Primordial Star Formation: Constraints on the IMF from Protostellar Feedback

Jonathan C. TanETH Zurich

Christopher F. McKeeUC Berkeley

Eric G. BlackmanUniversity of Rochester

Image from Scientific American and V. Bromm

Reionization

Metal Enrichment

Illumination

Progenitors of SN and GRBs?

Influence on Quasars, Globular Clusters, Galaxies?

“Simple” problem: initial conditions, chemistry,no feedback from other stars, weak B-fields(?)

First Stars and the Dawn of Complexity

depend onstellar mass (IMF)

CMB polarization (WMAP Kogut et al. 03)H 21cm (LOFAR Morales & Hewitt 03)

Z of halo stars (Christlieb et al. 03)

NIR bkg. intensity (Santos et al. 02NIR bkg. fluctuations (Kashlinsky et al. 04)

Observations

(Tumlinson, Venkatesan

& Shull 2004)

JWST (Weinmann & Lilly 2005)SWIFT (Bromm & Loeb 2002)

Hydrogen Ionizing Luminositiesalong the Primordial Main Sequence

Tumlinson & Shull 00; Bromm et al. 01;Ciardi et al. 01; Schaerer 02

Initial mass determines nucleosynthetic yields and final remnant

Heger & Woosley 2002

Near Infra-RedBackground

Potential signature of firststars in the NIR EBL (Salvaterra & Ferrara 02)

But zodiacal subtraction isuncertain.

EBL

galaxies

Overview of Structure Formation

1. Recombination z ≈1200, start of “dark ages”2. Thermal equilibrium matter-CMB until z ≈160

: independent of ze.g. globular clusters

3. Thermal decoupling,

Madau (2002)

4. “First Light”5. Reionization,

e.g. galaxies

Numerical Simulations: Methods

Abel, Bryan, Norman (2002):

Bromm, Coppi, Larson 1999; Abel, Bryan, Norman 2000,2002

Eulerian AMR; Riemann solvernon-eq. chemistry of 9 speciesoptically thin radiative losses: line cooling Compton heating/cooling

tot=1, =0 , b=0.06,z=100scale invariant power spectrum(128kpc)3 comovingIdentify region of 1st DM halowith ~106Msun, then focus herewith DM particle mass =1Msun

Grid refinement to resolve: Jeans mass, density contrasts, and cooling timescales

Numerical Simulations: Results

Abel, Bryan, Norman (2002)

1. Form pre-galactic halo ~105-6Msun

2. Form quasi-hydrostatic gas coreinside halo: M≈4000Msun,r ≈10pc,nH ≈10cm-3, fH2 ≈10-3, T>=200K

2. Rapid 3-body H2 formation for nH>1010cm-3

strong cooling supersonic inflow.

The initial conditions for primordial star formation

Chemical Composition Trace H2 formation: H + e— H— +

H + H— H2 + 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 contractionDensity structure: ~self-similar, r -2.2

More chemistry: at high density >108cm-3

H+H+H -> H2 + Hefficient cooling -> dynamical collapse

Rotation: core forms from mergers andcollapse along filaments: expect J>0fKep vcirc / vKep ~ 0.5

Abel, Bryan, Norman (2002)

The Accretion Rateand Formation Timescale

Density structure: self-similar, r -k, k≈2.2~singular polytropic sphere in virial and hydrostatic equilibrium P = K , =1.1

r -k

Ripamonti et al. 2002

Om

ukai & Nishi 1998

Abel et al. 2002

.Accretion rate: m*= * m / tff(m) f(m,K)(Tan & McKee 2004)

K=1.9x1012(T/300K)(nH/104cm-3)-0.1cgsK’=K/ 1.9x1012cgs*=1.4 (Hunter 1977)

m*(t=2Myr) ≈ 2000Msun

.“Isentropic Accretion”

Collapse to a Disk

Geometry of Streamlines

Conserve J during free-fallinside sonic point (Ulrich 1976)

rd = f2Kepr0 3.4 (M/Msun)9/7 AU

Anticipate accretion drivenby large scale grav. instabilitiesand local gravitational viscosity (Gammie 2001)

viscosity = cs h, <0.3

fragmentationtcool< 3-1

STAR

DISK

Toomre stability parameter

<1 -> unstable>1 -> stable

orbital angular velocity

soundspeed

surfacedensity

Are disks are stable with respect to fragmentation?

