THE FORMATION OF MASSIVE STARS · 2017-12-05 · THE FORMATION OF MASSIVE STARS Andrew Cunningham...

THE FORMATION OF MASSIVE STARS

η Carina (NASA, ESA, N. Smith)

THE FORMATION OF MASSIVE STARS

Andrew Cunningham Edith Falgarone Richard Klein Mark Krumholz Andrew Myers Stella Offner Jonathan Tan

with

Christopher F. McKee

Institute for Astronomy November 2, 2011

•Create most of the heavy elements

MASSIVE STARS:

Cas A Supernova Remnant

NASA/CXC/MIT/Umass Amherst/D. Stage ea


MASSIVE STARS:


•Energize the interstellar medium (ISM)–UV emission heats via photoelectric effect (~102 K)–Ionizing luminosity creates ionized gas (~104 K)–Stellar winds and supernovae create hot gas (~106 K)

MASSIVE STARS:

T. Megeath



•Govern the evolution of galaxies -Radiation pressure drives outflows

MASSIVE STARS:

M82

Red: IR (Spitzer)

Orange: HII (Hubble)

Blue: X-rays (Chandra)



•Regulate star formation•Govern the evolution of galaxies -Radiation pressure drives outflows•May have re-ionized the universe

MASSIVE STARS:

WHY DO WE KNOW SO LITTLE ABOUT MASSIVE STAR FORMATION?


• OBSERVATION:– Highly obscured (AV ~ 100-1000)– Far away (D 2 kpc)– Crowded (104 stars pc-3 at the center of Orion)

~>


• OBSERVATION:– Highly obscured (AV ~ 100-1000)– Far away (D 2 kpc)– Crowded (104 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)

~>

OUTLINE

OUTLINE *Basics

-Part I: Star Formation in Isothermal Gas:

-Part II: Star Formation in Turbulent Gas

Everything you ever wanted to know about star formation in three slides

OUTLINE

* Theoretical models of massive star formation

*Basics-Part I: Star Formation in Isothermal Gas:



OUTLINE


* Challenges in massive star formation:

-Ionizing radiation-Radiation pressure

-Constancy of the IMF




OUTLINE


* Observational predictions

* Challenges in massive star formation:

-Ionizing radiation-Radiation pressure

-Constancy of the IMF




Hierarchical Structure of Molecular Clouds

GMC

Clump -> star cluster

Core -> star/binary

Terminology:

Structure self-similar from stellar mass to GMC mass

(~ 1-10 Msun)

(~ 103 Msun)

(~ 105-6 Msun)

Supersonically turbulent: σ ~ 2.5 km s-1

CHARACTERISTICS OF REGIONS OF HIGH-MASS STAR FORMATION

(Plume et al. 1997; Shirley et al. 2003)

Mass ~ 4000 Msun

Radius ~ 0.5 pc

High-mass star-forming clumpsSound speed cs ~ 0.3 km s-1 (Temperature ~ 30 K)




Mass ~ 4000 Msun

Radius ~ 0.5 pc


⇒Surface density Σ ~ 1 g cm-2 (AV~200)Density ρ ~ 5 × 10-19 g cm-3 , nH ~ 2 × 105 cm-3

Compare typical Giant Molecular Cloud:

nH ~ 100 cm-3

Σ ~ 0.03 g cm-2




Mass ~ 4000 Msun

Radius ~ 0.5 pc


⇒Surface density Σ ~ 1 g cm-2 (AV~200)Density ρ ~ 5 × 10-19 g cm-3 , nH ~ 2 × 105 cm-3

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 18223-3, Spitzer/IRAC (color) and PdBI 93 GHz continuum

(contours), Beuther et al. (2005, 2007)

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 kρ ≈ 1.5

Core in IRDC 18223-3, Spitzer/IRAC (color) and PdBI 93 GHz continuum

(contours), Beuther et al. (2005, 2007)Core density profile in 3 wavelengths, Beuther et al. (2007)

Pioneers:

Jeans, Bonnor, Ebert, Larson, Shu

Star Formation in Isothermal Gas

BASICS: PART I

EVERYTHING YOU WANTED TO KNOW ABOUT STAR FORMATION: 1

Characteristic timescale set by self-gravity:

d2Rdt2 ~ R

t2 ~ GMR2

⇒ t2 ∝ R3

GM~ 1

Gρ


Characteristic timescale set by self-gravity:

d2Rdt2 ~ R

t2 ~ GMR2

⇒ t2 ∝ R3

GM~ 1

Gρ

Free-fall time: tff = (3π/32Gρ)1/2

= 1.4 x 105 (105 cm-3/n)1/2 yr

Characteristic mass:

