Star Formation in Disk Galaxies

Protostellar Feedback Processes and the Mass of the First Stars

Primordial Mini-Halo (Abel, Bryan, Norman) Jonathan Tan (University of Florida) In collaboration with: Christopher McKee (Berkeley) Eric Blackman (Rochester) Aravind Natarajan (CMU) Brian O’Shea (MSU) Britton Smith (Colorado) Dan Whalen (CMU) Aaron Boley (Florida) Sylvia Eksröm (Geneva) Cyril Georgy (Geneva) Lessons from local star formation

A complicated, nonlinear process Physics: Gravity vs pressure (thermal, magnetic, turbulence, radiation, cosmic rays) and shear. Heating and cooling, generation and decay of turbulence, generation (dynamo) and diffusion of B-ﬁelds, etc. Chemical evolution of dust and gas. Lessons from local star formation

Wide range of scales (~12 dex in space, time) and multidimensional. Uncertain/unconstrained initial conditions/boundary conditions. Lessons from local star formation

A complicated, nonlinear process Physics: Gravity vs pressure (thermal, magnetic, turbulence, radiation, cosmic rays) and Complete theory of star formation shear. Heating and cooling, generation and decay of turbulence, generation (dynamo) and diffusion of B-ﬁelds, etc. Chemical evolution of dust and gas. Analytic theory Wide range of scales (~12 dex in space, time) and multidimensional. Uncertain/unconstrained initial conditions/boundary conditions. Lessons from local star formation

Wide range of scales (~12 dex in Observations space, time) and multidimensional. Uncertain/unconstrained initial conditions/boundary conditions. Lessons from local star formation

Wide range of scales (~12 dex in Observations space, time) and multidimensional. Uncertain/unconstrained initial conditions/boundary conditions. The First Stars

Image from Scientiﬁc American and V. Bromm The First Stars

Image from Scientiﬁc American and V. Bromm Complete theory of Pop III star formation Analytic theory Numerical models Observations The First Stars

Image from Scientiﬁc American and V. Bromm Complete theory of Pop III star formation Analytic theory Numerical models The First Stars

Image from Scientiﬁc American and V. Bromm Complete theory of Pop III star formation Analytic theory Numerical models PopIII Initial Conditions The First Stars

Image from Scientiﬁc American and V. Bromm Complete theory of Pop III star formation Analytic theory Numerical models PopIII Initial Conditions Importance of First Stars and their Mass Observations CMB polarization (WMAP Page et al. 07) Reionization (H, He) H 21cm (LOFAR Morales & Hewitt 04)

Z of low Z halo stars (Beers & Christlieb 05, Metal Enrichment Scannapieco et al. 2006) proto-galaxies and IGM Z of Lya forest?(Schaye et al. 03 Norman et al. 04)

NIR bkg. intensity (Santos et al. 02; Fernandez & Komatsu 06) Illumination NIR bkg. ﬂuctuations (Kashlinsky et al. 04)

JWST (Weinmann & Lilly 2005) SN & GRBs? SWIFT (Bromm & Loeb 2002)

Progenitors of IMBHs/SMBHs? ULXs (Mii & Totani 2005) Quasars (Fan et al. 03; Willott et al. 03) Early Galaxies? NIR cts (Stark et al. 07)

Inﬂuence on structure formation: Supermassive Black Holes, Globular Clusters, Galaxies? -6 -3.5 Critical Z~10 (Omukai ea. 05) to 10 Z (Bromm & Loeb 2003) Importance of First Stars and their Mass Observations CMB polarization (WMAP Page et al. 07) Reionization (H, He) H 21cm (LOFAR Morales & Hewitt 04)

Z of low Z halo stars (Beers & Christlieb 05, Metal Enrichment Scannapieco et al. 2006) proto-galaxies and IGM Z of Lya forest?(Schaye et al. 03 Norman et al. 04)

NIR bkg. intensity (Santos et al. 02; Fernandez & Komatsu 06) Illumination NIR bkg. ﬂuctuations (Kashlinsky et al. 04)

JWST (Weinmann & Lilly 2005) SN & GRBs? SWIFT (Bromm & Loeb 2002)

Progenitors of IMBHs/SMBHs? ULXs (Mii & Totani 2005) Quasars (Fan et al. 03; Willott et al. 03) Early Galaxies? NIR cts (Stark et al. 07)

Tanvir, Berger et al. 2009

Z of low Z halo stars (Beers & Christlieb 05, Metal Enrichment Scannapieco et al. 2006) proto-galaxies and IGM Z of Lya forest?(Schaye et al. 03 Norman et al. 04)

NIR bkg. intensity (Santos et al. 02; Fernandez & Komatsu 06) Illumination NIR bkg. ﬂuctuations (Kashlinsky et al. 04)

JWST (Weinmann & Lilly 2005) SN & GRBs? SWIFT (Bromm & Loeb 2002)

Progenitors of IMBHs/SMBHs? ULXs (Mii & Totani 2005) Quasars (Fan et al. 03; Willott et al. 03) Early Galaxies? NIR cts (Stark et al. 07)

Inﬂuence on structure formation: Supermassive Black Holes, Globular Clusters, Galaxies? -6 -3.5 Critical Z~10 (Omukai ea. 05) to 10 Z (Bromm & Loeb 2003) Numerical Simulations: Results Abel, Bryan, Norman (2002) 1. Form pre-galactic minihalo 6 ~10 M

2. Form quasi-hydrostatic gas core inside halo:

M≈4000M, r ≈10 pc, -3 -3 nH ≈10 cm , fH2 ≈10 , T~>200K

3. Rapid 3-body H2 formation 10 -3 at nH>~10 cm . Strong cooling -> supersonic inﬂow. Numerical Simulations: Results Abel, Bryan, Norman (2002) 1. Form pre-galactic minihalo 6 ~10 M

2. Form quasi-hydrostatic gas core inside halo:

M≈4000M, r ≈10 pc, -3 -3 nH ≈10 cm , fH2 ≈10 , T~>200K

3. Rapid 3-body H2 formation 10 -3 at nH>~10 cm . Strong cooling -> supersonic inﬂow. 4. 1D simulations (Omukai & Nishi 1998): Form quasi-hydrostatic protostar nH ≈1016-17cm-3, T ≈2000 K: optically thick, adiabatic contraction -> hydrostatic core

with m*≈0.005M, r*≈14R Numerical Simulations: Results Abel, Bryan, Norman (2002) 1. Form pre-galactic minihalo 6 ~10 M

2. Form quasi-hydrostatic gas core inside halo:

M≈4000M, r ≈10 pc, -3 -3 nH ≈10 cm , fH2 ≈10 , T~>200K

with m*≈0.005M, r*≈14R More recent 3D sims. of Turk, Yoshida, Abel, Bromm, Norman etc. reach ~stellar densities, but then grind to a halt (small dynamical timescales), still at small (<

protostellar masses. We turn to analytic models... when does accretion stop? 100M?? Deﬁnitions McKee & Tan (2008); O’Shea et al. (2008; First Stars III Conference Summary)

Population III

Stars having a metallicity so low (Z

Population III.1 The initial conditions for the formation of Population III.1 stars (halos) are determined solely by cosmological ﬂuctuations.

Population III.2 The initial conditions for the formation of Population III.2 stars (halos) are signiﬁcantly affected by other astrophysical sources (external to their halo). Physical Processes in Pop III.1 star formation

Radiative Feedback (McKee & Tan 2008)

Protostellar Evolution (Omukai & Palla 2003; Tan & McKee 2004)

Magnetic Field Generation?

Rotation & Disk Structure; Fragmentation? (Tan & Blackman 2004)

Dark Matter Annihilation Heating? (Spolyar et al. 2008; Natarajan, Tan, O’Shea 2009)

Accretion Rate (Tan & McKee 2004)

Initial Conditions (Abel ea, Bromm ea, Yoshida ea, Omukai ea.) polytropic structure:

Analytic models for star formation, including efects of radiative and mechanical feedback

Tan & McKee 2004: Accretion rate, disk structure, protostellar evolution

Tan & Blackman 2004: Magnetic ﬁeld growth, mechanical feedback from outﬂows

McKee & Tan 2008: Radiative feedback (Ly-alpha radiation pressure, ionization)

Natarajan, Tan, O’Shea, in prep: DM annihilation Initial conditions: Entropy and Rotation Yoshida et al. 2006 Density structure: self-similar, k≈2.2

~singular polytropic sphere in virial and hydrostatic equilibrium

Model with γ=1.1 Initial conditions: Entropy and Rotation Yoshida et al. 2006 Density structure: self-similar, k≈2.2

~singular polytropic sphere in virial and hydrostatic equilibrium

Model with γ=1.1

H2 cooling -> 4 -3 Tmin ~ 200 K, ncrit ~ 10 cm Initial conditions: Entropy and Rotation Yoshida et al. 2006 Density structure: self-similar, k≈2.2

~singular polytropic sphere in virial and hydrostatic equilibrium

Model with γ=1.1

H2 cooling -> 4 -3 Tmin ~ 200 K, ncrit ~ 10 cm

Resulting accretion rate Physical Processes in Pop III.1 star formation

Radiative Feedback (McKee & Tan 2008)

Protostellar Evolution (Omukai & Palla 2003; Tan & McKee 2004)

Magnetic Field Generation?

Rotation & Disk Structure; Fragmentation? (Tan & Blackman 2004)

Dark Matter Annihilation Heating? (Spolyar et al. 2008; Natarajan, Tan, O’Shea 2009)

Accretion Rate (Tan & McKee 2004)

Initial Conditions (Abel ea, Bromm ea, Yoshida ea, Omukai ea.) polytropic structure:

Analytic models for star formation, including efects of radiative and mechanical feedback

Tan & McKee 2004: Accretion rate, disk structure, protostellar evolution

Tan & Blackman 2004: Magnetic ﬁeld growth, mechanical feedback from outﬂows

McKee & Tan 2008: Radiative feedback (Ly-alpha radiation pressure, ionization)

Natarajan, Tan, O’Shea, in prep: DM annihilation Physical Processes in Pop III.1 star formation

Radiative Feedback (McKee & Tan 2008)

Protostellar Evolution (Omukai & Palla 2003; Tan & McKee 2004)

Magnetic Field Generation?

Rotation & Disk Structure; Fragmentation? (Tan & Blackman 2004)

Dark Matter Annihilation Heating? (Spolyar et al. 2008; Natarajan, Tan, O’Shea 2009)

Accretion Rate (Tan & McKee 2004)

Initial Conditions (Abel ea, Bromm ea, Yoshida ea, Omukai ea.) polytropic structure:

Analytic models for star formation, including efects of radiative and mechanical feedback

Tan & McKee 2004: Accretion rate, disk structure, protostellar evolution

Tan & Blackman 2004: Magnetic ﬁeld growth, mechanical feedback from outﬂows

McKee & Tan 2008: Radiative feedback (Ly-alpha radiation pressure, ionization)

Natarajan, Tan, O’Shea, in prep: DM annihilation Physical Processes in Pop III.1 star formation

Radiative Feedback (McKee & Tan 2008)

Protostellar Evolution (Omukai & Palla 2003; Tan & McKee 2004)

Magnetic Field Generation?

Rotation & Disk Structure; Fragmentation? (Tan & Blackman 2004)

Dark Matter Annihilation Heating? (Spolyar et al. 2008; Natarajan, Tan, O’Shea 2009)

Accretion Rate (Tan & McKee 2004)

Initial Conditions (Abel ea, Bromm ea, Yoshida ea, Omukai ea.) polytropic structure:

Analytic models for star formation, including efects of radiative and mechanical feedback

Tan & McKee 2004: Accretion rate, disk structure, protostellar evolution

Tan & Blackman 2004: Magnetic ﬁeld growth, mechanical feedback from outﬂows

McKee & Tan 2008: Radiative feedback (Ly-alpha radiation pressure, ionization)

Natarajan, Tan, O’Shea, in prep: DM annihilation Physical Processes in Pop III.1 star formation

Radiative Feedback (McKee & Tan 2008)

Protostellar Evolution (Omukai & Palla 2003; Tan & McKee 2004)

Magnetic Field Generation?

