Transcript The Physics of Massive Star Formation

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)
Image: O’Dell & Wong (1995)
Talk Outline
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Initial conditions: massive clumps and
cores
Three things we don’t understand about
assembling a massive star
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Fragmentation
Competitive accretion
Feedback and the problem of accretion
Prospects and problems for the future
Sites of Massive Star Formation
(Plume et al. 1997; Shirley et al. 2003; Rathbone et al. 2005; Yonekura et al. 2005)
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Spitzer/IRAC (left) and Spitzer/MIPS
(right), Rathbone et al. (2005)
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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 linewidthsize relation
Virial parameter vir ~ 1
Massive Cores in Clumps
(Beuther & Shilke 2004, Sridharan et al. 2005,
Beuther, Sridharan, & Saito 2005, Garay 2005)
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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
Cores in IRDC 18454-0158, MSX 8
m (grayscale), 1.2 mm IRAM 30m
(contours), Sridharan et al. (2005)
Core in IRDC 18223-3, Spitzer/IRAC (color)
and PdBI 93 GHz continuum (contours),
Beuther, Sridharan, & Saito (2005)
Turbulent Core Model
(McKee & Tan 2003)
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Model cores as self-similar spheres at high
pressure, column density
High pressure and density gives free-fall time ~105
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)
The Core Population
(Motte, Andre, & Neri 1998, Reid & Wilson 2005, 2006, Stanke et al. 2006)
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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)
Assembling a Massive Star
Problem 1: Fragmentation
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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?
Fragmentation and Heating
(Krumholz, 2006, ApJL, 641, 45)
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Cores initially cold (10-20
K), mass is many thermal
Jeans masses
Pure hydro simulations
find many small fragments,
no massive stars (Dobbs,
RT calculation
Bonnell, & Clark 2005)
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However, accretion
luminosity can be 100 L
even onto 0.1 M stars
Analytic RT models show
this inhibits fragmentation
Barotropic EOS, no RT
Temperature and min. fragment
mass for RT (blue) and a
barotropic EOS (red) in a 50 M,
1 g cm-2 core
Radiation-Hydro Simulations
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
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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
Massive Cores Fragment Weakly
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Weak fragmentation  all core mass falls onto a
few stars, stellar IMF should resemble core MF
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Ratio of temperature computed with radiation
to temperature computed with barotropic
approximation when m* ≈ 4 M
Radiation critical
even at early times
due to large Lacc
The barotropic
approximation
severely the underestimates true
temperature  too
many fragments
Problem 2:
Competitive Accretion
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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.
Could Stars Gain Extra Mass?
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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
?
1 M
Simulation of star
cluster formation,
Bonnell, Vine, &
Bate (2004)
The Competitive Accretion Rate
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Stars can accrete by capturing unbound
gas (Bondi-Hoyle) or capturing other cores
Analytically compute fm from captures:
(Krumholz, McKee, & Klein, 2005, Nature, 438, 332)
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where co = core mass fraction ~ 0.1, u =
ratio of core escape velocity to clump
velocity dispersion,
This gives fm in terms of star mass M*,
clump mass M, virial ratio vir = KE / PE
Turbulent BH Accretion
(Krumholz, McKee, & Klein, 2005, 618, 757 and 2006, ApJ, 638, 369)
For fm due to gas accretion, use simulations to develop
model for Bondi-Hoyle accretion in a turbulent medium
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
The Turbulent BH Accretion Rate
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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
Is There Competitive Accretion?
(Krumholz, McKee, & Klein, 2005, Nature, 438, 332)
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Combining fm 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
Global Collapse in Gas Clumps
and Star Clusters
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Most clumps don’t
show infall in their line
profiles (Garay 2005)
Age spreads in star
clusters should be ~
tcr (~ 2 tff) if global
collapse occurs, but
they are usually 3 – 5
tcr (Tan, Krumholz, & McKee,
2006, ApJL, 641, 121)
tcr ≈ 0.6 Myr
Stellar age distribution in IC 348,
Palla & Stahler (2000)
Inconsistent with global collapse, CA
Global Collapse and
the Star Formation Rate
(Krumholz & Tan, 2006, ApJ, submitted)
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If clumps collapse,
mass forms stars in
~tcr. This gives a SFR.
Compare 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 in
observed systems (black), simulations (red),
and from a theoretical model (blue), as a
function of mean density
Inconsistent with GC, CA
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)
Problem 3: Feedback and the
Problem of Accretion
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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
Radiation Pressure
(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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 Massive stars approach their
Eddington limits while forming
Ideas to Break the
Radiation Pressure Barrier
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3D radiation hydrodynamic effects may
be important, so do
detailed simulations
to study them
Massive protostars
have outflows, just
like low mass stars;
consider their effects
!
Radiation-Hydro Simulations
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Radiation Beaming by Gas
(Yorke & Sonnhalter 2002; Krumholz, Klein, & McKee 2005)
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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
Have Radiation Bubbles Been
Detected Already?
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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, H20 Masers,
VLA, Torrelles et al. 2001
Massive Star Outflows
(Richer et al. 2000; Beuther et al. 2002, 2003, 2004)
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Observations show
massive stellar
outflows are wellcollimated
Force required to
drive outflows is ~10
– 103 L/c  outflows
probably hydromagnetic
IRAS 19217+1631, SMA,
Beuther et al. 2004
Outflows Help Accretion
(Krumholz, McKee, & Klein, ApJL, 2005, 618, 33)
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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
Problems for the Future
Magnetic Fields
(Crutcher 1999, 2005; Lai et al. 2001, 2002;
Bourke et al. 2001; Matthews et al. 2005)
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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
Better Physics in Simulations
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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
Simulation-Observation Coupling
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Simulated observation of radiation
bubble viewed edge-on in a tracer
of warm (>100 K) gas
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
Summary
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Massive stars form from massive cores
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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…
Plan B
Give up and appeal to intelligent design…