 2. IR RADIATION ON DUST Eddington luminosity L edd : radiative force balances gravity at L Edd = 4πGMc/(σ/µ) Maximum IR cross section per unit mass for dust in massive protostellar envelopes: σ/µ 8 cm 2 g -1 L Edd = 1600 (M/M sun ) L sun Predict growth of protostar stops for L > L Edd stars cannot grow past ~17 M sun But stars are observed to exist with M > 100 M sun HOW IS THIS POSSIBLE?

75 ADDRESSING THE PROBLEM OF RADIATION PRESSURE Effect of accretion disks Accreting gas has angular momentum and settles into a disk before accreting onto star Previous work has shown that disk shadow reduces the radiative force on the accreting gas (Nakano 1989; Jijina & Adams 1996; Yorke & Sonnhalter 2002)

76 ADDRESSING THE PROBLEM OF RADIATION PRESSURE Effect of accretion disks Accreting gas has angular momentum and settles into a disk before accreting onto star Previous work has shown that disk shadow reduces the radiative force on the accreting gas (Nakano 1989; Jijina & Adams 1996; Yorke & Sonnhalter 2002) 3D simulation of massive star formation with adaptive mesh refinement (AMR): Effect of Rayleigh-Taylor instabilities (Krumholz et al. 2009)

77 ADDRESSING THE PROBLEM OF RADIATION PRESSURE Effect of accretion disks Accreting gas has angular momentum and settles into a disk before accreting onto star Previous work has shown that disk shadow reduces the radiative force on the accreting gas (Nakano 1989; Jijina & Adams 1996; Yorke & Sonnhalter 2002) 3D simulation of massive star formation with adaptive mesh refinement (AMR): Effect of Rayleigh-Taylor instabilities (Krumholz et al. 2009) Effect of bipolar outflows on radiation pressure (Krumholz et al. 2005; Cunningham et al 2011)

78 3D RADIATION HYDRODYNAMIC CALCULATIONS Radiative transfer: gray, mixed frame, flux-limited diffusion t ρ + ρv = 0 t ρv + ρvv = - P - ρ φ + (κ R /c)f (Mass) (Momentum) t ρe + [(ρe+p)v] = - ρv φ - κ P (4πB-cE) - (κ R /c) v F (Energy) 2 φ = 4πGρ (Gravity) t E + F = κ P (4πB-cE) + (κ R /c) v F F 0 = - [cλ(e 0 ) / κ R ] E 0 (Radiative energy) (Flux limit) where e = 0.5 v 2 + u = gas energy density, E = radiation energy density; F 0 and E 0 in comoving frame. Accurate to lowest relevant order in v/c. (Krumholz et al. 2007)

79 3D Simulation of Massive Star Formation M = 100 M sun R initial = 0.1 pc ( n ~ 10 6 ) T initial = 20 K n initial r -3/2 Slow initial rotation No initial turbulence No outflows

80 3D Simulation of Massive Star Formation Density M = 100 M sun R initial = 0.1 pc ( n ~ 10 6 ) T initial = 20 K n initial r -3/2 Slow initial rotation No initial turbulence No outflows L(pc) = =1000 AU (Krumholz, Klein, McKee, Offner & Cunningham 2009)

81 3D Simulation of Massive Star Formation M = 100 M sun R initial = 0.1 pc ( n ~ 10 6 ) T initial = 20 K n initial r -3/2 Slow initial rotation No initial turbulence No outflows Density t (kyr) L(pc) = =1000 AU (Krumholz, Klein, McKee, Offner & Cunningham 2009)

82 3D Simulation of Massive Star Formation M = 100 M sun R initial = 0.1 pc ( n ~ 10 6 ) T initial = 20 K n initial r -3/2 Slow initial rotation No initial turbulence No outflows Plane of plots includes rotation axis Density range: g cm -3 Density t (kyr) L(pc) = =1000 AU (Krumholz, Klein, McKee, Offner & Cunningham 2009)

83 3D Simulation of Massive Star Formation Density t (kyr) M = 100 M sun R initial = 0.1 pc ( n ~ 10 6 ) T initial = 20 K n initial r -3/2 Slow initial rotation No initial turbulence No outflows Plane of plots includes rotation axis Density range: g cm -3 Radiative Rayleigh-Taylor instabilities allow gas to accrete and radiation to escape L(pc) = =1000 AU (Krumholz, Klein, McKee, Offner & Cunningham 2009)