Rotation & Disk Structure; Fragmentation? (Tan & Blackman 2004)

Dark Matter Annihilation Heating? (Spolyar et al. 2008; Natarajan, Tan, O’Shea 2009)

Accretion Rate (Tan & McKee 2004)

Initial Conditions (Abel ea, Bromm ea, Yoshida ea, Omukai ea.) polytropic structure:

Analytic models for star formation, including efects of radiative and mechanical feedback

Tan & McKee 2004: Accretion rate, disk structure, protostellar evolution

Tan & Blackman 2004: Magnetic ﬁeld growth, mechanical feedback from outﬂows

McKee & Tan 2008: Radiative feedback (Ly-alpha radiation pressure, ionization)

Natarajan, Tan, O’Shea, in prep: DM annihilation Physical Processes in Pop III.1 star formation

Radiative Feedback (McKee & Tan 2008)

Protostellar Evolution (Omukai & Palla 2003; Tan & McKee 2004)

Magnetic Field Generation?

Rotation & Disk Structure; Fragmentation? (Tan & Blackman 2004)

Dark Matter Annihilation Heating? (Spolyar et al. 2008; Natarajan, Tan, O’Shea 2009)

Accretion Rate (Tan & McKee 2004)

Initial Conditions (Abel ea, Bromm ea, Yoshida ea, Omukai ea.) polytropic structure:

Analytic models for star formation, including efects of radiative and mechanical feedback

Tan & McKee 2004: Accretion rate, disk structure, protostellar evolution

Tan & Blackman 2004: Magnetic ﬁeld growth, mechanical feedback from outﬂows

McKee & Tan 2008: Radiative feedback (Ly-alpha radiation pressure, ionization)

Natarajan, Tan, O’Shea, in prep: DM annihilation Physical Processes in Pop III.1 star formation Stellar Evolution Schaerer 2002

Radiative Feedback (McKee & Tan 2008)

Protostellar Evolution (Omukai & Palla 2003; Tan & McKee 2004)

Magnetic Field Generation?

Rotation & Disk Structure; Fragmentation? (Tan & Blackman 2004)

Dark Matter Annihilation Heating? (Spolyar et al. 2008; Natarajan, Tan, O’Shea 2009)

Accretion Rate (Tan & McKee 2004)

Initial Conditions (Abel ea, Bromm ea, Yoshida ea, Omukai ea.) polytropic structure:

Analytic models for star formation, including efects of radiative and mechanical feedback

Tan & McKee 2004: Accretion rate, disk structure, protostellar evolution

Tan & Blackman 2004: Magnetic ﬁeld growth, mechanical feedback from outﬂows

McKee & Tan 2008: Radiative feedback (Ly-alpha radiation pressure, ionization)

Natarajan, Tan, O’Shea, in prep: DM annihilation Collapse to a disk around a central protostar

fKep Rotation: core forms from mergers and collapse along ﬁlaments: expect J>0

fKep ≡ vcirc / vKep ~ 0.5 Collapse to a disk around a central protostar

fKep Rotation: core forms from mergers and collapse along ﬁlaments: expect J>0

fKep ≡ vcirc / vKep ~ 0.5

STAR

DISK Collapse to a disk around a central protostar

fKep Rotation: core forms from mergers and collapse along ﬁlaments: expect J>0

fKep ≡ vcirc / vKep ~ 0.5

Expect accretion within the disk is driven by large scale gravitational instabilities and local gravitational viscosity (Gammie 2001). viscosity

ν = α cs h, α <0.3 STAR

DISK Collapse to a disk around a central protostar

fKep Rotation: core forms from mergers and collapse along ﬁlaments: expect J>0

fKep ≡ vcirc / vKep ~ 0.5

Expect accretion within the disk is driven by large scale gravitational instabilities and local gravitational viscosity (Gammie 2001). viscosity

ν = α cs h, α <0.3 STAR We now construct simple models for the protostar and disk DISK Collapse to a disk around a central protostar

fKep Rotation: core forms from mergers and collapse along ﬁlaments: expect J>0

fKep ≡ vcirc / vKep ~ 0.5

Expect accretion within the disk is driven by large scale gravitational instabilities and local gravitational viscosity (Gammie 2001). viscosity

ν = α cs h, α <0.3 STAR We now construct simple models for the protostar and disk [Toomre stable] DISK Evolution of the Protostar depends on Accretion Rate (Stahler et al. 1980; Palla & Stahler 1991; Nakano 1995; Omukai & Palla 2003; Tan & McKee 2004; Hosokawa & Omukai 2009; Ohkubo et al. 2009)

Assume polytropic stellar structure and continuous sequence of equilibria One zone model: follow energy of protostar as it accretes Evolution of the Protostar depends on Accretion Rate (Stahler et al. 1980; Palla & Stahler 1991; Nakano 1995; Omukai & Palla 2003; Tan & McKee 2004; Hosokawa & Omukai 2009; Ohkubo et al. 2009)

Assume polytropic stellar structure and continuous sequence of equilibria One zone model: follow energy of protostar as it accretes 6 Deuterium burning for Tc>10 K

Structural rearrangement after tKelvin Eddington model for β

Solve for r*(m*), until reach main sequence Evolution of the Protostar depends on Accretion Rate (Stahler et al. 1980; Palla & Stahler 1991; Nakano 1995; Omukai & Palla 2003; Tan & McKee 2004; Hosokawa & Omukai 2009; Ohkubo et al. 2009)

Assume polytropic stellar structure and continuous sequence of equilibria One zone model: follow energy of protostar as it accretes 6 Deuterium burning for Tc>10 K

Structural rearrangement after tKelvin Eddington model for β

Solve for r*(m*), until reach main sequence high accretion rate r*

low accretion rate main sequence m* Evolution of the Protostar depends on Accretion Rate (Stahler et al. 1980; Palla & Stahler 1991; Nakano 1995; Omukai & Palla 2003; Tan & McKee 2004; Hosokawa & Omukai 2009; Ohkubo et al. 2009)

Assume polytropic stellar structure and continuous sequence of equilibria One zone model: follow energy of protostar as it accretes 6 Deuterium burning for Tc>10 K

Structural rearrangement after tKelvin Eddington model for β

Solve for r*(m*), until reach main sequence high accretion rate r* Here we assume dark matter annihilation heating is negligible low accretion rate main sequence m* Protostar Evolution: Ionizing Luminosity

Boundary Layer

Accretion Disk Protostar Evolution: Ionizing Luminosity

Star Boundary Layer

Accretion Disk Protostar Evolution: Ionizing Luminosity Total

Star Boundary Layer

Accretion Disk Protostar Evolution: Ionizing Luminosity Total Protostar Evolution: Ionizing Luminosity Total

Main Sequence (Schaerer 2002) Protostar Evolution: Ionizing Luminosity Total

fKep=0.5

Spherical, fKep=0 Main Sequence (Schaerer 2002)

Spectrum depends on initial rotation c.f. Omukai & Palla (2003) Overview of Radiative Feedback McKee & Tan (2008)

Hollenbach et al. (1994)

See also Omukai & Inutsuka (2002); Hosokawa & Omukai (2009) Feedback-limited accretion McKee & Tan (2008)

Self-consistent model for growth & evolution of protostar including: -accretion rate(t) -accretion disk(t,r,z) -protostellar structure(t) -ionizing feedback(t) Feedback-limited accretion McKee & Tan (2008)

Self-consistent model for growth & evolution of protostar including: -accretion rate(t) -accretion disk(t,r,z) -protostellar structure(t) -ionizing feedback(t) No. 1, 2007 POPULATION III STAR FORMATION IN ÃCDM UNIVERSE. I. 69

TABLE 1 Simulation Parameters

Run L box l min m DM mgas, init mgas, max 20 40 halo

L0_30 simulations: 4 L0_30A...... 0.3 115.3 2.60 0.40 5.43 ; 10À 0.1964 1.873 1.153 2.557 4 L0_30B ...... 0.3 115.3 2.60 0.40 5.43 ; 10À 0.1952 2.176 1.322 2.858 4 L0_30C ...... 0.3 115.3 2.60 0.40 5.43 ; 10À 0.1995 1.981 1.319 2.778 4 L0_30D...... 0.3 115.3 2.60 0.40 5.43 ; 10À 0.1922 2.727 1.702 3.022 L0_45 simulations: 3 L0_45A...... 0.45 173.0 8.76 1.35 1.83 ; 10À 0.1879 2.669 1.873 3.615 3 L0_45B ...... 0.45 173.0 8.76 1.35 1.83 ; 10À 0.1860 2.726 1.872 3.343 3 L0_45C ...... 0.45 173.0 8.76 1.35 1.83 ; 10À 0.1906 2.375 1.563 3.293 3 L0_45D...... 0.45 173.0 8.76 1.35 1.83 ; 10À 0.1861 1.959 1.191 3.827 L0_60 simulations: 3 L0_60A...... 0.6 230.6 20.8 3.20 4.34 ; 10À 0.1815 2.458 1.790 3.154 3 L0_60B ...... 0.6 230.6 20.8 3.20 4.34 ; 10À 0.1802 3.049 1.956 3.340 3 L0_60C ...... 0.6 230.6 20.8 3.20 4.34 ; 10À 0.1815 2.840 2.121 3.466 3 L0_60D...... 0.6 230.6 20.8 3.20 4.34 ; 10À 0.1959 2.700 1.814 4.147

1 Notes.—Lbox is the size of the simulation volume in comoving hÀ Mpc; lmin is the minimum comoving spatial resolution element in comoving AU; m DM is the dark matter particle mass within the highest resolution static nested grid in units of M ; mgas,init is the mean baryon mass resolution within the highest resolution static nested grid in units of M , at the beginning of the simulation; mgas,max is the mean baryon mass resolution within the highest level grid cell at the end of the simulation in units of

M ; is the dispersion in overdensities of the baryon gas within the highest resolution static nested grid at the beginning of the simulation; 20 and 40 are the mean overdensity of all gas within 20 and 40 virial radii of the halo whose core is collapsing, at the epoch of collapse (calculated as described in the text), in units of bc; halo is the statistical probability of the halo in which the primordial protostellar cloud forms, at the redshift of collapse, assuming Gaussian statistics and the same Eisenstein & Hu CDM power spectrum as is used to initialize our calculations (Eisenstein & Hu 1999). the dark matter density is smoothed on a comoving scale of cal simulations the Jeans length must be resolved by at least four 0.5 pc (a proper scale of 0.025 pc at z 20). This is reason- grid cells, is always maintained by a significant margin. Simu- able because at that radius in all of our calculations the gravi- lations that force the Jeans length to be resolved by a minimum tational potential is completely dominated by the baryons. of 4 and 64 cells produce results that are essentially identical to Grid cells are adaptively refined based on several criteria: those presented here. baryon and dark matter overdensities in cells of 4.0 and 8.0, re- 3. EVOLUTION OF A REPRESENTATIVE spectively, and checks to ensure that the pressure jump and/or PROTOSTELLAR CORE energy ratios between adjoining cells never exceed 5.0, that the cooling time in a given cell is always longer than the sound cross- In this section we describe in detail the collapse of a single ing time of that cell, and that the Jeans length is always resolved primordial protostellar core out of the ensemble discussed in 4. by at least 16 cells. This guarantees that the Truelove criterion This simulation, L0_30A, was selected out of the four simula-x 1 (Truelove et al. 1997), which is an empirical result showing that tions performed in a 0.3 hÀ Mpc comoving volume. The results in order to avoid artificialA gravitational Population fragmentation in numeri- of Popdescribed hereIII.1 are qualitatively Halos similar for all of the calculations TABLE 2 O’Shea &Norman 2007 Halo Properties

