STAR FORMATION:

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STAR FORMATION
PROBLEMS AND PROSPECTS
Chris McKee
with thanks to Richard Klein, Mark Krumholz, Eve
Ostriker, and Jonathan Tan
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THE BIG QUESTIONS IN STAR FORMATION
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Length and Time Scales in Galactic Star Formation
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ZENOS PARADOX (ALMOST) IN COMPUTATIONS OF STAR
FORMATION
Time step Dt ? 1/(Gr)1/2
Truelove et al. (1998) calculations of star
formation now
Density increase of 109 ? Dt decrease of 104.5
ABN (2002) calculations of primordial star
formation
Density increase of 1017 ? Dt decrease of 108.5
In both cases, calculation stopped before
formation of protostar.
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CHARACTERISTIC GRAVITATIONAL MASS
Kinetic energy/mass gravitational energy/mass
(MJ Jeans mass)
?2 GMJ/r
M ? r3 ? MJ ?3/(G3 ?)1/2 ?4/(G3 P)1/2
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I. MACROPHYSICS
FORMATION OF GIANT MOLECULAR CLOUDS (GMCs)
GMCs form by gravitational instability, not
coagulation
Top-down, not bottom-up - (Elmegreen)
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Significant issue does turbulence damp out as
quickly as indicated by periodic box simulations?
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YES
1. Star formation occurs in clusters over times
long compared to a crossing time (Palla
Stahler Tan)
2. Cloud lifetimes are long compared to a
crossing time
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NO
2. Critique of Palla Stahler claim of long-term
star formation in Taurus (Hartmann)
3. OB associations can form in unbound clouds
with ?vir 2 (Clark et al)
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PREDICTING THE PROPERTIES OF EQUILIBRIUM GMCs
(Chieze Elmegreen Holliman McKee)
If cloud is in approximate equilibrium, virial
theorem implies
ltPgt Psurface 0.5 GS2
(S surface density)
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PREDICTING THE CHARACTERISTIC STELLAR MASS FROM
THE WEIGHT OF THE ISM
Gravitationally bound structures in equilibrium
GMCs (clumps and cores) have ? ?GMC
(8PISM/G)1/2
Possible problem Works well for solar
neighborhood, but does it work elsewhere? (See
later)
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MAGNETIC FIELDS
The strength of the magnetic field is directly
proportional to our ignorance --- paraphrase of
Lo Woltjer
Basic issue Are magnetic fields of crucial
importance in star formation (Mouschovias), or
are they negligible (Padoan Nordlund) ?
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MAGNETIC FIELDS OBSERVATIONS
Crutcher finds M M? and Alfven Mach number 1
Determining the role of magnetic fields is one of
the critical problems in star formation.
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THE IMF
Observations consistent with universal
characteristic mass (1/3)Msun and high mass
slope, dN/d ln m ? m-1.35 (Salpeter)
Possible exceptions include paucity of O stars in
the outer parts of galaxies like M31
CONCLUSION IMF determined in molecular clouds
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Computing the Star Formation Rate From the
Physics of Turbulence

• GMCs roughly virialized, turbulent KE PE
• For sub-parts, linewidth-size relation ? KE r4
• PE r5, so most GMC sub-parts are unbound. Only
  overdense regions bound.
• Compute fraction f dense enough to be bound from
  PDF of densities.
• SFR f MGMC / tff
• Find f 1 for any virialized object with high
  Mach no.

(Krumholz McKee, 2005, ApJ, submitted)
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SFR in the Galaxy

• Estimate cloud free-fall times from direct
  observation (Milky Way) or ISM pressure (other
  galaxies)
• SFR from molecular mass, f, and tff
• Application to MW ? SFR 2 ? 5 Msun / yr.
• Observed MW SFR 3 Msun / yr

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Result SFR in Galactic DisksThe
Kennicutt-Schmidt Law From First Principles
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II. MICROPHYSICS GRAVITATIONAL COLLAPSE
Paradigm Inside-out collapse of centrally
concentrated core
Accretion rate Bonnor-Ebert mass per free-fall
time
Isothermal, ? ?p 1 (Shu)
Non-isothermal ? ?p ? 1 (McLaughlin Pudritz)
Non-isentropic ? ? ?p ? 1 (Fatuzzo, Adams
Myers)
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THE CLASSICAL PROBLEMS OF STAR FORMATION
1. Angular momentum
Rotational velocity due to differential rotation
of Galaxy is
0.05 km s-1 in 2 pc cloud
? Specific angular momentum is j rv 3 ? 1022
cm2 s-1
Angular momentum of solar system is dominated by
Jupiter
and is much less j 1018 cm2 s-1
Protostars generally have accretion disks, but
these have
angular momentum solar system and ltlt ISM value.
SOLUTION Angular momentum removed by magnetic
fields