84 Column Density Looking Down the Rotation Axis t (kyr) L(pc) = =1000 AU

85 Column Density Looking Down the Rotation Axis Protostars marked by + in 2 rightmost frames Column density range: g cm -2 t (kyr) L(pc) = =1000 AU

86 Column Density Looking Down the Rotation Axis Protostars marked by + in 2 rightmost frames Column density range: g cm -2 At t = 55 kyr, two massive stars with m * = 39 and 27 M sun ; a third star has m * = 0.15 M sun t (kyr) L(pc) = =1000 AU

87 Column Density Looking Down the Rotation Axis Protostars marked by + in 2 rightmost frames Column density range: g cm -2 At t = 55 kyr, two massive stars with m * = 39 and 27 M sun ; a third star has m * = 0.15 M sun t (kyr) Radiation pressure affects morphology of gas, but not growth of protostars. 55 L(pc) = =1000 AU

88 Collapse of 100 M sun Core L = 0.25 pc L = 2000 AU Column density along axis Density in plane with axis

89 Collapse of 100 M sun Core L = 0.25 pc L = 2000 AU Column density along axis Density in plane with axis

90 Conclusion of simulation with radiation pressure but no outflows: Rayleigh Taylor instability and disk formation allow accretion to overcome radiation pressure

91 PROTOSTELLAR OUTFLOWS REDUCE RADIATION PRESSURE Protostars have powerful, collimated outflows Mass ejection rate ~ ( ) accretion rate Wind velocity ~ Keplerian velocity at stellar surface Outflow is driven by magnetic forces associated with the rotating, magnetized disk

92 Observation of magnetized jet from a high-mass protostar IRAS L=17,000 L sun 6 cm (contours) Synchrotron emission M 10 M sun if dominated by one star 850 µm (gray scale) Thermal emission (Carrasco-Gonzalez et al. 2010)

93 PROTOSTELLAR OUTFLOWS REDUCE RADIATION PRESSURE Protostars have powerful, collimated outflows Mass ejection rate ~ ( ) accretion rate onto protostar Wind velocity ~ Keplerian velocity at stellar surface Outflow is driven by magnetic forces associated with the rotating, magnetized disk Wind cavity channels radiation away from infalling gas, reducing radiation pressure by ~ factor 5 for the calculated case of a 50 M sun star in a 50 M sun envelope (Krumholz, McKee & Klein 2005)

94 3D Monte Carlo radiative transfer in cavities with different shapes

95 Simulations with collimated outflows at t=0.2 t ff M=300 M sun Resolution ~ 30 AU (Cunningham et al. 2011)

96 Simulations with collimated outflows at t=0.2 t ff Clouds with different surface densities: Σ = 1 g cm -2 M=300 M sun Σ = 2 g cm -2 Σ = 2 g cm -2 (no wind) Resolution ~ 30 AU Σ = 10 g cm -2 (Cunningham et al. 2011)

97 Simulations with collimated outflows at t=0.2 t ff Clouds with different surface densities: Σ = 1 g cm -2 M=300 M sun Σ = 2 g cm x x x 0.01 Σ = 2 g cm -2 (no wind) Resolution ~ 30 AU Σ = 10 g cm -2 (Cunningham et al. 2011)

98 Simulations with collimated outflows at t=0.2 t ff Σ = 1 g cm -2 M=300 M sun Σ = 2 g cm -2 Resolution ~ 30 AU Σ = 2 g cm -2 (no wind) Σ = 10 g cm -2 (Cunningham et al. 2011)

99 Simulations with collimated outflows at t = 0.6 t ff Results on outflows: Reduce radiation pressure by allowing escape Σ = 1 g cm -2 Σ = 2 g cm -2 m pri ~20 M sun Σ = 2 g cm (no wind) -2 m pri ~20 M sun Σ = 10 g cm -2 m pri ~35 M sun m pri ~35 M sun

