Transcript Document

What limits the
masses of the
first stars?
Jonathan C. Tan
University of Florida
ETH Zurich
Christopher F. McKee
UC Berkeley
Eric G. Blackman
University of Rochester
Abel, Bryan, Norman
Image from Scientific American and V. Bromm
Importance of First Stars and their IMF
Observations
Reionization
CMB polarization (WMAP Kogut et al. 03)
H 21cm (LOFAR Morales & Hewitt 03)
Metal Enrichment
Z of halo stars (Christlieb et al. 03)
Illumination
NIR bkg. intensity (Santos et al. 02
NIR bkg. fluctuations (Kashlinsky et al. 04)
Progenitors of SN
and GRBs?
JWST
SWIFT
(Weinmann & Lilly 2005)
(Bromm & Loeb 2002)
Influence on Quasars, Globular Clusters, Galaxies?
“Simple” problem: initial conditions, chemistry,
no feedback from other stars, weak B-fields(?)
Hydrogen Ionizing Luminosities
along the Primordial Main Sequence
Tumlinson & Shull 2000; Bromm et al. 2001;
Ciardi et al. 2001; Schaerer 2002
Initial mass determines nucleosynthetic yields
and final remnant
Heger & Woosley 2002
Near Infra-Red
Background
EBL
galaxies
Potential signature of first
stars in the NIR EBL
(Santos, Bromm, Kamionkowski 2002;
Salvaterra & Ferrara 2003)
But zodiacal subtraction
is uncertain
(Dwek, Arendt, Krennrich 2005)
Numerical Simulations: Methods
Bromm, Coppi, Larson 1999; Abel, Bryan, Norman 2000,2002
Abel, Bryan, Norman (2002):
Eulerian AMR; Riemann solver
non-eq. chemistry of 9 species
optically thin radiative losses:
line cooling
Compton heating/cooling
tot=1, =0 , b=0.06,z=100
scale invariant power spectrum
(128kpc)3 comoving
Identify region of 1st DM halo
with ~106Msun, then focus here
with DM particle mass =1Msun
Grid refinement to resolve:
Jeans mass, density contrasts,
and cooling timescales
Numerical Simulations: Results
1. Form pre-galactic
halo ~105-6Msun
2. Form quasihydrostatic gas core
inside halo:
M≈4000Msun,r ≈10pc,
nH ≈10cm-3, fH2 ≈10-3,
T>=200K
3. Rapid 3-body H2
formation for
nH>1010cm-3
strong cooling
supersonic inflow.
Abel, Bryan, Norman (2002)
The initial conditions for
primordial star formation
Chemical Composition
Trace H2 formation:
H + e—  H — + 
H + H —  H 2 + e—
Tmin ~= 200 K, ncrit ~= 104 cm-3
MBE = 380Msun cs=1.2 km/s
The initial conditions for
primordial star formation
Tmin ~= 200 K, ncrit ~= 104 cm-3
MBE = 380Msun cs=1.2 km/s
Centrally concentrated cloud, inefficient
cooling -> quasi-hydrostatic contraction
Density structure: ~self-similar, r -2.2
More chemistry: at high density >108cm-3
H+H+H -> H2 + H
efficient cooling -> dynamical collapse
Rotation: core forms from mergers and
collapse along filaments: expect J>0
fKep  vcirc / vKep  ~ 0.5
Abel, Bryan, Norman (2002)
The Accretion Rate
and Formation Timescale
r
-k
Density structure: self-similar, r -k, k≈2.2
~singular polytropic sphere in virial
and hydrostatic equilibrium P = K , =1.1
.
Accretion rate: m*= * m / tff(m)  f(m,K)
(Tan & McKee 2004)
Abel et al. 2002
“Isentropic Accretion”
Schaerer 2002
.
K=1.9x1012(T/300K)(nH/104cm-3)-0.1cgs
K’=K/ 1.9x1012cgs
*=1.4 (Hunter 1977)
Collapse to a Disk
Geometry of Streamlines
rd = f2Kepr0  3.4 (M/Msun)9/7 AU
Expect accretion within the disk
is driven by large scale gravitational
instabilities and local gravitational
viscosity (Gammie 2001).
STAR
DISK
Conserve J during free-fall
inside sonic point (Ulrich 1976)
viscosity
= cs h,
<0.3
fragmentation
tcool< 3-1
Toomre stability parameter
sound
speed
orbital angular
velocity
<1
>1
-> unstable
-> stable
surface
density
Are disks are stable with respect to fragmentation?
Disk Models
(Tan & McKee 2004; Tan & Blackman 2004)
=0.3
Surface density
Thickness
Ionization
Temperature
Tc , Teff
Toomre Q
Disks are
stable
.
