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)
From Stars to Planets
University of Florida
April 11, 2007
Talk Outline
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From core to star
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Initial fragmentation
Disk formation and
evolution
Binary formation
Radiation pressure and
feedback
Competitive accretion
Final summary
Massive core (PdBI, contours)
inside IRDC (Spitzer IRAC,
colors), Beuther et al. (2007)
The Core Mass Function
(Motte, Andre, & Neri 1998, Johnstone et al. 2001, Reid & Wilson
2005, 2006, Lombardi et al. 2006, Charlie Lada’s talk)
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The core MF is similar
to the stellar IMF, but
shifted to higher
masses a factor of 2 – 4
Seen in many regions,
many observational
tracers
Correspondence
suggests a 1 to 1,
constant efficiency, core
to star mapping
Core mass function in Pipe Nebula
(red) vs. stellar IMF (gray) (Alves,
Lombardi, & Lada 2007)
From Core to Star
Stage 1: Initial Fragmentation
(Krumholz, 2006, ApJL, 641, 45)
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Massive cores are
much larger than MJ
(~ M), so one might
expect them to
fragment while
collapsing (e.g. Dobbs et al.
2005)
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However, accretion
can produce > 100 L
even when protostars
are < 1 M
Temperature vs. radius in a
massive core before star
formation (red), and once
protostar begins accreting (blue)
Radiation-Hydro Simulations
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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 2007, ApJ, 656, 959, and KKM, 2007, ApJS,
submitted, astro-ph/0611003)
Mass conservation
Momentum conservation
Gas energy conservation
Rad. energy conservation
Self-gravity
Simulation of a Massive Core
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
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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
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Column density with (upper) and
without (lower) RT, for identical
times and initial conditions
With RT: 6 fragments,
most mass accretes
onto single largest star
through a massive disk
Without RT: 23
fragments, many stellar
collisions, disk smaller
and less massive
Conclusion: radiation
inhibits fragmentation,
qualitatively changes
star formation process
Stage 2: Massive Disks
(Kratter & Matzner 2006, Kratter, Matzner & Krumholz, 2007, in preparation)
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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, 2007, ApJ, 656, 959)
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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
azimuthally isothermal
Disks reach Q ~ 1,
unstable to fragment
formation
Surface density (upper) and Toomre
Q (lower); striping is from projection
Observing Massive Disks
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
TIntegrated
TB inof
simulated
velocity in
1000
simulated
s / pointing
1000ALMA
s / pointing
observation
ALMA of
observation
disk at 0.5
B as a function
ofkpc
disk
in at
CH0.5
kpc
220.7472
in CH3CN
GHz
220.7472
(KKM 2007,
GHz ApJ,
(KKMsubmitted)
2007, ApJ, submitted)
3CN
Stage 3: Binary Formation
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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)
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Mass ratio for 26 detached elcipsing
binaries in the SMC (Pinsonneault &
Stanek 2006)
Most massive known
binary is WR20a: M1 =
82.7 M, q = 0.99 ±
0.05 (Rauw et al. 2005)
Close Binaries
(Krumholz & Thompson, 2007, ApJ, in press, astro-ph/0611822)
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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”
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WR20a
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Minimum semi-major axis for RLOF as a
function of accretion rate
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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
Stage 4: Radiation Pressure
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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)
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Dust absorbs UV &
visible, re-radiates IR
Dust sublimes at T ~
1200 K, r ~ 30 AU
Radiation > gravity for
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For 50 M ZAMS star,
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In reality, accretion isn’t spherical.
Investigate 3D behavior with Orion.
Simulations of Radiation Pressure
(KKM, 2005, IAU 227)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Beaming by Disks and Bubbles
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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)
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Gas
temperature
distributions
with
Radiation
and gravitational
forces
awith
50 and
M star,
50 M
without
outflow
 envelope
Massive stars outflows
launched inside dust
destruction zone
Result: outflow cavities
optically thin, radiation
can leak out of them
Simulate with MC
radiative transfer code
Find factor of ~10
reduction in radiation
pressure force on
accreting gas
Stage 5: Competitive Accretion
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Once initial core is accreted, could a star
gain additional mass from gas that wasn’t
bound to it originally via BH accretion?
If so, no core to star mapping exists
Simulation of star
cluster formation,
Bonnell, Vine, &
Bate (2004)
Accretion in a Turbulent Medium
(Krumholz, McKee, & Klein, 2006, ApJ, 638, 369; 2005, Nature, 438, 332)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
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Result: virialized turbulence  negligible accretion
Implication: CA significant only if turbulence decays,
cluster collapses to stars in ~1 crossing time
Global Collapse and
the Star Formation Rate
(Krumholz & Tan, 2007, ApJ, 654, 304)
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Compare SFR
required for CA to
observed SFR in
dense gas (e.g. Gao &
Solomon 2004, Wu et al. 2005)
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Global collapse gives
Ratio of free-fall time to depletion time vs.
density in observed systems (red) and
simulations where CA occurs (black)
Observed SFRs much too low for CA to occur!
Summary
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Massive stars form from massive cores
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Massive cores fragment only weakly.
MC produce massive, unstable disks.
Close massive binaries likely experience
mass transfer, which explains massive twins.
Radiation pressure does not halt accretion.
CA is not significant in typical clumps.
Mass and spatial distributions of massive
stars are inherited from massive cores
However, every new bit of physics added
has revealed something unexpected…
Plan B
Give up and appeal to intelligent design…