100 Simulations with collimated outflows at t = 0.6 t ff Results on outflows: Reduce radiation pressure by allowing escape Disk gas cooler more fragmentation (lower primary mass with wind) Σ = 1 g cm -2 Σ = 2 g cm -2 Σ = 2 g cm (no wind) -2 m pri ~20 M sun m pri ~20 M sun Σ = 10 g cm -2 m pri ~35 M sun m pri ~35 M sun

101 Simulations with collimated outflows at t = 0.6 t ff Results on outflows: Reduce radiation pressure by allowing escape Disk gas cooler more fragmentation (lower primary mass with wind) Σ = 1 g cm -2 Σ = 2 g cm -2 Σ = 2 g cm (no wind) -2 m pri ~20 M sun m pri ~20 M sun Results for Σ=2 without winds ~ same as Σ=10 with winds (Trapping of radiation increases with Σ) Σ = 10 g cm -2 m pri ~35 M sun m pri ~35 M sun

102 CONCLUSIONS ON RADIATION PRESSURE Outward force due to radiation pressure can exceed the inward force of gravity during the formation of massive stars

103 CONCLUSIONS ON RADIATION PRESSURE Outward force due to radiation pressure can exceed the inward force of gravity during the formation of massive stars Radiative Rayleigh-Taylor instabilities allow continued accretion in absence of outflows; no evidence yet that radiation pressure affects stellar mass

104 CONCLUSIONS ON RADIATION PRESSURE Outward force due to radiation pressure can exceed the inward force of gravity during the formation of massive stars Radiative Rayleigh-Taylor instabilities allow continued accretion in absence of outflows; no evidence yet that radiation pressure affects stellar mass Geometrical effects due to disks and outflow cavities reduce the radiation pressure on the accreting gas; also cool the gas, increasing fragmentation

105 CONCLUSIONS ON RADIATION PRESSURE Outward force due to radiation pressure can exceed the inward force of gravity during the formation of massive stars Radiative Rayleigh-Taylor instabilities allow continued accretion in absence of outflows; no evidence yet that radiation pressure affects stellar mass Geometrical effects due to disks and outflow cavities reduce the radiation pressure on the accreting gas; also cool the gas, increasing fragmentation Currently not known whether the maximum mass of a star is set by processes associated with its formation or with instabilities in the star itself

106 THE IONIZATION PROBLEM Larson & Starrfield (1971) estimated that a 25 M sun star could ionize its natal core, halting accretion

107 THE IONIZATION PROBLEM Larson & Starrfield (1971) estimated that a 25 M sun star could ionize its natal core, halting accretion At high densities, spherical accretion is effective at trapping HII region, allowing accretion to continue (Omukai & Inutsuka 2002; Keto 2002, 2003)

108 THE IONIZATION PROBLEM Larson & Starrfield (1971) estimated that a 25 M sun star could ionize its natal core, halting accretion At high densities, spherical accretion is effective at trapping HII region, allowing accretion to continue (Omukai & Inutsuka 2002; Keto 2002, 2003) But, angular momentum of accreting gas allows HII region to expand along poles, halting accretion outside the accretion disk (Keto 2007; McKee & Tan 2008)

109 Expansion of HII Region in Rotating Accretion Flow First stars: Large accretion rates (> 10-3 M sun yr -1 ) imply breakout of HII region at poles for m * ~ 100 M sun (McKee & Tan 2008) Contemporary stars: Lower accretion rates allow breakout at lower masses (Keto 2007)

110 For the first stars, disk photoevaporation terminates accretion Estimated mass of first stars: M sun (McKee & Tan 2008) (Hollenbach et al 1994) For contemporary stars, dust may absorb ionizing photons, allowing accretion to continue

111 METALLICITY AND THE UNIVERSALITY OF THE IMF Reducing the metallicity reduces the opacity expect reduction in thermal feedback (Myers, Krumholz, Klein & McKee 2011)

112 Vary metallicity by factor 20 at Σ = 2 g cm -2 High Sigma : Σ = 10 g cm -2 at 0.2 solar Most massive star Fraction of mass in most massive star All stars

113 Vary metallicity by factor 20 at Σ = 2 g cm -2 High Sigma : Σ = 10 g cm -2 at 0.2 solar Fragmentation insensitive to metallicity variations Most massive star Fraction of mass in most massive star All stars (Calculations stopped when m * ~10 M sun )

114 METALLICITY AND THE UNIVERSALITY OF THE IMF (Myers, Krumholz, Klein & McKee 2011) Reducing the metallicity reduces the opacity expect reduction in thermal feedback -- NO!