Kinetic energy/mass ~ gravitational energy/mass

cs2 ≡ P/ρ ∼ GM/R ⇒ M ~ Rcs

2/G





2/G

Radius: R ~ cstff ~ cs/(Gρ)1/2





2/G


⇒ Mass ~ Rcs2/G ~ cs

3tff/G ~ cs3/(G3ρ)1/2





2/G


⇒ Mass ~ Rcs2/G ~ cs

3tff/G ~ cs3/(G3ρ)1/2


Bonnor-Ebert mass = maximum mass of stable isothermal sphere:

MBE = 1.18 cthermal3 /(G3ρ)1/2

Gravity not important for masses M << MBE


Characteristic accretion rate:

m*· ~ mBE / tff ~ cs3/(G3ρ)1/2 × (Gρ)1/2 ~ cs

3/G




3/G

For a singular isothermal sphere (Shu 1977):

m*· = 0.975 cs3 / G

= 1.5 x 10-6 (T/ 10 K)3/2 Msun yr-1




3/G


m*· = 0.975 cs3 / G

= 1.5 x 10-6 (T/ 10 K)3/2 Msun yr-1

An isothermal gas at 10 K takes 6.5 x 105 yr to form a 1 Msun star

6.5 x 107 yr to form a 100 Msun star>> age of star (~ 3 Myr)




3/G


m*· = 0.975 cs3 / G

= 1.5 x 10-6 (T/ 10 K)3/2 Msun yr-1

An isothermal gas at 10 K takes 6.5 x 105 yr to form a 1 Msun star

6.5 x 107 yr to form a 100 Msun star>> age of star (~ 3 Myr)

NEED TO GENERALIZE THEORY

Pioneers in observation:Larson, Falgarone, Solomon, Myers, Goodman

Pioneers in theory:Gammie Ostriker & Stone, MacLow, Padoan & Nordlund, Vazquez-Semadeni

Star Formation in Turbulent Gas

BASICS: PART II

LINEWIDTH-SIZE RELATION IN TURBULENT GASIncompressible turbulence (Kolmogorov 1941)

Energy cascade from driving scale to dissipation scale:



Supersonic turbulence:



Supersonic turbulence:Linewidth-size relations




Larson (1981) discovered the linewidth-size relation in the ISM

Linewidth-size relations





What drives the turbulence in molecular gas?






What drives the turbulence in molecular gas?Supernovae (Mac Low & Klessen 2004)







Star formation (Norman & Silk 1980; McKee 1989; Matzner 2002; Nakamura & Li 2005)







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)


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?)

Turbulent Linewidth-Size Relation for Galactic Molecular Gas

ΔvNT = (1.4 ± 0.5 dex) Lpc1/2 km/s


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

Turbulent linewidth-size relation for gravitationally unbound gas:


Virialized linewidth-size relation for gravitationally bound gas:


for bound clouds with αvir ~ 1 (Heyer ea 2009)



for bound clouds with αvir ~ 1 (Heyer ea 2009)

Converting to FWHM, Δv=2.355 σ :


2

Turbulent linewidth-size relation (unbound)

Virialized linewidth-size relation (bound)GMCs

Generalized Linewidth-Size Relation for Bound and Unbound Gas


2

High latitude molecular clouds

High-mass star-forming regions

GMCs

Generalized Linewidth-Size Relation for Bound and Unbound Gas

(Falgarone & McKee 2011)

Generalization of Theory of Low-Mass Star Formation in Isothermal Cores to High-Mass Star Formation in Turbulent Cores

(McKee & Tan 2002, 2003)


However, for massive stars, σ is highly supersonic; it depends on scale and must be determined self-consistently.

Accretion rate ~ σ3/G (formation time ~ free-fall time) m*·(McKee & Tan 2002, 2003)



Accretion rate ~ σ3/G (formation time ~ free-fall time) m*·

Virial equilibrium ⇒ σ2 ~ GM/R

(McKee & Tan 2002, 2003)





Surface density Σ = M/πR2

m*·⇒ ∝ G1/2 (M Σ)3/4

Accretion rate determined by core mass M and surface density Σ: High Σ ⇒ high accretion rate

(McKee & Tan 2002, 2003)






m*·⇒ ∝ G1/2 (M Σ)3/4


(McKee & Tan 2002, 2003)