Disk Models

Surface density

Thickness

Ionization

TemperatureTc , Teff

Toomre Q

=0.3

m*

.17x10-3Msun/yr 6.4x10-3Msun/yr 2.4x10-3Msun/yr

(Shakura &Sunyaev 1973; Tan & McKee 2004; Tan & Blackman 2004)

Disks arestable

One zone model:follow energy ofprotostar as it

accretes

Evolution of the Protostar depends on Accretion Rate

Deuterium burning for Tc>106KStructural rearrangement after tKelvin

Eddington model for Solve for r*(m*), until reach main sequence

Assume polytropic stellar structure and continuous sequence of equilibria

(Stahler et al. 1980; Palla & Stahler 1991; Nakano 1995; Behrend & Maeder 2001; Omukai & Palla 2001, 2003; Tan & McKee 2003)

r*

m*

Evolution of the Protostar

Initial conditionm* = 0.04 Msun

r* = 14 Rsun

(Ripamonti et al. 02)

Protostar is large (~100 Rsun) until it is older than tKelvin

Contraction to Main SequenceAccretion along Main Sequence

Comparison with Stahler et al. (1986), Omukai & Palla (2001)

Photosphere

Accretion Shock

Main Sequence(Schaerer 2002)

:Radius

Evolution of the Protostar:Luminosity

Boundary Layer

Accretion Disk

Internal

Total

Evolution of the Protostar :IonizingLuminosity

Spherical, fKep=0

fKep=0.5Total

Internal

Boundary Layer

Accretion Disk

Main Sequence(Schaerer 2002)

Spectrum depends on initial rotationc.f. Omukai & Palla (2003)

Growth of the HII RegionBalance ionizing flux vs recombinations and infall

Find stellar mass at breakoutrHII = rg

polar; equatorial

Breakout mass vs rotation

Infall likely to be suppressedfor rHII>rg , where vesc=ci

HII Region

1 in HI around HII region :

Photons diffuse in freq. and spaceNormalize J to appropriate Velocity field: Voigt profile D ;Line profile: damping wings

Ly- and FUV Radiation Pressure

L

Escape after n scatterings, or 2 photon decayfreq. shift ; mean free path at escapediffusion 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

Mass Limits vs. Core Rotation

Breakout in polar direction

Disk Photoevaporation

Weak wind case:

for zero age main sequence

.

Hollenbach et al. 94

Equate with mass accretion rate

Mass Limits vs. Core Rotation

Disk Photo-evaporation

When does accretion end?

Ly- Radiation Pressure

Ionization

Disk Evaporation

Hydromagnetic Outflows

Declining accretion versus increasing feedback

m* >~ 20-30 Msun (polar)

m* >~ 100 Msun

m* ~ 100-200 Msun

m* >~ 100-500 Msun

Tan & Blackman (2004)

McK

ee &

Tan

, in

prep

ConclusionsConvergent initial conditions for star formation: set by H2 cooling

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 radiationpressure 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?

Mostly thermal pressure support + slow cooling -> no fragmentation -> single ~massive star in each mini-halo

Evolution of accretion and outflow rates

Vertical structure of disk

Evolution of ionizing luminosity with varying mdot

Evolution of Lyman-Werner photon luminosity

overview

Radial profile of disk

Radial profile allowing for varying mdot

Comparison: then and now

The first stars The latest starsH2 cooling, T~200K CO/dust cooling, T~10-20Kns ~104cm-3; M~300Msun ns ~106cm-3; dn/dM ~ M-2

thermal pressure nonthermal (B) pressure, turbulent-> single, isolated stars -> fragmentation to star cluster

ionization, Ly-, Rad.pressure on dustMHD outflows? MHD outflows

Combined feedback of many stars

Initial Conditions for Star Formation from Abel, Bryan, Norman 02

core rotation (ABN)