115 METALLICITY AND THE UNIVERSALITY OF THE IMF Reducing the metallicity reduces the opacity (Myers, Krumholz, Klein & McKee 2011) expect reduction in thermal feedback -- NO! Thermal feedback unaffected by reduction in metallicity since temperature in a dusty envelope almost independent of opacity κ: (Chakrabarti & McKee 2005, 2008)

116 METALLICITY AND THE UNIVERSALITY OF THE IMF Reducing the metallicity reduces the opacity (Myers, Krumholz, Klein & McKee 2011) expect reduction in thermal feedback -- NO! Thermal feedback unaffected by reduction in metallicity since temperature in a dusty envelope almost independent of opacity κ: (Chakrabarti & McKee 2005, 2008) k T 0.5 in extended dusty envelopes => T independent of κ

117 METALLICITY AND THE UNIVERSALITY OF THE IMF Reducing the metallicity reduces the opacity (Myers, Krumholz, Klein & McKee 2011) expect reduction in thermal feedback -- NO! Thermal feedback unaffected by reduction in metallicity since temperature in a dusty envelope almost independent of opacity κ: (Chakrabarti & McKee 2005, 2008) k T 0.5 in extended dusty envelopes => T independent of κ Makes high-mass IMF insensitive to variations in metallicity

118 OBSERVATIONAL PREDICTIONS 1. Massive stars form in cores with surface density Σ ~ 1 g cm -2

119 Observed Clusters with Massive Stars Have Σ ~ 1 g cm -2 McKee & Tan (2003)

120 OBSERVATIONAL PREDICTIONS 1. Massive stars form in cores with surface density Σ ~ 1 g cm The IMF should follow the Core Mass Function, scaled down by a factor of a few (Matzner & McKee 2000; McKee & Tan 2002, 2003)

121 The Core Mass Function (Motte, Andre, & Neri 1998, Testi & Sargent 1998, Johnstone et al. 2001, Reid & Wilson 2005, 2006, Lombardi et al. 2006, Alves et al. 2007) The core MF is similar to the stellar IMF, but shifted to higher mass a factor of a few Correspondence suggests a 1 to 1 mapping from core mass to star mass Dense core mass function (DCMF) in Pipe Nebula vs. stellar IMF (gray) (Alves, Lombardi, & Lada 2007)

122 The Core Mass Function (Motte, Andre, & Neri 1998, Testi & Sargent 1998, Johnstone et al. 2001, Reid & Wilson 2005, 2006, Lombardi et al. 2006, Alves et al. 2007) The core MF is similar to the stellar IMF, but shifted to higher mass a factor of a few Correspondence suggests a 1 to 1 mapping from core mass to star mass Dense core mass function (DCMF) in Pipe Nebula vs. stellar IMF (gray) (Alves, Lombardi, & Lada 2007) Predict similar result for massive cores (see Beuther & Schilke 2004; Bontemps et al 2010) --- ALMA observations will test this

123 OBSERVATIONAL PREDICTIONS 1. Massive stars form in cores with surface density Σ ~ 1 g cm The IMF should follow the Core Mass Function, scaled down by a factor of a few (Matzner & McKee 2000) 3. Massive disks should accompany massive protostars, in contrast with predictions of competitive accretion or stellar coalescence models (caveat: magnetic fields have not been included)

124 Massive Disk Properties M disk / M * , r disk ~ 1000 AU Global gravitational instability creates strong m = 1 spiral pattern Spiral waves drive rapid accretion; α eff ~ 1 Disks reach Q ~ 1, form a few stellar fragments Surface density (upper) and Toomre Q (lower) (Krumholz, Klein, & McKee, 2007)