Run zcoll Mvir Rvir Tvir Mb fbar k dm k gas

L0_30 simulations: L0_30A...... 19.28 4.18 ; 105 118.1 1120.0 4.59 ; 104 0.823 0.050 0.022 55.1 L0_30B ...... 22.19 2.92 ; 105 91.7 1009.6 2.91 ; 104 0.753 0.066 0.029 3.3 L0_30C ...... 20.31 6.92 ; 105 132.9 1646.8 7.56 ; 104 0.819 0.053 0.034 17.3 L0_30D...... 24.74 1.36 ; 105 64.0 671.4 1.29 ; 104 0.711 0.046 0.014 12.7 L0_45 simulations: L0_45A...... 28.70 2.41 ; 105 67.4 1131.7 2.03 ; 104 0.631 0.108 0.056 8.4 L0_45B ...... 26.46 2.42 ; 105 72.7 1052.8 2.28 ; 104 0.706 0.019 0.019 34.0 L0_45C ...... 24.74 5.21 ; 105 100.1 1645.6 5.21 ; 104 0.750 0.054 0.015 97.4 L0_45D...... 28.67 5.89 ; 105 90.5 2060.0 5.71 ; 104 0.727 0.059 0.071 11.4 L0_60 simulations: L0_60A...... 24.10 3.96 ; 105 93.8 1338.0 4.29 ; 104 0.813 0.052 0.027 26.0 L0_60B ...... 25.64 3.82 ; 105 87.3 1385.6 3.72 ; 104 0.730 0.047 0.056 11.0 L0_60C ...... 28.13 1.68 ; 105 60.7 876.9 1.29 ; 104 0.575 0.027 0.016 40.0 L0_60D...... 32.70 2.85 ; 105 62.5 1440.9 2.06 ; 104 0.542 0.049 0.033 10.0

Notes.—Mean halo properties at the collapse redshift. Here zcoll is the collapse redshift of the halo, deﬁned as the redshift at which the central baryon density of the halo 10 3 reaches nH 10 cm ; M , R , and T are the halo virial mass, radius, and temperature at that epoch, respectively;M is the total baryon mass within the virial radius at ’ À vir vir vir b that epoch, and fbar is the baryon mass fraction (in units of b/ m); kdm and kgas are the halo dark matter and gas spin parameters, respectively, and is the angle of separation (in degrees) between the bulk dark matter and gas angular momentum vectors.Mvir and Mb are in units of M , Rvir is in units of proper parsecs, and Tvir is in units of kelvins.

Numerical Kʼ Proﬁles and Accretion Rates Tan, Smith et al., in prep zcoll=22.19

. . m*(infall,SPS)=mevap

m*f(SPS)=220M

m*f(infall)=310M Numerical Kʼ Proﬁles and Accretion Rates Tan, Smith et al., in prep zcoll=32.70

. . m*(infall,SPS)=mevap

m*f(SPS)=690M

m*f(infall)=59M Pop III.1 IMF [m*f(infall)] Tan, Smith et al., in prep

Highly tentative... Pop III.1 m*f versus z Model uncertainties -Dark Matter Annihilation Heating Delayed contraction to the main sequence

-HII region breakout

-Disk photoevaporation

-Protostellar evolution Model uncertainties -Dark Matter Annihilation Heating Delayed contraction to the main sequence

-HII region breakout Rayleigh-Taylor instabilities (Whalen & Norman 2008) Diversion of accretion ﬂow to equatorial plane (rather than radial expulsion)

-Disk photoevaporation

-Protostellar evolution Model uncertainties -Dark Matter Annihilation Heating Delayed contraction to the main sequence

-HII region breakout Rayleigh-Taylor instabilities (Whalen & Norman 2008) Diversion of accretion ﬂow to equatorial plane (rather than radial expulsion)

-Disk photoevaporation Normalization of basic Hollenbach et al. model Effect of protostellar outﬂow Non-spherical large-scale accretion to core

-Protostellar evolution Model uncertainties -Dark Matter Annihilation Heating Delayed contraction to the main sequence

-HII region breakout Rayleigh-Taylor instabilities (Whalen & Norman 2008) Diversion of accretion ﬂow to equatorial plane (rather than radial expulsion)

-Disk photoevaporation Normalization of basic Hollenbach et al. model Effect of protostellar outﬂow Non-spherical large-scale accretion to core

-Protostellar evolution Rotation, especially anisotropic ionizing ﬂux Model uncertainties -Dark Matter Annihilation Heating Delayed contraction to the main sequence

-HII region breakout Rayleigh-Taylor instabilities (Whalen & Norman 2008) Diversion of accretion ﬂow to equatorial plane (rather than radial expulsion)

-Disk photoevaporation Normalization of basic Hollenbach et al. model Effect of protostellar outﬂow Non-spherical large-scale accretion to core

-Protostellar evolution Rotation, especially anisotropic ionizing ﬂux Model uncertainties -Dark Matter Annihilation Heating Delayed contraction to the main sequence

-HII region breakout Rayleigh-Taylor instabilities (Whalen & Norman 2008) Diversion of accretion ﬂow to equatorial plane (rather than radial expulsion)

-Disk photoevaporation Normalization of basic Hollenbach et al. model Effect of protostellar outﬂow Non-spherical large-scale accretion to core

For m*=140M, T =105K -> 7x104K ( =80º) -Protostellar evolution eff θ Fi reduced by factor of 3 Rotation, especially anisotropic ionizing ﬂux m*,max -> 1.4 m*,max = 200M Model uncertainties -Dark Matter Annihilation Heating Delayed contraction to the main sequence

-HII region breakout Rayleigh-Taylor instabilities (Whalen & Norman 2008) Diversion of accretion ﬂow to equatorial plane (rather than radial expulsion)

-Disk photoevaporation Normalization of basic Hollenbach et al. model Effect of protostellar outﬂow Non-spherical large-scale accretion to core

For m*=140M, T =105K -> 7x104K ( =80º) -Protostellar evolution eff θ Fi reduced by factor of 3 Rotation, especially anisotropic ionizing flux m*,max -> 1.4 m*,max = 200M Heating by WIMP Dark Matter Annihilation? Spolyar, Freese, Gondolo (2008) conclude WIMP annihilation heating is important for n > 1013cm-3 or r < 20 AU. Could delay or halt collapse: dark matter powered -3 protostar. Main uncertainties: ρDM(r<10 pc), mχ, <σv>, ftrap Heating by WIMP Dark Matter Annihilation? Spolyar, Freese, Gondolo (2008) conclude WIMP annihilation heating is important for n > 1013cm-3 or r < 20 AU. Could delay or halt collapse: dark matter powered No. 1, 2009 DARK-3 MATTER ANNIHILATION AND PRIMORDIAL STAR FORMATION 577 protostar. Main uncertainties: ρDM(r<10 pc), mχ, <σv>, ftrap Natarajan, Tan, O’Shea (2009) examined the ρDM profiles of 3 simulated minihalos, finding steepening for r<0.5pc, i.e. where -2 baryons dominate. Here ρDM∝r .

Figure 2. Dark matter density profiles (spherical averages) for simulations A (top), B (middle), and C (bottom) are shown with the open squares. Power law fits to the outer, well-resolved regions (fit #1) are shown with the dashed lines, while fits to the inner (but not innermost—see text), less well-resolved, regions (fit #2) are shown with the dotted lines. 2 significant steepening compared to the outer regions. This is σav a + bv + is largely constant, that is, the constant $ %≈ ··· likely to be the result of adiabatic contraction, since it occurs at term a is non-zero. We may then estimate σav using the sim- $ % a scale 1 pc where the density of baryons begins to dominate. ple freeze-out condition nχ (T ) σav H (T ) at the freeze-out ∼ F $ % = F We emphasize again that the simulation points on which DM temperature TF. nχ is the particle number density, and H is the fits #2 are based correspond to bins with only a small (<100) Hubble parameter. Since the entropy per comoving volume re- number of particles and must be treated with caution. We do mains constant as the universe expands, we may equate nχ /s note, however, that on the very innermost scales ( 0.01 pc) at freeze-out with the value today, to solve for σav . Deter- ∼ $ % the dark matter density profiles in the numerical simulations are mined in this way, σav depends on the particle mass mχ only $ % even steeper than the analytic DM fits #2. through the quantity x/√g. x mχ /TF while g is the num- If adiabatic contraction of dark matter in the baryon- ber of relativistic degrees of freedom= at freeze-out. Following dominated potential is responsible for sculpting these profiles, Green et al. (2005), we find that for the range of mχ we consider one expects that the maximum steepness of the dark matter (10 GeV to 1 TeV), x varies from 25 to 27. Assuming x 25, density profile will be equal to that of the baryons, which has we find that g varies from 65 to 100≈ in the relevant mass≈ range been shown in simulations to have an approximate power law (see, i.e., Jungman et al. 1996; Kolb & Turner 1990). In our 2.2 profile of ρgas r− (see Section 3.2). The baryonic den- following analysis, we neglect the mass dependence of x/ g ∝ √ sity profile inevitably flattens in its center, so that the power (i.e., a factor of 1.15 as mχ varies from 10 GeV to 1000 GeV), law profile is only valid inwards to some core radius r . This 26 3 1 c and we assume σav 3 10− cm s− (see, e.g., Jungman core radius shrinks as collapse proceeds. In situations where et al. 1996). We$ shall%≈ see× that much larger uncertainties result we are interested in the global luminosity provided by WIMP from the shape of the dark matter density distribution. annihilation in the halo (Section 3.3), we will assume that the The variation of H (r) on the WIMP mass, mχ , is also shown dark matter density profile also exhibits this core radius, inside in Figure 3. We consider cases with mχ 10 GeV and 1 TeV, of which its density is also constant. For the fiducial case, we that is, factors of 10 below and above our fiducial= value. Once the assume a dark matter particle mass of mχ 100 GeV, which is 1 = simple mχ− dependence of H (r) (Equation (10)) is accounted typical for a weakly interacting particle. We then consider factor for, we see that remaining variations in H(r) are within about a of 10 variations in this mass. factor of 2. These are due to the mχ dependencies of the photon The photon multiplicity function dNγ /dEγ for mixed multiplicity function, the energy integral, and the S(r, r ,E) gaugino-higgsino dark matter is given by the form (Bergstrom¨ ) bx 1.5 function. et al. 1998; Feng et al. 2001) dNγ /dx ae− /x where ! " = It is also informative to compare H (r) to the energy generated x Eγ /mχ and (a, b) are constants for the particular anni- by WIMP annihilation per unit volume, per unit time hilation= channel. We average over the important annihilation channels, namely WW, ZZ, tt, bb, and uu, considered by the ¯ ¯ 2 1 authors (given in Feng et al. (2001), and average¯ over the dif- ρ (r) σav dN G(r) χ $ % dx x γ . (12) ferent channels to obtain (a 0.9,b 9.56). We assume that = 2m dx = = χ #0 580 NATARAJAN, TAN, & O’SHEA Vol. 692