m*
17x10-3Msun/yr 6.4x10-3Msun/yr 2.4x10-3Msun/yr
Evolution of the Protostar depends on Accretion Rate
(Stahler et al. 1980; Palla & Stahler 1991; Nakano 1995; Behrend & Maeder 2001;
Omukai & Palla 2001, 2003; Tan & McKee 2003)
Assume polytropic stellar structure and continuous sequence of equilibria
One zone model:
follow energy of
protostar as it
accretes
Deuterium burning for Tc>106K
Structural rearrangement after tKelvin
Eddington model for 
Solve for r*(m*), until reach main sequence
r*
m*
Evolution of the Protostar
Initial condition
m* = 0.04 Msun
r* = 14 Rsun
(Ripamonti et al. 02)
:Radius
Photosphere
Accretion Shock
Main Sequence
(Schaerer 2002)
Protostar is large (~100 Rsun) until it is older than tKelvin
Contraction to Main Sequence
Accretion along Main Sequence
Evolution of the Protostar:Luminosity
Total
Boundary Layer
Accretion Disk
Star
Evolution of the Protostar
:Ionizing
Luminosity
Total
fKep=0.5
Star
Boundary Layer
Accretion Disk
Spherical, fKep=0
Main Sequence
(Schaerer 2002)
Spectrum depends on initial rotation
c.f. Omukai & Palla (2003)
Growth of the HII Region
Balance ionizing flux vs
recombinations and infall
Infall likely to be suppressed
for rHII>rg , where vesc=ci
HII Region
Find stellar mass at breakout
rHII = rg
polar; equatorial
Breakout mass vs rotation
Ly- and FUV Radiation Pressure
1 in HI around HII region :
Photons diffuse in freq. and space
Normalize J to appropriate
Velocity field: Voigt profile D ;
Line profile: damping wings
Escape after n scatterings, or 2 photon decay
freq. shift
; mean free path at escape
diffusion scale
must equal size of region,
and
total path length of photons is n1/2L so mean intensity boosted by factor
(Neufeld 90) :
Evaluate NH from harmonic mean of sightlines from star
L
Mass Limits vs. Core Rotation
Breakout in polar direction
Overview
Disk Photoevaporation
Hollenbach et al. 94
.
Mass loss rate:
for zero age main sequence
Equate with mass accretion rate
Accretion rate reduced by
expansion of HII region
Accretion continues
from regions shadowed
by the accretion disk.
Need to calculate vertical
structure of disk.
Radial profile of disk
Evolution of accretion and outflow rates
Self-consistent model for
growth and evolution of
protostar, including:
- declining accretion rate
- accretion disk (r,z)
- protostellar structure
- ionizing & FUV feedback
Final mass is
When does accretion end?
McKee & Tan, in prep
Declining accretion versus increasing feedback
Ly- Radiation Pressure
Ionization
Disk Evaporation
Hydromagnetic Outflows
Tan & Blackman (2004)
m* >~ 20-30 M (polar)
m* >~ 100 M
m* ~ 200 M
m* >~ 100-500 M
Comparison: then and now
The first stars
H2 cooling, T~200K
ns ~104cm-3; M~200M
thermal pressure
-> single, isolated stars
The latest stars
CO/dust cooling, T~10-20K
ns ~106cm-3; dn/dM ~ M-2
nonthermal (B) pressure, turbulent
-> fragmentation to star cluster
ionization, Ly-,
MHD outflows?
Rad.pressure on dust
MHD outflows
Combined feedback of many stars
Implications for supernovae and enrichment
However, initial stellar mass
is not the final pre-SN mass
(Meynet & Maeder)
Feedback on neighboring cores
via dissociation of H2
tdissociation = tff --->
-> Limit to rate of Pop III star formation
Implications for SMBH formation
It is difficult to form a star that is massive enough
so its final pre-SN mass is >260M.
Thus Pop III stellar remnants are likely to be relatively
low-mass black holes.
Conclusions
Convergent initial conditions for star formation: set by H2 cooling
Mostly thermal pressure support + slow cooling
-> no fragmentation -> single ~massive star in each mini-halo
Accretion rate + semi-analytic model for protostellar evolution:
large (~AU) protostar, contracts to main sequence for m*>30M
This is when feedback processes start to become important
Feedback processes depend on core rotation and are complicated:
Gradual reduction in SF efficiency because of ionizing and radiation
pressure feedback for m*>30M. Final mass, ~100-200M,
likely to be set by ionizing feedback on the accretion disk
Implications of massive star formation in each mini-halo?
Are low-mass zero metallicity stars possible?
How effective is external feedback?
Is this mode of star formation inevitable in all zero metal DM halos?
Are these the seeds of supermassive black holes?
Evolution of ionizing luminosity with
varying mdot
Evolution of Lyman-Werner photon
luminosity
overview
Radial profile allowing for varying mdot
Initial Conditions for Star Formation from
Abel, Bryan, Norman 02
core rotation (ABN)
Numerical Simulations: Methods
Bromm, Coppi, Larson 1999; Abel, Bryan, Norman 2000,2002
Abel, Bryan, Norman (2002):
Eulerian AMR; Riemann solver
non-eq. chemistry of 9 species
optically thin radiative losses:
line cooling
Compton heating/cooling
tot=1, =0 , b=0.06,z=100
scale invariant power spectrum
(128kpc)3 comoving
Identify region of 1st DM halo
with ~106Msun, then focus here
with DM particle mass =1Msun
Grid refinement to resolve:
Jeans mass, density contrasts,
and cooling timescales
Disk Photoevaporation
Weak wind case:
.
for zero age main sequence
Equate with mass accretion rate
Hollenbach et al. 94
Mass Limits vs. Core Rotation
Disk Photoevaporation
Overview of Structure Formation
1. Recombination z ≈1200, start of “dark ages”
2. Thermal equilibrium matter-CMB until z ≈160
: independent of z
e.g. globular clusters
3. Thermal decoupling,
4. “First Light”
5. Reionization,
e.g. galaxies
Madau (2002)