125 Observing Massive Disks (Krumholz, Klein, & McKee, 2007) Density > cm 3 all species in LTE T > K can use high temp. lines to avoid envelope contamination Inner disk column density ~ 10 3 g cm 2 dust optical depth ~ 1 at 100 GHz Bad: kinematics in central few hundred AU impossible with ALMA (need EVLA for lower frequencies) Good: spiral arms have optical depth ~ 1 in dust / strong lines, very easy to do with ALMA Large IR telescopes can observe disks along directions of relatively low obscuration

126 Prediction for ALMA: Imaging spectroscopy of rotating m = 1 spiral Simulated 1000 s / pointing ALMA observation of edge-on disk at 0.5 kpc in CH 3 CN (12-11) GHz, T up = 69 K (Krumholz, Klein & McKee 2007)

127 Prediction for ALMA: Imaging spectroscopy of rotating m = 1 spiral Simulated 1000 s / pointing ALMA observation of edge-on disk at 0.5 kpc in CH 3 CN (12-11) GHz, T up = 69 K (Krumholz, Klein & McKee 2007)

128 CONCLUSIONS * Massive stars form in regions of high surface density (Σ ~ 1 g cm -2 ) that are self-gravitating and obey the virialized linewidth-size relation [σ (ΣR) 1/2 ]

129 CONCLUSIONS * Massive stars form in regions of high surface density (Σ ~ 1 g cm -2 ) that are self-gravitating and obey the virialized linewidth-size relation [σ (ΣR) 1/2 ] *Observations are consistent with formation of massive stars via a process similar to that of low-mass stars ( disks, hydromagnetic outflows), but including turbulence Turbulent Core model: Massive stars form in ~ 10 5 yr

130 CONCLUSIONS * Massive stars form in regions of high surface density (Σ ~ 1 g cm -2 ) that are self-gravitating and obey the virialized linewidth-size relation [σ (ΣR) 1/2 ] *Observations are consistent with formation of massive stars via a process similar to that of low-mass stars ( disks, hydromagnetic outflows), but including turbulence Turbulent Core model: Massive stars form in ~ 10 5 yr *Radiation pressure would stop spherically symmetric accretion for m * > 20 M sun. Continued accretion enabled by disks, Rayleigh-Taylor instabilities and outflows

131 CONCLUSIONS * Massive stars form in regions of high surface density (Σ ~ 1 g cm -2 ) that are self-gravitating and obey the virialized linewidth-size relation [σ (ΣR) 1/2 ] *Observations are consistent with formation of massive stars via a process similar to that of low-mass stars ( disks, hydromagnetic outflows), but including turbulence Turbulent Core model: Massive stars form in ~ 10 5 yr

132 CONCLUSIONS * Massive stars form in regions of high surface density (Σ ~ 1 g cm -2 ) that are self-gravitating and obey the virialized linewidth-size relation [σ (ΣR) 1/2 ] *Observations are consistent with formation of massive stars via a process similar to that of low-mass stars ( disks, hydromagnetic outflows), but including turbulence Turbulent Core model: Massive stars form in ~ 10 5 yr *Photoionization sets the mass of the first stars; role in contemporary massive star formation not yet known

133 THE FUTURE WILL BE REVOLUTIONARY OBSERVATIONS with ALMA will provide high-resolution imaging spectroscopy of high-mass star-forming regions

134 THE FUTURE WILL BE REVOLUTIONARY OBSERVATIONS with ALMA will provide high-resolution imaging spectroscopy of high-mass star-forming regions SIMULATIONS will include all relevant physics The state of the art today: Cunningham et al (2011) include turbulence, radiation pressure and protostellar outflows, but no ionization or magnetic fields Peters et al. (2010) include ionization but no radiation pressure, protostellar outflows, initial turbulence or magnetic fields Wang et al. (2010) include turbulence, outflows and magnetic fields, but no radiation pressure or ionization

135 THE FUTURE WILL BE REVOLUTIONARY OBSERVATIONS with ALMA will provide high-resolution imaging spectroscopy of high-mass star-forming regions SIMULATIONS will include all relevant physics The state of the art today: Cunningham et al (2011) include turbulence, radiation pressure and protostellar outflows, but no ionization Peters et al. (2010) include ionization but no radiation pressure, protostellar outflows or initial turbulence Wang et al. (2010) include turbulence, outflows and magnetic fields, but no radiation pressure or ionization Our understanding of massive star formation should be transformed in the next 2-3 years

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