WIMP Annihilation Heating Rate / Baryonic Cooling Rate

m χ=10GeV

m χ =100GeV

m χ =1TeV

Figure 5. Ratio of dark matter annihilationModels heating assume rate, Hannihilation(r), to baryonic rate cooling coefficient rate, C <(σr),v>=3x10 for dark-26 mattercm3 densitys-1 fits #1 (top panels) and #2 (bottom panels) for simulations A (solid lines), B (long-dashed lines), C (dot-dashed lines) for mχ 100 GeV. Results for simulation A with mχ 10 GeV (dotted lines) and mχ 1 TeV (dashed lines) are also shown. = = = the central part of the halo for α > 1.5 (Equation (12)), which to 100 AU, and is independent of the much smaller core χ ∼ is the case for all DM fits #2. We solve for the core radius, rc, for radius, which adjusts itself so as to provide enough WIMP each simulation via the condition Lχ (r ) Lgas(r ), annihilation luminosity to match that radiated away by the that is, →∞ = →∞ baryons. We note our solution has made the approximation that the 3 3 4πrc ∞ 2 4πrc baryonic properties used to estimate Lgas do not include the H(rc)+4π dr r H (r) C(rc) effects of WIMP annihilation heating. This effect would lead to 3 r = 3 ! c hotter temperatures and more efficient cooling, so that the actual +4π ∞ dr r2 C(r). (16) equilibrium structure would be somewhat smaller and denser. r Energy transport from the hotter inner part of the halo to the ! c outer cooler part, either via convection or radiation, would be This is an equilibrium condition in the sense that the energy needed to set up a hydrodynamic equilibrium; that is, a dark generation rate by dark matter annihilation heating balances that matter powered (proto)star. The size of this star would be set radiated away by the baryons. Note that for the profiles analyzed by the τ 1 surface, beyond which the energy flux from the here, both heating and cooling luminosities are dominated by interior is= free to escape. The results of Yoshida et al. (2006) the central regions; that is, the integrals converge to a finite value imply that the cooling efficiency has dropped to 0.1 by the time as r . Note also that the local heating will dominate local n 1012 cm 3, corresponding to about 30 AU. This is an →∞ H − cooling in an inner region that is somewhat larger than rc, and approximate= upper limit to the initial size of the protostar, since cooling will dominate heating outside of this region. the actual gas temperature will be somewhat hotter and a larger Figure 6 shows the luminosity profiles for DM fit #2 for fraction of the radiated energy would be in the continuum (as simulations A, B, and C with mχ 100 GeV,and for simulation opposed to line radiation). = A with mχ 10 GeV and 1 TeV. Also shown is L for = gas the fiducial model. With mχ 100 GeV, the core radii for 3.4. Subsequent Evolution of the Dark Matter Powered = simulations A, B, C are rc 7.4, 2.2, 19 AU, respectively, and Protostar = Lχ (r ) 1460, 1540, 781 L , respectively. The dark Since there is a large mass reservoir at large r that is →∞ = # 12 matter density in these cores are ρχ,c 1.5 10 , 7.5 undergoing cooling, baryons will continue to accrete to the 12 11 3 = × × 10 , 3.0 10 GeV cm− , respectively. For simulation A central protostar, deepening the gravitational potential and thus × with mχ 10 GeV and 1 TeV, we find rc 37, 0.93 AU, causing more dark matter to be concentrated here also. For = = respectively, Lχ (r ) 960, 1510 L , respectively, and simulation A, DM fit#2 and mχ 100 GeV with rc 7.4 AU, 10 →∞ =13 3 # = = ρχ,c 6.2 10 , 9.2 10 GeV cm− , respectively. the mass inside rc is 0.17 M , and the accretion rate is close = × × 1 # 1 The constancy of these total luminosities is set by the baryonic to 0.1 M yr− with infall speeds of about 4 km s− (Yoshida cooling luminosity, which is dominated by the region from 10 et al. 2006# ), which are mildly supersonic. As the central mass ∼ 580 NATARAJAN, TAN, & O’SHEA Vol. 692

WIMP Annihilation Heating Rate / Baryonic Cooling Rate

m χ=10GeV

m χ =100GeV

m χ =1TeV

WIMP Annihilation Heating Rate / Baryonic Cooling Rate

m χ=10GeV

m χ =100GeV

m χ =1TeV

See also Spolyar et al. 2009

Talks by Freese, Iocco Summary: Population III.1 Star Formation

• Quasi equilibrium massive cores form in dark matter mini halos (simulations of structure formation) • Standard accretion physics suggests single (or binary) stars form in each minihalo • Mass likely to set by radiative (ionization) feedback -> m* ~ 100M⦿ • Dark Matter (WIMP) annihilation may change this story. • Pop III.2: may be lower-mass stars due to external radiative feedback, but more complicated. Summary: Population III.1 Star Formation

Enclosed Luminosity Proﬁles of “Equilibrium” Conﬁgurations

=1TeV) χ (m =100GeV) =10GeV) χ χ χ L (m (m L χ L χ

=100GeV) χ (m gas L χ L Enclosed Luminosity Proﬁles of “Equilibrium” Conﬁgurations

=1TeV) χ (m =100GeV) =10GeV) χ χ χ L (m (m L χ L χ

=100GeV) χ (m gas L χ L Enclosed Luminosity Proﬁles of Subsequent evolution: “Equilibrium” Conﬁgurations Baryons continue to accrete causing the star to need a larger luminosity to be supported.

Even if no additional DM accretes, the WIMP annihilation =1TeV) luminosity still rises χ dramatically as the star (m =100GeV) =10GeV) χ χ χ L (m (m contracts: L χ L χ

Contraction from 10AU to 1AU 6 leads to L~10 L, enough to support a ~100M star. The depletion time becomes similar to the growth time ~105yr. =100GeV) χ (m gas L χ L Enclosed Luminosity Proﬁles of Subsequent evolution: “Equilibrium” Conﬁgurations Baryons continue to accrete causing the star to need a larger luminosity to be supported.

Even if no additional DM accretes, the WIMP annihilation =1TeV) luminosity still rises χ dramatically as the star (m =100GeV) =10GeV) χ χ χ L (m (m contracts: L χ L χ

Contraction from 10AU to 1AU 6 leads to L~10 L, enough to support a ~100M star. The depletion time becomes similar to the growth time ~105yr. =100GeV) WIMP annihilation heating may χ (m gas delay contraction to the main L χ L sequence and thus radiative feedback truncation of accretion, which could lead to supermassive Pop III.1 stars. 3 protostar formation) to 2.58cs /G at small radii (Hunter 1977), an increase of a factor 3.7. This demonstrates that caution should be exercised in inferring accretion rates at late times from those measured at early times. Spolyar et al. [33] considered the effect of heating due to WIMP dark matter annhilation on the collapse of Pop III.1 pre-stellar cores. In their fiducial model of the dark matter density profile and for a WIMP mass of 100 GeV, heating dominates cooling (as evaluated 13 −3 Protostellar accretion rate by Yoshida et al. [31]) for nH > 10 cm , i.e. in the 3inner ∼ 20 AU. In this case the collapse can be expected protostarTan formation) & McKee 2008 to 2.58csto/ beG haltedat small inside this radii region (Hunter and a quasi-hydrostatic 1977), an increase of a factor 3.7.object Thiscreated, demonstrates although detailed models that of the dynamics remain to be worked out. However, as more baryons caution should be exercised infrom inferring the outer accretion regions cool and rates join at this central core, late times from those measuredthe at luminosity early times. needed to support it increases rapidly with mass; the increase provided by WIMP annihilation FIGURE 1. Mass accretionSpolyar rate onto et the al. protostar [33]+disk considered as is uncertain. the However, effect in of view heating of the fact that most a function of theirdue total to mass WIMPm∗d for the dark case of matternegligible annhilationof the later accretion on theof baryons collapse should occur through stellar feedback. Solid line is the fiducial model from Tan & a disk (see below), which would tend to enhance the " McKee [26] (withofK = Pop1) from III.1 eq. (4). pre-stellarDotted line is from cores. the baryon In their to dark fiducial matter mass model ratio in the of central disk and 1D model of Omukai & Nishi [27]. Dashed line is the analytic star, we expect any heating due to WIMP annhilation result from Ripamontithe et dark al. [28]. Dot-dashed matterline density is the settling profile and for a WIMP mass inflow rate at the final stage of the simulation of Abel et al. [23], will diminish in importance as the stellar mass grows. now as a functionof of the 100 enclosed GeV, mass. Note heating that the decline dominates of It should cooling be noted that (as the evaluated WIMP annhilation heating this rate at small masses is due to the lack of the full set of high rate depends13 sensitively−3 on the density profile of the density cooling processesby Yoshida in their simulation. et al.Long-dashed [31]) forline nHdark> matter,10 whichcm is so, far i.e. not in adequately the resolved in is the equivalentinner quantity∼ from20 Yoshida AU. et In al.[31]. thisDot-long- case thenumerical collapse simulations can of be Pop expected III.1 core formation. dashed line is the sink particle accretion rate of Bromm & Loeb [25]. to be halted inside this region and a quasi-hydrostatic object created, although detailedProtostar models and of the Accretion dynamics Disk Evolution choose a fiducialremain value of f tod = 1 be/3 appropriate worked for out. disk However, as more baryons masses limited by enhanced viscosity due to self-gravity. Assuming dark matter annhilation does not have a sig- We compare thisfrom analytic the accretion outer rate regions (for the case cool of nificant and join effect this on the central main phase core, of protostellar accre- no feedback) withthe numerical luminosity estimates in needed Fig. 1. to supporttion and noting it increases that there may rapidly be a range of accretion O’Shea & Norman [32] studied the properties of Pop rates depending on the formation redshift [32], we now III.1 pre-stellarwith cores mass; as a function the of increase redshift. They providedconsider by what WIMP happens annihilation to the collapsing gas as it forms found that cores at higher redshift are hotter in their a protostar and accretion disk at rates that are initially is uncertain. However, in view−2 of the−1 fact that" most FIGURE 1. Mass accretion rate onto the protostar+diskouter as regions, have higher free electron fractions and ∼> 10 M$ yr (i.e. eq. 4 with K ∼ 1). − Rotation of the infalling gas has a dramatic effect on a function of their total mass m∗d for the case of negligibleso form largerof amounts the of later H2 (via accretion H ), although of these baryons should occur through stellar feedback. Solid line is the fiducial model from Tanare always & smalla disk fractions (see of the below), total mass. which As the wouldthe evolution tend of the to protostar, enhance since it the leads to lower gas " centers of the cores contract above the critical density of densities and optical depths in the regions near the stellar McKee [26] (with K = 1) from eq. (4). Dotted line is from4 the−3 surface that are above and below the disk. This leads 10 cm , thosebaryon with higher to H2 darkfractions matter are able to mass cool ratio in the central disk and smaller photospheric radii and thus higher temperature 1D model of Omukai & Nishi [27]. Dashed line is the analyticmore effectivelystar, and thus we maintain expect lower any temperatures heating due to WIMP annhilation result from Ripamonti et al. [28]. Dot-dashed line is the settlingto the point of protostar formation. The protostar thus radiation fields that can then have a stronger dynamical accretes from lower-temperaturewill diminish gas in and importance the accretion influence as the on stellar the infall. mass Following grows. the treatment of Tan & inflow rate at the final stage of the simulation of Abel et al. [23], 3 3/2 McKee [26], we parameterize the rotation in terms of rates, proportional to cs ! T , are smaller. Measuring now as a function of the enclosed mass. Note that the declineinfall o ratesf at theIt time should of protostar be formation noted at that the scale the WIMP annhilation heating vrot(rsp) of M = 100M$,rate O’Shea depends & Norman find sensitively accretion rates of on the densityf profileKep ≡ of, the (5) this rate at small masses is due to the lack of the full set of high−4 −1 −2 −1 ∼ 10 M$ yr at z = 30, rising to ∼ 2 × 10 M$ yr vKep(rsp) density cooling processes in their simulation. Long-dashedat linez = 20. Thisdark corresponds matter, to a which range in K is" of so 0.20 far not adequately resolved in the ratio of the rotational velocity to the Keplerian veloc- is the equivalent quantity from Yoshida et al.[31]. Dot-long-to 2.4. However, for Hunter’s mildly subsonic solution, numerical simulations of Popity III.1 measured core at the formation. sonic point at r . Averaging in spher- which we have suggested is closest to the numerical sp dashed line is the sink particle accretion rate of Bromm & Loeb ical shells, Abel, Bryan, & Norman [23] found f ∼ 0.5 simulations, the accretion rate increases from 0.70c3/G Kep s independent of radius, so we adopt this as a fiducial [25]. at large radii (r ' c t, where t = 0 is the moment of s value. If angular momentum is conserved inside the sonic Protostar and Accretion Disk Evolution choose a fiducial value of fd = 1/3 appropriate for disk masses limited by enhanced viscosity due to self-gravity. Assuming dark matter annhilation does not have a sig- We compare this analytic accretion rate (for the case of nificant effect on the main phase of protostellar accre- no feedback) with numerical estimates in Fig. 1. tion and noting that there may be a range of accretion O’Shea & Norman [32] studied the properties of Pop rates depending on the formation redshift [32], we now III.1 pre-stellar cores as a function of redshift. They consider what happens to the collapsing gas as it forms found that cores at higher redshift are hotter in their a protostar and accretion disk at rates that are initially −2 −1 " outer regions, have higher free electron fractions and ∼> 10 M$ yr (i.e. eq. 4 with K ∼ 1). − Rotation of the infalling gas has a dramatic effect on so form larger amounts of H2 (via H ), although these are always small fractions of the total mass. As the the evolution of the protostar, since it leads to lower gas centers of the cores contract above the critical density of densities and optical depths in the regions near the stellar 4 −3 surface that are above and below the disk. This leads 10 cm , those with higher H2 fractions are able to cool more effectively and thus maintain lower temperatures smaller photospheric radii and thus higher temperature to the point of protostar formation. The protostar thus radiation fields that can then have a stronger dynamical accretes from lower-temperature gas and the accretion influence on the infall. Following the treatment of Tan & 3 3/2 McKee [26], we parameterize the rotation in terms of rates, proportional to cs ! T , are smaller. Measuring infall rates at the time of protostar formation at the scale vrot(rsp) of M = 100M$, O’Shea & Norman find accretion rates of fKep ≡ , (5) −4 −1 −2 −1 ∼ 10 M$ yr at z = 30, rising to ∼ 2 × 10 M$ yr vKep(rsp) at z = 20. This corresponds to a range in K" of 0.20 the ratio of the rotational velocity to the Keplerian veloc- to 2.4. However, for Hunter’s mildly subsonic solution, ity measured at the sonic point at r . Averaging in spher- which we have suggested is closest to the numerical sp ical shells, Abel, Bryan, & Norman [23] found f ∼ 0.5 simulations, the accretion rate increases from 0.70c3/G Kep s independent of radius, so we adopt this as a fiducial at large radii (r ' c t, where t = 0 is the moment of s value. If angular momentum is conserved inside the sonic point, then the accreting gas forms a disk with an outer radius 2 9/7 fKep m∗d,2 "−10/7 rd = 1280 K AU, ! 0.5 " ! !¯∗d " 2 9/7 f m∗ → 1850 Kep ,2 AU, (6) ! 0.5 " K"10/7