Turbulent cores are scale-free ⇒ model as singular polytropic spheres (McLaughlin & Pudritz 1996, 1997)






m*·⇒ ∝ G1/2 (M Σ)3/4


Numerical evaluation ⇒ massive stars form in about 105 yr:t*f = 1.3 x 105 (m*f /30 Msun)1/4 Σ−3/4 yr

(McKee & Tan 2002, 2003)

Turbulent cores are scale-free ⇒ model as singular polytropic spheres (McLaughlin & Pudritz 1996, 1997)

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)




-Competitive accretion (Zinnecker 1982; Bonnell et al 1997)

-Problems: Fails in a turbulent medium (Krumholz, McKee & Klein 2005)

-Variant: Fragmentation-induced starvation (Peters et al. 2010)

or if radiation pressure becomes important (Edgar & Clarke 2004)

* Bondi-Hoyle accretion by many protostars from a common reservoir




* Stellar coalescence (Bonnell, Bate & Zinnecker 1998)

-Massive stars form as a result of physical collisions of low-mass

-Requires stellar densities much higher than observedstars, naturally overcoming radiation pressure problem

-Competitive accretion (Zinnecker 1982; Bonnell et al 1997)

-Problems: Fails in a turbulent medium (Krumholz, McKee & Klein 2005)

-Variant: Fragmentation-induced starvation (Peters et al. 2010)

or if radiation pressure becomes important (Edgar & Clarke 2004)

* Bondi-Hoyle accretion by many protostars from a common reservoir

CHALLENGES IN MASSIVE STAR FORMATIONLarson & Starrfield (1971)

CHALLENGES IN MASSIVE STAR FORMATION

* Formation time exceeds stellar lifetime for m* > 60 Msun

Possible solution: increase T ⇒ higher ρ, shorter free-fall time

Larson & Starrfield (1971)




* Radiation pressure on dust (a fundamental problem)






(1) UV radiation on inner dust shell > gravity for m* > 20 Msun

Possible solution: mass build-up in shell, instability








(2) IR radiation from dust shell > gravity for m* > 25 Msun

(Current values for opacity, stellar luminosity ⇒ m*crit = 17 Msun)








(2) IR radiation from dust shell > gravity for m* > 25 Msun

(Current values for opacity, stellar luminosity ⇒ m*crit = 17 Msun)

* Formation time > time to reach main sequence ⇒ HII regionIonizes natal cloud for m* > 25 Msun Possible solution: increase cloud density by lower star formation

efficiency, higher T, turbulence


Wolfire & Cassinelli (1987)

THE RADIATION PRESSURE PROBLEM1. UV radiation at the dust destruction front near the protostar

Require momentum in accretion flow at dust destruction radiusto exceed momentum in radiation field:

Wolfire & Cassinelli (1987)

THE RADIATION PRESSURE PROBLEM1. UV radiation at the dust destruction front near the protostar

Satisfied by Turbulent Core model:for 30 Msun star

Eddington luminosity Ledd: radiative force balances gravity at

LEdd = 4πGMc/(σ/µ)

Maximum IR cross section per unit mass for dust in massive protostellar envelopes: σ/µ ≈ 8 cm2 g-1

⇒ LEdd = 1600 (M/Msun) Lsun

2. IR RADIATION ON DUST THE RADIATION PRESSURE PROBLEM






Predict growth of protostar stops for L > LEdd

⇒ stars cannot grow past ~17 Msun






Predict growth of protostar stops for L > LEdd

⇒ stars cannot grow past ~17 Msun

But stars are observed to exist with M > 100 Msun

HOW IS THIS POSSIBLE?

ADDRESSING THE PROBLEM OF RADIATION PRESSURE

− Effect of accretion disksAccreting gas has angular momentum and settles into a disk before accreting onto starPrevious 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)




− 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)

3D RADIATION HYDRODYNAMIC CALCULATIONS

Radiative transfer: gray, mixed frame, flux-limited diffusion

∂t ρ + ∇⋅ ρv = 0

∂t ρv + ∇⋅ ρvv = - ∇P - ρ∇φ + (κR/c)F

∂t ρe + ∇⋅ [(ρe+P)v] = - ρv⋅∇φ - κP(4πB-cE) - (κR/c) v⋅F

∇2φ = 4πGρ

∂t E + ∇⋅F = κP(4πB-cE) + (κR/c) v⋅F

F0 = - [cλ(E0) / κR] ∇E0

where e = 0.5 v2 + u = gas energy density, E = radiation energy density;F0 and E0 in comoving frame. Accurate to lowest relevant order in v/c.