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2. Magnetic flux
Typical interstellar magnetic field 5 mG
? Flux in 1 Msun sphere of ISM (r 2 pc) is 6 ?
1032 Mx
Net flux in Sun is 1 G ? p Rsun2 5 ? 1021 Mx
-Issue not fully resolved yet.
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PROTOSTELLAR JETS AND OUTFLOWS
Jet velocity v 200 km s-1 Keplerian
Mass loss rate in outflow fraction of accretion
rate onto star
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PROTOSTELLAR JETS AND OUTFLOWS
Due to MHD winds driven by magnetic field
threading the accretion disk and/or the star.
Detailed understanding lacking.
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PROTOSTELLAR DISKS
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MASSIVE STAR FORMATION
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HOW DO MASSIVE STARS FORM?
(Plume et al. 1997)
High-mass star-forming clumps
Supersonically turbulent s 2.5 km s-1
Radius 0.5 pc
? Virial mass 4000 Msun
?
Surface density S 1 g cm-2
Corresponding visual extinction AV 200 S mag
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EFFECT OF RADIATION PRESSURE
Wolfire Cassinelli 1987
Necessary condition momentum in accretion flow
at dust destruction radius must exceed momentum
in radiation field.
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TURBULENT CORE MODEL FOR MASSIVE STAR FORMATION
McKee Tan 2002, 2003
BASIC ASSUMPTION
Star-forming clumps and cores within them are
part of a self-similar, self-gravitating
turbulent structure in approximate hydrostatic
equilibrium. Cores are supported in large part
by turbulent motions.
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TURBULENT CORE MODEL
PROTOSTELLAR ACCRETION RATE
see Stahler, Shu Taam 1980
m instantaneous protostellar mass
tff (3p/32Gr)1/2 free-fall time evaluated at
r(m)
f numerical parameter ? (1)
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RESULTS FOR MASSIVE STAR FORMATION
Protostellar accretion rate for ? ? r -1.5
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Accretion rate is large enough to overcome
radiative momentum

m
? 4.6 x 10-4 (mf/ 30 Msun)3/4 S3/4
(m/mf)1/2 Msun yr-1
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Critique of Turbulent Core Model for Massive Star
Formation
Dobbs, Bonnell, Clark
Simulations of star formation in cores with ? ?
r-1.5
Equation of state isothermal or barotropic above
10-14 g cm-3
Isothermal collapse results in many small
fragments barotropic collapse in a few.
In no case did a massive star form (although
simulation ran only until 10 of mass had gone
into stars).
Require radiation-hydrodynamic simulations to
address this
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Massive Star Formation Simulations Required
Physics

• Real radiative transfer and protostellar models
  are required, even at early stages.
• Example dM/dt 10-3 Msun/yr, m 0.1 Msun, R
  10 Rsun ? L 30 Lsun!
• This L can heat 10 Msun of gas to 1000 K in 300
  yr. At nH 108 cm-3, tff 4000 yr ? high
  accretion rates suppress fragmentation.
• Most energy is released at sub-grid scales in the
  final fall onto star. A barotropic approximation
  cannot model this effect

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NUMERICAL SIMULATIONS
2D Yorke Sonnhalter (2002)
Accurate grain opacities and multi-component
grain model
(only 23 Msun with gray opacity)
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3D simulations with turbulent initial conditions,
high accretion rates, and radiative transfer (not
barotropic approxmation) show no fragmentation.
Protostar has currently grown to gt 20 Msun
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ALTERNATE MODELS OF STAR FORMATION
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ISSUE HOW DO STARS FORM IN CLUSTERS?
Solution unknown at present
NGC 3603
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STAR FORMATION PROBLEMS AND PROSPECTS
SUMMARY
Prospect for progress are good AMR codes are
becoming widely available and are ideally suited
for multiscale problems
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STAR FORMATION PROBLEMS AND PROSPECTS
SUMMARY
MICROPHYSICS
Problem How do stars form--by gravitational
collapse, gravitational accretion, or stellar
mergers?
Prospect May require more computer power to
resolve this, since calculation of formation of
even one star is a challenge.
Problem How do massive stars form in the face of
radiation pressure?
Prospect Good progress being made, but 3D
calculations with adequate radiative transfer and
dust models are in the future. Formation of
clusters with massive stars is a yet greater
challenge.
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Problem Planet formation
Prospect It will be some time before a single
simulation can treat the enormous range of scales
needed for an accurate simulation.
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