where the → is for the case with fd = 1/3. The first gas to collapse has a small disk- circularization radius and falls directly on to the protostar. The size of the protostar depends on the accretion rate during its formation history. At lower masses there is a balance in the size set by the need to Protostellar radius Tan & McKee 2008 point, then the accreting gas forms a disk with an outer radiate the luminosity, which is mostly due to accretion, with a photospheric temperature that is likely to be close radius to ∼ 6000 K because the opacity due to H− rapidly 2 9/7 declines below this temperature. Under the assumption FIGURE 2. Evolution of protostellar radius with mass, based fKep m∗d,2 "−10/7 of spherical accretion, Stahler, Palla, & Salpeter [34] on the model of Tan & McKee [26]. All models shown have rd = 1280 K AU, found the protostellar radius to be a rotation parameter fKep = 0.5. The solid line shows the ! 0.5 " ! !¯∗d " evolution of the fiducial model with K" = 1, a Shakura-Sunyaev 0.27 0.41 disk viscosity parameter of " = 0.01, and a reduction of 9/7 r∗ & 67(m∗/M') m˙ ∗,−2 R', (7) ss 2 accretion rate due to feedback effects [15], which becomes fKep m∗,2 → 1850 AU, (6) ≡ −2 −1 important for m∗ ∼> 50M'. The star joins the main sequence "10/7 wherem ˙ ∗,−2 m˙ ∗/(10 M' yr ). For the accretion ! 0.5 " K rates typical of primordial star formation we see that the [36], shown by the long dashed line, at about 80M'. The dot- − size is large, but small compared to the disk radius for dashed line, visible only from 50 100M', shows the same where the → is for the case with f = 1/3. model but with no reduction in accretion rate due to feedback d masses ∼> M'. effects. The dot-long-dashed line, visible up to about 20M' The first gas to collapse has a small disk- As the star grows in mass its internal luminosity in- shows the fiducial model, but with "ss = 0.3 (appropriate for creases rapidly and begins to dominate over accretion lu- viscosity driven by self-gravity [37]). The dotted line shows the circularization radius and falls directly on to the " minosity [35, 26]. Once the star is older than its instanta- fiducial model but with K = 2, while the dashed line shows the " protostar. The size of the protostar depends on the neous Kelvin-Helmholz time (i.e. its gravitational energy K = 0.5 case. accretion rate during its formation history. At lower divided by its internal luminosity), it begins to contract masses there is a balance in the size set by the need to towards the main sequence configuration. At this time there is an associated temporary swelling of the outer by simple Shakura-Sunyaev "ss-disk models. Two di- radiate the luminosity, which is mostly due to accretion, layers of star by a factor of about two due to structural re- mensional simulations of clumpy, self-gravitating disks & −1 arrangements inside the star. According to Schaerer [36], show self-regulation with "ss (#tth) up to a maxi- with a photospheric temperature that is likely to be close & − the main sequence radius for nonrotating stars is mum value "ss 0.3 [37], where # is the orbital angular to ∼ 6000 K because the opacity due to H rapidly 4 velocity, tth ≡ $kTc,d/(%Teff,d) is the thermal timescale, 0.55 declines below this temperature. Under the assumption FIGURE 2. r∗Evolution& 4.3m∗,2 ofR' protostellar(main sequence radius) with(8) mass,$ basedis the surface density, Tc,d is the disk’s central (mid- on the model of Tan & McKee [26]. All models shownplane) have temperature, and Teff,d the effective photospheric of spherical accretion, Stahler, Palla, & Salpeter [34] ≤ ≤ a rotationto within parameter 6% for 0.4f m∗,=2 03..5. If theThe starsolid continuesline to showstemperature the at the disk’s surface. Fragmentation occurs found the protostellar radius to be accrete and gain mass,Kep it will approximately follow this evolution of the fiducial model with K" = 1, a Shakura-Sunyaevwhen #tth ∼< 3: this condition has the best chance of be- mass-size relation, although rotation will tend to swell ing satisfied in the outermost parts of the disk that are still 0.27 0.41 disk viscositythe equatorial parameter surface layers of " somewhat.= 0.01, The and evolution a reduction of r∗ & 67(m∗/M') m˙ ∗,−2 R', (7) ss optically thick. However, Tan & Blackman [40] consid- of the protostellar radius is shown for several models in accretion rate due to feedback effects [15], which becomesered the gravitational stability of constant "ss = 0.3 disks ≡ −2 −1 importantFig. 2 for m∗ > 50M'. The star joins the main sequencefed at accretion rates given by eq. 4 and found that the wherem ˙ ∗,−2 m˙ ∗/(10 M' yr ). For the accretion The high accretion∼ rates of primordial protostars make [36], shown by the long dashed line, at about 80M'. Theopticallydot- thick parts of the disk remained Toomre stable rates typical of primordial star formation we see that the it likely that the disk will build itself up to a mass that dashed line, visible only from 50 − 100M', shows the( sameQ > 1) during all stages of the growth of the protostar. size is large, but small compared to the disk radius for is significant compared to the stellar mass. At this point We therefore expect that most Pop III.1 accretion disks, modelthe but disk with becomes no reduction susceptible in to accretion global (m rate= 1 due mode) to feedback masses > M'. at least in their early stages, will grow in mass and mass ∼ effects.gravitational The dot-long-dashed instabilities [38,line, 39], which visible are expectedup to about to 20surfaceM' density to the point at which gravitational insta- As the star grows in mass its internal luminosity in- showsbe the efficient fiducial at driving model, inflow but to with the star,"ss = thus0. regulating3 (appropriatebilities, for both global and local, then mediate accretion to creases rapidly and begins to dominate over accretion lu- viscositythe disk driven mass. by Thus self-gravity we assume [37]). a fixed The ratiodotted of diskline to showsthe the star. " minosity [35, 26]. Once the star is older than its instanta- fiducialstellar model mass, butfd with= 1/3,K in= our2, models. while the dashed line showsIn the addition to gravitational instabilities, the magneto- K" = 0.5Accretion case. through the disk may also be driven by lo- rotational instability (MRI) may develop if dynamically neous Kelvin-Helmholz time (i.e. its gravitational energy cal instabilities, the effects of which can be approximated divided by its internal luminosity), it begins to contract towards the main sequence configuration. At this time there is an associated temporary swelling of the outer by simple Shakura-Sunyaev "ss-disk models. Two di- layers of star by a factor of about two due to structural re- mensional simulations of clumpy, self-gravitating disks & −1 arrangements inside the star. According to Schaerer [36], show self-regulation with "ss (#tth) up to a maximum value "ss & 0.3 [37], where # is the orbital angular the main sequence radius for nonrotating stars is 4 velocity, tth ≡ $kTc,d/(%Teff,d) is the thermal timescale, 0.55 r∗ & 4.3m∗,2 R' (main sequence) (8) $ is the surface density, Tc,d is the disk’s central (midplane) temperature, and Teff,d the effective photospheric to within 6% for 0.4 ≤ m∗,2 ≤ 3. If the star continues to temperature at the disk’s surface. Fragmentation occurs accrete and gain mass, it will approximately follow this when #tth ∼< 3: this condition has the best chance of be- mass-size relation, although rotation will tend to swell ing satisfied in the outermost parts of the disk that are still the equatorial surface layers somewhat. The evolution optically thick. However, Tan & Blackman [40] consid- of the protostellar radius is shown for several models in ered the gravitational stability of constant "ss = 0.3 disks Fig. 2 fed at accretion rates given by eq. 4 and found that the The high accretion rates of primordial protostars make optically thick parts of the disk remained Toomre stable it likely that the disk will build itself up to a mass that (Q > 1) during all stages of the growth of the protostar. is significant compared to the stellar mass. At this point We therefore expect that most Pop III.1 accretion disks, the disk becomes susceptible to global (m = 1 mode) at least in their early stages, will grow in mass and mass gravitational instabilities [38, 39], which are expected to surface density to the point at which gravitational insta- be efficient at driving inflow to the star, thus regulating bilities, both global and local, then mediate accretion to the disk mass. Thus we assume a fixed ratio of disk to the star. stellar mass, fd = 1/3, in our models. In addition to gravitational instabilities, the magneto- Accretion through the disk may also be driven by lo- rotational instability (MRI) may develop if dynamically cal instabilities, the effects of which can be approximated and " R 4

Protostellar Disk Radial Structure , hibit local 300 , evaluated at , $ y is neglected); 100 = ∗ r ottom the panels show (1) surface , for which ; (3) midplane ionization fractions " # M 100 , 10 , 1 = ∗ m 01 and . 0 stability parameter, and Rosseland mean opacity = ss Q ! poral averages of the disk, which, being turbulent, would ex (the dotted lines show results for when the ionization energ d , , Toomre c T orb n , and ratio of gas pressure to total pressure, r / h , respectively, i.e. from eq. 4 with no feedback. From top to b 1 − yr " M 3 − 10 × ; (4) disk midplane temperature, ) + 4 2 . Protostellar disk structure [40] for models with 2 , He 4 , . + 6 ; (2) ratio of scaleheight to radius, , " He 17 , + =( ∗ ˙ ﬂuctuations. FIGURE 3. of H the midplane. Note that all quantities are azimuthal and tem (5) number of orbits before accretion to the star, m density,

FIGURE 3. Protostellar disk structure [40] for models with !ss = 0.01 and m∗ = 1,10,100M", for which r∗ = 100,300,4R" and −3 −1 m˙ ∗ =(17,6.4,2.4) × 10 M" yr , respectively, i.e. from eq. 4 with no feedback. From top to bottom the panels show (1) surface density, "; (2) ratio of scaleheight to radius, h/r, and ratio of gas pressure to total pressure, #; (3) midplane ionization fractions + + 2+ of H , He , He ; (4) disk midplane temperature, Tc,d (the dotted lines show results for when the ionization energy is neglected); (5) number of orbits before accretion to the star, norb, Toomre Q stability parameter, and Rosseland mean opacity $, evaluated at the midplane. Note that all quantities are azimuthal and temporal averages of the disk, which, being turbulent, would exhibit local ﬂuctuations. Protostellar Disk Vertical Structure