(Krumholz et al. 2007)

(Mass)

(Momentum)

(Energy)(Gravity)

(Radiative energy)

(Flux limit)

3D Simulation of Massive Star Formation

M = 100 MsunRinitial = 0.1 pc

Slow initial rotation

Tinitial = 20 K

No initial turbulenceNo outflows

(⇒ n ~ 106)

ninitial ∝ r -3/2

L(pc) = 0.3 .075 .019 .005=1000 AU


Density



Tinitial = 20 K


(⇒ n ~ 106)

ninitial ∝ r -3/2

(Krumholz, Klein, McKee, Offner & Cunningham 2009)

t (kyr)

17.5

25

34

42

55

L(pc) = 0.3 .075 .019 .005=1000 AU


Density



Tinitial = 20 K


(⇒ n ~ 106)

ninitial ∝ r -3/2


t (kyr)

17.5

25

34

42

55

L(pc) = 0.3 .075 .019 .005=1000 AU


Density

Plane of plots includes

Density range:rotation axis

10-19 - 10-12 g cm-3



Tinitial = 20 K


(⇒ n ~ 106)

ninitial ∝ r -3/2


t (kyr)

17.5

25

34

42

55

L(pc) = 0.3 .075 .019 .005=1000 AU


Density

Plane of plots includes

Density range:rotation axis

10-19 - 10-12 g cm-3

Radiative Rayleigh-Taylorinstabilities allow gas toaccrete and radiationto escape



Tinitial = 20 K


(⇒ n ~ 106)

ninitial ∝ r -3/2


t (kyr)

17.5

25

34

42

55

L(pc) = 0.3 .075 .019 .005=1000 AU

Column Density Looking Down the Rotation Axis

t (kyr)

17.5

25

34

42

55

L(pc) = 0.3 .075 .019 .005=1000 AU


Protostars marked by + in 2 rightmost frames

Column density range: 0.1-1000 g cm-2

t (kyr)

17.5

25

34

42

55

L(pc) = 0.3 .075 .019 .005=1000 AU




At t = 55 kyr, two massive stars with m* = 39 and 27 Msun; a third star has m* = 0.15 Msun

t (kyr)

17.5

25

34

42

55

L(pc) = 0.3 .075 .019 .005=1000 AU




At t = 55 kyr, two massive stars with m* = 39 and 27 Msun; a third star has m* = 0.15 Msun

Radiation pressure affects morphology of gas, but not growth of protostars.

Collapse of 100 Msun Core

L = 0.25 pc

L = 2000 AU

Column density along axis

Density in plane with axis

Conclusion of simulation with radiation pressure but no outflows:

Rayleigh Taylor instability and disk formation allow accretion to overcome radiation pressure

PROTOSTELLAR OUTFLOWS REDUCE RADIATION PRESSURE

Protostars have powerful, collimated outflows

Mass ejection rate ~ (0.1-0.3) × accretion rate

Wind velocity ~ Keplerian velocity at stellar surface

Outflow is driven by magnetic forces associated with the rotating, magnetized disk

(Carrasco-Gonzalez et al. 2010)

6 cm (contours)

850 µm (gray scale)

Observation of magnetized jet from a high-mass protostar

IRAS 18162-2048

L=17,000 Lsun

⇒ M ≈ 10 Msun

if dominated by one star

Synchrotron emission

Thermal emission

PROTOSTELLAR OUTFLOWS REDUCE RADIATION PRESSURE

Protostars have powerful, collimated outflows

Mass ejection rate ~ (0.1-0.3) × 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 Msun star in a 50 Msun envelope (Krumholz, McKee & Klein 2005)

3D Monte Carlo radiative transfer in cavities with different shapes

Simulations with collimated outflows at t=0.2 tff

M=300 Msun

Resolution ~ 30 AU

(Cunningham et al. 2011)


M=300 Msun

Resolution ~ 30 AU


Σ = 2 g cm-2

Σ = 2 g cm-2

(no wind)

Σ = 10 g cm-2

Σ = 1 g cm-2

Clouds with different surface densities:


M=300 Msun

Resolution ~ 30 AU


Σ = 2 g cm-2

Σ = 2 g cm-2

(no wind)

Σ = 10 g cm-2

Σ = 1 g cm-2

Clouds with different surface densities:

0.25 x 0.25 0.01 x 0.01 0.01 x 0.01


Σ = 1 g cm-2

Σ = 2 g cm-2

Σ = 2 g cm-2

(no wind)