FIGURE 4. Vertical structure of the accretion disk at r = FIGURE 6. Protostellar H-ionizing photon luminosities for $ $ 10r∗ " 43R# for m∗ = 100 M#, K = 1, fKep = 0.5 and no models with K = 0.5,1,2(dashed, solid, dotted lines). The reduction in accretion efﬁciency due to feedback. total luminosity is shown with the higher line and the accretion luminosity (boundary layer + inner disk) is shown with the lower line. The zero age main sequence H-ionizing luminosities [36] are indicated with the long-dashed line.

plified by large factors. For typical rotation parameters fKep " 0.5, this radiation pressure becomes larger than the ram pressure of the infalling gas in the polar directions for stellar masses of order 20M#. However, once the infall is reversed at the poles, the Lyman-! photons can escape and the accretion in other directions proceeds relatively unimpeded. Thus we expect Lyman-! radiation pressure to have only a minor effect on the accretion efficiency. The next feedback effect to occur is the expansion of the H II region to distances larger than the gravitational FIGURE 4. Vertical structure of the accretion disk at r = FIGURE 6. Protostellar H-ionizingescape radius photonr for luminosities ionized gas. This distancefor is $ $ g 10r∗ " 43R# for m∗ = 100 M#, K = 1, fKep = 0.5 and no models with K = 0.5,1,2(dashed, solid, dotted lines). The G" m∗ 2.5 ≡ Edd d reduction in accretion efficiency due to feedback. total luminosity is shown with the higherrg line2 and= 260 the"Edd accretionm∗d,2 AU, (18) FIGURE 5. Protostellar bolometric luminosities for models ci ! T4 " with K$ = 0.5,1,2(luminositydashed, solid, dotted (boundarylines). In each layer case the+ inner disk) is shown with the total luminosity is shown with the higher line and the accretion 4 lower line. The zero age main sequencewhere T4 H-ionizingis the ionized gas luminosit temperatureies in units of 10 K luminosity (boundary layer + inner disk) is shown with the and we have taken the gravitating mass to be m and lower line. The Eddington[36] are limit indicated is indicated with with the dot-long- the long-dashed line. ∗d dashed line and the zero age main sequence luminosity [36] we have allowed for the decrease in the radius due to with the long-dashed line. radiation pressure from electron scattering through the factor L "Edd ≡ 1 − , (19) region is confinedplified there. As by the large ionizing factors. luminosity in- For typical rotation parametersLEdd creases, the H II region can begin to expand into the in- where L = 4 Gmc/ is the Eddington limit. fKep " 0.5, this radiation pressureEdd becomes# $Thomson larger than falling envelope, penetrating furthest along the rotation Shortly after the H II region reaches rg, pressure forces axes. At the ionized-neutralthe ram boundary, pressure radiation of the pressure infallingin the ionizedgas in gas the become polar large direc- enough to reverse the feedback is exertedtions due for to resonant stellar scattering masses of FUV of orderinfall to 20 theM protostar.#. However, This effect once will occur first in the radiation in the Lyman-! damping wings. As a result polar directions, typically at about 50M# in our fiducial of the high columnthe densities infall of is neutral reversed gas around at the the poles,model. For the rotation Lyman- parameters! photonsfKep " 0.5, expansion in H II region, thiscan radiation escape is trapped and and the the pressure accretion am- inthe other equatorial directions directions (just proceeds above the accretion disk) relatively unimpeded. Thus we expect Lyman-! radiation pressure to have only a minor effect on the accretion efficiency. The next feedback effect to occur is the expansion of the H II region to distances larger than the gravitational escape radius rg for ionized gas. This distance is

G" m∗ 2.5 ≡ Edd d rg 2 = 260"Edd m∗d,2 AU, (18) FIGURE 5. Protostellar bolometric luminosities for models ci ! T4 " with K$ = 0.5,1,2(dashed, solid, dotted lines). In each case the total luminosity is shown with the higher line and the accretion 4 where T4 is the ionized gas temperature in units of 10 K luminosity (boundary layer + inner disk) is shown with the and we have taken the gravitating mass to be m and lower line. The Eddington limit is indicated with the dot-long- ∗d dashed line and the zero age main sequence luminosity [36] we have allowed for the decrease in the radius due to with the long-dashed line. radiation pressure from electron scattering through the factor L "Edd ≡ 1 − , (19) region is confined there. As the ionizing luminosity in- LEdd creases, the H II region can begin to expand into the in- where LEdd = 4#Gmc/$Thomson is the Eddington limit. falling envelope, penetrating furthest along the rotation Shortly after the H II region reaches rg, pressure forces axes. At the ionized-neutral boundary, radiation pressure in the ionized gas become large enough to reverse the feedback is exerted due to resonant scattering of FUV infall to the protostar. This effect will occur first in the radiation in the Lyman-! damping wings. As a result polar directions, typically at about 50M# in our fiducial of the high column densities of neutral gas around the model. For rotation parameters fKep " 0.5, expansion in H II region, this radiation is trapped and the pressure am- the equatorial directions (just above the accretion disk) FIGURE 4. Vertical structure of the accretion disk at r = FIGURE 6. Protostellar H-ionizing photon luminosities for $ $ 10r∗ " 43R# for m∗ = 100 M#, K = 1, fKep = 0.5 and no models with K = 0.5,1,2(dashed, solid, dotted lines). The reduction in accretion efficiency due to feedback. total luminosity is shown with the higher line and the accretion luminosity (boundary layer + inner disk) is shown with the lower line. The zero age main sequence H-ionizing luminosities [36] are indicated with the long-dashed line.

plified by large factors. For typical rotation parameters FIGURE 4. Vertical structure of the accretion disk at r = FIGURE 6. Protostellar H-ionizingfKep photon" 0.5, this luminosities radiation pressure for becomes larger than $ $ the ram pressure of the infalling gas in the polar direc- 10r∗ " 43R# for m∗ = 100 M#, K = 1, f = 0.5 and no models with K = 0.5,1,2(dashed, solid, dotted lines). The Kep tions for stellar masses of order 20M#. However, once reduction in accretion efficiency due to feedback. total luminosity is shown with the higherthe infall line is reversed and the at accret the poles,ion the Lyman-! photons luminosity (boundary layer + innercan disk) escape is and shown the accretion with in theother directions proceeds Protostellar Luminositylower line. The zero age main sequencerelatively H-ionizing unimpeded. luminosit Thus weies expect Lyman-! radia- [36] are indicatedTan & McKee with 2008 the long-dashedtion pressureline. to have only a minor effect on the accretion efficiency. The next feedback effect to occur is the expansion of the H II region to distances larger than the gravitational escape radius r for ionized gas. This distance is plified by large factors. For typical rotationg parameters G" m∗ 2.5 f " 0.5, this radiation pressure becomes≡ Edd d larger than Kep rg 2 = 260"Edd m∗d,2 AU, (18) FIGURE 5. Protostellar bolometric luminosities for models ci ! T4 " with K$ = 0.5,1,the2(dashed, ram solid, pressure dotted lines). of In eachthe case infalling the gas in the polar direc- total luminosity is shown with the higher line and the accretion 4 tions for stellar masses of orderwhere 20MT4#is. the However, ionized gas temperature once in units of 10 K luminosity (boundary layer + inner disk) is shown with the and we have taken the gravitating mass to be m and lower line. The Eddingtonthe infall limit is indicated reversed with the atdot-long- the poles, the Lyman-! photons ∗d dashed line and the zero age main sequence luminosity [36] we have allowed for the decrease in the radius due to with the long-dashedcanline. escape and the accretion in otherradiation directions pressure from proceeds electron scattering through the factor relatively unimpeded. Thus we expect Lyman-! radia-L "Edd ≡ 1 − , (19) region is confinedtion there. pressure As the ionizing to have luminosity only a in- minor effect on the accretionLEdd creases, the H IIefficiency.region can begin to expand into the in- where LEdd = 4#Gmc/$Thomson is the Eddington limit. falling envelope, penetrating furthest along the rotation Shortly after the H II region reaches rg, pressure forces axes. At the ionized-neutralThe next boundary, feedback radiation effect pressure to occurin the ionized is the gas expansion become large of enough to reverse the feedback is exertedthe H dueII toregion resonant to scattering distances of FUV largerinfall than to the the protostar. gravitational This effect will occur first in the radiation in the Lyman-! damping wings. As a result polar directions, typically at about 50M# in our fiducial escape radius rg for ionized gas. This distance is of the high column densities of neutral gas around the model. For rotation parameters fKep " 0.5, expansion in H II region, this radiation is trapped and the pressure am- the equatorial directions (just above the accretion disk) G" m∗ 2.5 ≡ Edd d rg 2 = 260"Edd m∗d,2 AU, (18) FIGURE 5. Protostellar bolometric luminosities for models ci ! T4 " with K$ = 0.5,1,2(dashed, solid, dotted lines). In each case the total luminosity is shown with the higher line and the accretion 4 where T4 is the ionized gas temperature in units of 10 K luminosity (boundary layer + inner disk) is shown with the and we have taken the gravitating mass to be m and lower line. The Eddington limit is indicated with the dot-long- ∗d dashed line and the zero age main sequence luminosity [36] we have allowed for the decrease in the radius due to with the long-dashed line. radiation pressure from electron scattering through the factor L "Edd ≡ 1 − , (19) region is confined there. As the ionizing luminosity in- LEdd creases, the H II region can begin to expand into the in- where LEdd = 4#Gmc/$Thomson is the Eddington limit. falling envelope, penetrating furthest along the rotation Shortly after the H II region reaches rg, pressure forces axes. At the ionized-neutral boundary, radiation pressure in the ionized gas become large enough to reverse the feedback is exerted due to resonant scattering of FUV infall to the protostar. This effect will occur first in the radiation in the Lyman-! damping wings. As a result polar directions, typically at about 50M# in our fiducial of the high column densities of neutral gas around the model. For rotation parameters fKep " 0.5, expansion in H II region, this radiation is trapped and the pressure am- the equatorial directions (just above the accretion disk) Protostellar Ionizing Luminosity Tan & McKee 2008

plified by large factors. For typical rotation parameters fKep " 0.5, this radiation pressure becomes larger than the ram pressure of the infalling gas in the polar directions for stellar masses of order 20M#. However, once the infall is reversed at the poles, the Lyman-! photons can escape and the accretion in other directions proceeds relatively unimpeded. Thus we expect Lyman-! radiation pressure to have only a minor effect on the accretion efficiency. The next feedback effect to occur is the expansion of FIGURE 4. Vertical structure of the accretion disk at r = FIGURE 6. Protostellar H-ionizing photon luminositiesthe H forII region to distances larger than the gravitational $ $ 10r∗ " 43R# for m∗ = 100 M#, K = 1, fKep = 0.5 and no models with K = 0.5,1,2(dashed, solid, dotted lines).escape The radius rg for ionized gas. This distance is reduction in accretion efficiency due to feedback. total luminosity is shown with the higher line and the accretion G" m∗ 2.5 luminosity (boundary layer + inner disk) is shown with the≡ Edd d rg 2 = 260"Edd m∗d,2 AU, (18) FIGURE 5. Protostellar bolometric luminosities for models ci ! T4 " lower line.with K The$ = 0 zero.5,1,2( agedashed, main solid, sequence dotted lines). H-ionizing In each case the luminosities [36] aretotal indicated luminosity with is shown the withlong-dashed the higher lineline. and the accretion 4 where T4 is the ionized gas temperature in units of 10 K luminosity (boundary layer + inner disk) is shown with the and we have taken the gravitating mass to be m and lower line. The Eddington limit is indicated with the dot-long- ∗d dashed line and the zero age main sequence luminosity [36] we have allowed for the decrease in the radius due to with the long-dashed line. radiation pressure from electron scattering through the plified by large factors. For typical rotation parametersfactor L fKep " 0.5, this radiation pressure becomes larger than "Edd ≡ 1 − , (19) L the ramregion pressure is confined of there. the infalling As the ionizing gas luminosity in the polar in- direc- Edd creases, the H II region can begin to expand into the in- where LEdd = 4#Gmc/$Thomson is the Eddington limit. tions forfalling stellar envelope, masses penetrating of order furthest 20 alongM# the. However, rotation onceShortly after the H II region reaches rg, pressure forces the infallaxes. is At reversed the ionized-neutral at the boundary, poles, radiation the Lyman- pressure! photonsin the ionized gas become large enough to reverse the can escapefeedback and is exertedthe accretion due to resonant in other scattering directions of FUV proceedsinfall to the protostar. This effect will occur first in the radiation in the Lyman-! damping wings. As a result polar directions, typically at about 50M# in our fiducial relativelyof the unimpeded. high column densities Thus of we neutral expect gas around Lyman- the ! model.radia- For rotation parameters fKep " 0.5, expansion in tion pressureH II region, to this have radiation only is a trapped minor and effect the pressure on the am- accretionthe equatorial directions (just above the accretion disk) efficiency. The next feedback effect to occur is the expansion of the H II region to distances larger than the gravitational escape radius rg for ionized gas. This distance is