Σ = 10 g cm-2

M=300 Msun

Resolution ~ 30 AU


Simulations with collimated outflows at t = 0.6 tff

Results on outflows:

Reduce radiation pressure by allowing escape

mpri ~20 Msun

mpri ~20 Msun

mpri ~35 Msun

mpri ~35 Msun

Σ = 1 g cm-2

Σ = 2 g cm-2

Σ = 2 g cm-2

Σ = 10 g cm-2

(no wind)




mpri ~20 Msun

mpri ~20 Msun

mpri ~35 Msun

mpri ~35 Msun

Σ = 1 g cm-2

Σ = 2 g cm-2

Σ = 2 g cm-2

Σ = 10 g cm-2

(no wind)

Disk gas cooler ⇒ more fragmentation (lower primary mass with wind)




Results for Σ=2 without winds ~ same as Σ=10 with winds (Trapping of radiation increases with Σ)

mpri ~20 Msun

mpri ~20 Msun

mpri ~35 Msun

mpri ~35 Msun

Σ = 1 g cm-2

Σ = 2 g cm-2

Σ = 2 g cm-2

Σ = 10 g cm-2

(no wind)

Disk gas cooler ⇒ more fragmentation (lower primary mass with wind)

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




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

THE IONIZATION PROBLEM

Larson & Starrfield (1971) estimated that a 25 Msun 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)



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)

Expansion of HII Region in Rotating Accretion Flow

(McKee & Tan 2008)

First stars:Large accretion rates (> 10-3 Msun yr-1) imply breakout of HII region at poles for m* ~ 100 Msun

Contemporary stars:

Lower accretion rates allow breakout at lower masses (Keto 2007)

For the first stars, disk photoevaporation terminates accretion

(Hollenbach et al 1994)

Estimated mass of first stars: 100-200 Msun (McKee & Tan 2008)

For contemporary stars, dust may absorb ionizing photons, allowing accretion to continue

METALLICITY AND THE UNIVERSALITY OF THE IMF(Myers, Krumholz, Klein & McKee 2011)

Reducing the metallicity reduces the opacity

⇒ expect reduction in thermal feedback

All stars

Most massive star

Fraction of mass in most massive star

Vary metallicity by factor 20 at Σ = 2 g cm-2

“High Sigma”: Σ = 10 g cm-2

at 0.2 solar

All stars

Most massive star

Fraction of mass in most massive star

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

(Calculations stopped when m*~10 Msun)



⇒ 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)




kT ≈ 0.5 in extended dusty envelopes => T independent of κ






kT ≈ 0.5 in extended dusty envelopes => T independent of κ



Makes high-mass IMF insensitive to variations in metallicity

OBSERVATIONAL PREDICTIONS

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

McKee & Tan (2003)

Observed Clusters with Massive Stars Have Σ ~ 1 g cm-2



2. The IMF should follow the Core Mass Function, scaled down by a factor of a few (Matzner & McKee 2000; McKee & Tan 2002, 2003)

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)

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



2. 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)

Massive Disk Properties

• Mdisk / M* ≈ 0.2 – 0.5, rdisk ~ 1000 AU

• Global gravitational instability creates strong m = 1 spiral pattern

• Spiral waves drive rapid accretion; αeff ~ 1

• Disks reach Q ~ 1, form a few stellar fragments Surface density (upper) and Toomre Q (lower)

(Krumholz, Klein, & McKee, 2007)

Observing Massive Disks(Krumholz, Klein, & McKee, 2007)

• Density > 1010 cm–3 ⇒ all species in LTE• T > 50 – 100 K ⇒ can use high temp. lines to avoid envelope

contamination• Inner disk column density ~ 103 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

Prediction for ALMA:

Simulated 1000 s / pointing ALMA observation of edge-on disk at 0.5 kpc in CH3CN (12-11) 220.7 GHz, Tup = 69 K (Krumholz, Klein & McKee 2007)

Imaging spectroscopy of rotating m = 1 spiral

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 ~ 105 yr



*Radiation pressure would stop spherically symmetric accretion for m* > 20 Msun. Continued accretion enabled by disks, Rayleigh-Taylor instabilities and outflows





*Photoionization sets the mass of the first stars; role in contemporary massive star formation not yet known

THE FUTURE WILL BE REVOLUTIONARYOBSERVATIONS 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


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

THE FORMATION OF MASSIVE STARS · 2017-12-05 · THE FORMATION OF MASSIVE STARS Andrew Cunningham...

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