TABLE 1. Mass Scales of Population III.1 Protostellar Feedback

! 4 ∗ † ∗∗ K fKep Ti/(10 K) m∗,pb (M#) m∗,eb (M#) m∗,evap (M#) 1 0.5 2.5 45.3 50.4 137‡ 1 0.75 2.5 37 41 137 1 0.25 2.5 68 81 143 1 0.125 2.5 106 170 173 1 0.0626 2.5 182 330§ 256 1 0.5 5.0 35 38 120 1 0.25 5.0 53.0 61 125 0.5 0.5 2.5 23.0 24.5 57 2.0 0.5 2.5 85 87 321

∗ Mass scale of HII region polar breakout. † Mass scale of HII region near-equatorial breakout. ∗∗ Mass scale of disk photoevaporation limited accretion. ‡ Fiducial model. § This mass is greater than m∗,evap in this case because it is calculated without allowing for a reduction inm ˙ ∗ during the evolution due to polar HII region breakout. that the resulting maximum stellar mass is The uncertainties in these mass estimates include: (1) the assumption that the gas distribution far from the star 28/47 12/47 14/47 !60/47 0.24 !∗d !¯∗d "S K 2.5 is approximately spherical — in reality it is likely to be Max m∗ f ,2 = 6.3 26/47 . (1 + fd) ! T4 " flattened towards the equatorial plane, thus increasing the (23) fraction of gas that is shadowed by the disk and raising Recall that !∗d is the instantaneous star formation the final protostellar mass; (2) uncertainties in the disk efficiency—i.e., the ratio of the accretion rate onto the photoevaporation mass loss rate due to corrections to the star to the rate that would have occurred in the absence Hollenbach et al. [49] rate from the flow starting inside rg of feedback. Here this ratio is just the shadowing factor, and from radiation pressure corrections; (3) uncertainties fsh, i.e. the fraction of the sky as seen from the protostar in the H II region breakout mass due to hydrodynamic that is blocked by the disk. For this simple analytic es- instabilities and 3D geometry effects; (4) uncertainties in timate, we make the approximation that the shadowing the accretion rate at late times, where self-similarity may sets in when the stellar mass reaches m1, so that !∗d = 1 break down [25]; (5) the effect of rotation on protostellar until the mass of the central star reaches m1 and !∗d = fsh models, which will lead to cooler equatorial surface tem- thereafter. It is then straightforward to show that peratures and thus a reduced ionizing flux in the direction of the disk; (6) the simplified condition,m ˙ evap > m˙ ∗d, fsh !¯∗ = , (24) used to mark the end of accretion; and (7) the possible d − − 1 (1 fsh)(m1/m∗d) effect of protostellar outflows (discussed below). provided that m∗d ≥ m1. Note that the average efficiency !¯∗d = 1 at the onset of shadowing (m∗d = m1) and that !¯∗d → fsh at late times m∗d ' m1. Normalizing fsh to a Mechanical Feedback typical value of 0.2 we find 0.24 Protostellar outflows, thought to be launched by large- !60/47 2.5 scale magnetic fields threading the inner accretion disk, Max m∗ f ,2 = 1.45K ! T4 " are ubiquitous from present-day protostars. The momen- 28/47 12/47 tum flux in these flows typically exceeds that due to f !¯∗ × sh d , (25) radiation pressure by several orders of magnitude. As !0.2" !0.25" described above, Tan & Blackman [40] discussed how where we have set the ionizing luminosity factor "S = 1 turbulence in a stratified disk that generates helicity is 1 the necessary condition for production of dynamically- and the disk mass fraction fd = 3 ; we have normalized !¯∗d to a value of 0.25, which is approximately correct strong large-scale magnetic fields by dynamo action. ! for K = 1 and for m1 ) 50M# and m∗d = 200M#. This They then considered the effect of such an outflow on analytic estimate therefore also suggests that for the fidu- the surrounding minihalo gas, following the analysis cial case (K! = 1) the mass of a Pop III.1 star should be of Matzner & McKee [50]. The force distribution of ) 140M#. centrifugally-launched hydromagnetic outflows is colli- Magnetic Fields: Saturation Points Tan & Blackman (2004)

Exponential growth of Gravito-Turbulence seed ﬁeld (B~10-16G) MRI-Turbulence eventually becomes Unsaturated resistively limited (Blackman & Field 2002). Saturated Growth limited . by disk lifetime t ~ m*/m*

Growth limited by local accretion time in disk

(αss=0.01, 0.3) Magnetic Fields: Saturation Points Tan & Blackman (2004)

Growth limited by local accretion Either Gravito- or MRI- time in disk (α =0.01, 0.3) driven turbulence can ss provide viscosity to remove angular momentum. Magnetic Fields: Inverse Helical Dynamo Blackman & Field (2002) Turbulence in disk amplifies field strength, eventually saturating due to back reaction of B-field (Tan & Blackman 2004). Large-scale helicity is generated in each hemisphere, leading to strong, coherent, large-scale B-fields, which rise up to form a corona and outflow. Magnetic Fields: Dynamical Efect of Outflows Tan & Blackman (2004); Machida ea. (2006)

Outﬂow momentum angular distribution (Matzner & McKee 1999)

Outﬂow power from Poynting ﬂux

Efciency of accretion from core due to outflow ejected if the outflow continues. Nevertheless, we see that radiative feedback and disk-shadowing are more important, i.e. lead to smaller efficiencies, than mechanical feedback for masses ∼> 50M" in the fiducial case. The outflow would need to operate until m∗ ∼ 1000M" to re- duce !w to the value of !∗d seen at m∗ $ 100M". The possibility of lateral deflection of gas streamlines by the outflow is not treated by the above analysis, but we expect this would tend to increased !w. This effect can be studied with numerical simulations. Machida et al. [52] have carried out 3D MHD simulations of the very earliest stages of protostellar outflow feedback, up to times when the protostar has just formed with m∗ ∼< 0.01M". Such simulationsInstantaneous need to be advanced to later stages Star to explore Formation Efficiency ejected if the outflow continues. Nevertheless, we see the effects of a realistic 3D geometry on the outflow-core that radiative feedback and disk-shadowing are more im- interaction and star formation efficiency. portant, i.e. lead to smaller efficiencies, than mechanical While mechanical feedback is unlikely to dominate over radiative feedback, it may influence details of the FIGURE 11. Evolution of star formation efficiency, !w, due feedback for masses > 50M" in the fiducial case. The radiative feedback processes. Even a small outflow cav- to erosion of a 1000M" gas core by protostellar outflows winds ∼ % ∼ ity when m∗ ∼ 20M" will help dissipate Ly-" photons for the fiducial fKep = 0.5 and K = 1 case, with "ss = 0.01, and outflow would need to operate until m∗ 1000M" to re- and prevent a build up of dynamically important radia- ignoring radiative feedback processes [40]. The density profile of the initial core is specified by dM/d =(1/4 )Q( )M, duce to the value of ∗ seen at m∗ $ 100M". The tion pressure at this stage. An outflow will tend to facili- # $ µ !w ! d − 2 n 1 − 2 n tate H II region breakout in polar directions by lowering with µ = cos% and Q(µ) = (1 µ ) / 0 (1 µ ) dµ. Solid possibility of lateral deflection of gas streamlines by the line is n = 0 (isotropic core), dotted is n!= 1, dashed is n = 2, gas densities and injecting additional momentum. As it outflow is not treated by the above analysis, but we ex- long-dashed is n = 3, dot-dashed is n = 4. The dot-long-dashed is launched from the surface of the disk, a dense bipo- line shows the instantaneous efficiency, !∗d, due to radiative lar outflow can confine the protostellar ionizing flux in feedback processes (i.e. H II region breakout, limited by disk- pect this would tend to increased !w. This effect can be % equatorial directions and prevent it reaching outer disk to shadowing) for the fiducial model (fKep = 0.5, K = 1, Ti,4 = studied with numerical simulations. Machida et al. [52] cause photoevaporation [53]. However, Tan & Blackman 2.5), indicating their greater importance at m∗ ∼> 50M". have carried out 3D MHD simulations of the very earliest [40] showed that the fiducial outflow would not be dense stages of protostellar outflow feedback, up to times when enough to significantly shield the disk from the ionizing luminosities of primordial protostars once m∗ ∼> 40M". are much larger than the few km/s typical of minihalos. the protostar has just formed with m∗ ∼< 0.01M". Such On the other hand, the outflow is likely to impact the Note, however, that in addition to unbinding gas from structure of the ionized disk atmosphere and thus affect minihalos, the pressure forces associated with ionized simulations need to be advanced to later stages to explore the photoevaporation mass loss rate, perhaps similar to regions can shock-compress adjacent neutral regions and the effects of a realistic 3D geometry on the outflow-core the “strong stellar wind” case of Hollenbach et al. [49]. promote gravitational collapse, and this possibility is interaction and star formation efficiency. discussed in the next section. Stars with masses in the range shown in Table 1 are able to completely ionize While mechanical feedback is unlikely to dominate Impact of Pop III.1 Stars for Larger-Scale at least their local minihalo, and more typically a much over radiative feedback, it may influence details of the FIGURE 11. FeedbackEvolution and of starMetal formation Production efficiency, large, due volume of the surrounding intergalactic medium. !wFor recent numerical simulations of photoevaporation of radiative feedback processes. Even a small outflow cav- to erosion of a 1000M" gas core by protostellar outflowsminihalos winds see Whalen et al. [54] and references therein. The predicted final protostellar% masses (i.e. the initial ity when m∗ ∼ 20M" will help dissipate Ly-" photons for the fiducialstellar masses)fKep = for0.5 the and rangeK = of1 model case, parameters with "ss we= 0.01,Lyman-Werner and band radiation destroys H2 molecules, ignoring radiativehave considered feedback are summarized processes in [40]. Table 1. The The density stars prreducingofile the cooling efficiency of the gas. We can es- and prevent a build up of dynamically important radia- timate the distance over which star formation is sup- of the initialare all core “massive” is specified (i.e. m∗ > 8M by")dM and will/d thus=( have1/ sig-4 )Q( )M, # $ pressedµ from the work of Glover & Brand [55]. Assum- tion pressure at this stage. An outflow will tend to facili- nificant radiative and mechanical2 feedbackn 1 on their2 sur-n with = cos and Q( ) = (1 − ) / (1 − ) d .ingSolid that the core is in approximate hydrostatic equilib- tate H II region breakout in polar directions by lowering µ roundings,% and theµ potential forµ substantial0 metal enrich-µ µ line is n =ment0 (isotropic via core-collapse core), or pair-instabilitydotted is n!= supernovae.1, dashed is nrium= and2, is characterized by an entropy parameter K, we gas densities and injecting additional momentum. As it find [15] that the time to dissociate H is less than the long-dashedIonization,is n = 3, outflow,dot-dashed wind andis supernovan = 4. The feedbackdot-long-dashed can 2 free-fall time t if the core is within a distance is launched from the surface of the disk, a dense bipo- line showslead the to the instantaneous disruption and unbinding efficiency, of gas from, due nearby to radiative ff !∗d 1/2 minihalos In particular ionization is likely to be the first S 10−3 f f 24 lar outflow can confine the protostellar ionizing flux in feedback processes (i.e. H II region breakout, limited by diDsk-= LW abs diss pc, and most important feedback effect to initiate unbinding: 49 −1 21/40 % "10 s x2 0.01 # %1/4 equatorial directions and prevent it reaching outer disk to shadowing)ionizing for the radiation fiducial heats model up the gas (fKep to temperatures= 0.5, K =∼ 1, Ti,4 = n¯4 K (28) cause photoevaporation [53]. However, Tan & Blackman 2.5), indicating25,000 their K [16, greater 17], depending importance on the at temperaturem∗ ∼> 50M of ". the radiation field, with corresponding sound speeds that of the protostar, where SLW is the photon luminosity in [40] showed that the fiducial outflow would not be dense the Lyman-Werner bands, x2 is the fractional abundance enough to significantly shield the disk from the ionizing luminosities of primordial protostars once m∗ ∼> 40M". are much larger than the few km/s typical of minihalos. On the other hand, the outflow is likely to impact the Note, however, that in addition to unbinding gas from structure of the ionized disk atmosphere and thus affect minihalos, the pressure forces associated with ionized the photoevaporation mass loss rate, perhaps similar to regions can shock-compress adjacent neutral regions and the “strong stellar wind” case of Hollenbach et al. [49]. promote gravitational collapse, and this possibility is discussed in the next section. Stars with masses in the range shown in Table 1 are able to completely ionize Impact of Pop III.1 Stars for Larger-Scale at least their local minihalo, and more typically a much Feedback and Metal Production large volume of the surrounding intergalactic medium. For recent numerical simulations of photoevaporation of The predicted final protostellar masses (i.e. the initial minihalos see Whalen et al. [54] and references therein. stellar masses) for the range of model parameters we Lyman-Werner band radiation destroys H2 molecules, have considered are summarized in Table 1. The stars reducing the cooling efficiency of the gas. We can estimate the distance over which star formation is sup- are all “massive” (i.e. m∗ > 8M") and will thus have significant radiative and mechanical feedback on their sur- pressed from the work of Glover & Brand [55]. Assum- roundings, and the potential for substantial metal enrich- ing that the core is in approximate hydrostatic equilib- ment via core-collapse or pair-instability supernovae. rium and is characterized by an entropy parameter K, we Ionization, outflow, wind and supernova feedback can find [15] that the time to dissociate H2 is less than the lead to the disruption and unbinding of gas from nearby free-fall time tff if the core is within a distance 1/2 minihalos In particular ionization is likely to be the first S 10−3 f f 24 D = LW abs diss pc, and most important feedback effect to initiate unbinding: 49 −1 21/40 "10 s x2 0.01 # %1/4 ionizing radiation heats up the gas to temperatures ∼ n¯4 K 25,000 K [16, 17], depending on the temperature of (28) the radiation field, with corresponding sound speeds that of the protostar, where SLW is the photon luminosity in the Lyman-Werner bands, x2 is the fractional abundance Disk Models (Tan & McKee 2004; Tan & Blackman 2004) α=0.3 Surface density

Thickness

Ionization

Temperature

Tc , Teff

Toomre

. 17x10-3M /yr m*  Disk Models (Tan & McKee 2004; Tan & Blackman 2004) α=0.3 Surface density

Thickness

Ionization

Temperature

Tc , Teff

Toomre

. 17x10-3M /yr 6.4x10-3M /yr m*   Disk Models (Tan & McKee 2004; Tan & Blackman 2004) α=0.3 Surface density

Thickness

Ionization

Temperature

Tc , Teff

Toomre

. 17x10-3M /yr 6.4x10-3M /yr 2.4x10-3M /yr m*    Disk Models (Tan & McKee 2004; Tan & Blackman 2004) α=0.3 Surface density

Thickness

Ionization

Temperature

Tc , Teff

Toomre Disks are stable . 17x10-3M /yr 6.4x10-3M /yr 2.4x10-3M /yr m*    Implications of IMF for supernovae and metal enrichment

Metal production and dispersal via winds and supernovae depends on m*

Pair Instability SNe for m*>140M, Massive BH formation for m*>260M

Fate of NON-ROTATING metal-free stars (Heger & Woosley 2002)

However, rapid rotation can lead to signiﬁcant mass loss (Meynet et al. 2004, 2006; Hirschi 2006), so initial stellar mass is not necessarily the ﬁnal pre-SN mass. Abundance patterns from metal poor halo stars

Heger & Woosley (2008)

Christlieb et al. 2007

Gaussian IMF peaked at 11M with Single star: 20.5M width ±0.3dex -> very massive Pop III stars are rare in environments probed by Galactic halo stars. Implications for SMBH formation It appears difcult 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. Implications for SMBH formation It appears difcult 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. 9 3x10 M BH at z=6.41 Fan et al. & Willott et al. (2003) Age of Universe is 872Myr Time since z=20 is 690Myr Salpeter growth time is 45Myr (for radiative efciency = 0.1)

So need an initial mass of 660M Implications for SMBH formation It appears difcult 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. 9 3x10 M BH at z=6.41 Fan et al. & Willott et al. (2003) Age of Universe is 872Myr Time since z=20 is 690Myr Salpeter growth time is 45Myr (for radiative efciency = 0.1)

So need an initial mass of 660M However, actual accretion rates of PopIII remnants are likely to be much smaller (10-3) than Eddington (O’Shea et al. 2004). It appears to be difcult to form SMBHs from PopIII star remnants. Is there a diferent astrophysical mechanism? Feedback and Pop III.2 Star Formation

Pop III.1 stars will likely ionize their host minihalo, suppress H2 formation in very nearby halos, drive ionization fronts into nearby halos (perhaps inducing star formation - Whalen et al. 08)

Pop III.2 stars have their initial conditions signiﬁcantly affected by astrophysical sources.

We expect the primary effect is due to ionizing radiation: gas that has been ionized and then recombines, has a high residual e- fraction, which catalyzes H2 and HD production.

HD cooling -> K’ ~0.1. Greif & Bromm (2006) estimate m*~ 10M Transition to Pop II:

Critical Metallicity (Zcrit) for cooling to be dominated by metals

The cooling rate due to primordial coolants (H2, HD) will depend on temperature, density and ionization history.

The cooling rate due to metals will depend on temperature, density, abundance pattern, dust content.

Critical Metallicity (Zcrit) for cooling to be dominated by metals

The cooling rate due to primordial coolants (H2, HD) will depend on temperature, density and ionization history.

The cooling rate due to metals will depend on temperature, density, abundance pattern, dust content.

-3.5 Estimates of Zcrit : 10 fine structure lines C, O and no H2 (Bromm & Loeb 2003) 10-6 small dust grains (Omukai et al. 2005) -2 ~10 for gas phase metals if include H2 (Jappsen et al. 2007) Stellar evolution is likely to have a more sensitive dependence -8 on metallicity (Zcrit~10 ) i.e. CNO cycle (Meynet) Transition from Pop III • Pop III cores supported by thermal pressure • Present-day cores and protoclusters supported by magnetic fields and turbulence • Magnetic fields and turbulence unlikely to be efective in post-PopIII regions (B-fields probably too weak; turbulence damps out) Transition from Pop III • Pop III cores supported by thermal pressure • Present-day cores and protoclusters supported by magnetic fields and turbulence • Magnetic fields and turbulence unlikely to be efective in post-PopIII regions (B-fields probably too weak; turbulence damps out) • Post-PopIII regions may be able to cool efectively via HD and/or metals-dust

• If cs << virial velocity of halo, then gas should collapse to form a rotationally supported thin disk: possible fragmentation. (Lodato & P. Natarajan 2006; Clark, Glover & Klessen 2007) However, continued infall and merging of halos may maintain turbulence (Wise & Abel 2007) Conclusions Approximately convergent initial conditions for star formation: set by H2 cooling. Mostly thermal pressure support + slow cooling -> no/little (disk) fragmentation -> single ~massive star in each mini-halo (no clusters of primordial stars). DM heating? Conclusions Approximately convergent initial conditions for star formation: set by H2 cooling. Mostly thermal pressure support + slow cooling -> no/little (disk) fragmentation -> single ~massive star in each mini-halo (no clusters of primordial stars). DM heating? Need analytic model to follow the growth of the protostar: accretion rate; accretion disk; protostellar evolution; feedback.

Large (~AU) protostar, contracts to main sequence for m*>30M This is when feedback processes start to become important. Conclusions Approximately convergent initial conditions for star formation: set by H2 cooling. Mostly thermal pressure support + slow cooling -> no/little (disk) fragmentation -> single ~massive star in each mini-halo (no clusters of primordial stars). DM heating? Need analytic model to follow the growth of the protostar: accretion rate; accretion disk; protostellar evolution; feedback.

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 accretion rate: Gradual reduction in SF efciency because of ionizing and radiation pressure feedback for m*>30M. Final mass in ﬁducial case (K’=1, fKep=0.5), is ~160M, set by ionizing feedback on core and disk. Changing accretion rate by factor of ~5 (K’=0.5-2) leads to ﬁnal masses in the range ~60 - 300M (seeds for SMBHs?) Conclusions Approximately convergent initial conditions for star formation: set by H2 cooling. Mostly thermal pressure support + slow cooling -> no/little (disk) fragmentation -> single ~massive star in each mini-halo (no clusters of primordial stars). DM heating? Need analytic model to follow the growth of the protostar: accretion rate; accretion disk; protostellar evolution; feedback.

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 accretion rate: Gradual reduction in SF efciency because of ionizing and radiation pressure feedback for m*>30M. Final mass in fiducial case (K’=1, fKep=0.5), is ~160M, set by ionizing feedback on core and disk. Changing accretion rate by factor of ~5 (K’=0.5-2) leads to final masses in the range ~60 - 300M (seeds for SMBHs?) Impact of PopIII stars on subsequent SF: suppressed cooling due to FUV background; enhanced cooling from metals/dust and ionization catalyzed H2/HD -> rotational supported, fragmenting cores? Eventual build up of B-field support to resemble present- day SF clusters. Conclusions Approximately convergent initial conditions for star formation: set by H2 cooling. Mostly thermal pressure support + slow cooling -> no/little (disk) fragmentation -> single ~massive star in each mini-halo (no clusters of primordial stars). DM heating? Need analytic model to follow the growth of the protostar: accretion rate; accretion disk; protostellar evolution; feedback.

Implications of massive star formation in each mini-halo? Are low-mass zero metallicity stars possible? How efective is external feedback? Is this mode of star formation inevitable in all zero metal DM halos? How do supermassive black holes form? Hydrogen Ionizing Luminosities along the Primordial Zero Age Main Sequence

Tumlinson & Shull 2000; Bromm et al. 2001; Ciardi et al. 2001; Schaerer 2002 Implications of IMF for supernovae and metal enrichment

Metal production and dispersal via winds and supernovae depends on m*

Pair Instability SNe for m*>140M, Massive BH formation for m*>260M

Fate of NON-ROTATING metal-free stars (Heger & Woosley 2002)

However, rapid rotation can lead to signiﬁcant mass loss (Meynet et al. 2004, 2006; Hirschi 2006), so initial stellar mass is not necessarily the ﬁnal pre-SN mass. Growth of Cosmic Structure During the Dark Ages

1. Recombination z ≈1200, start of “dark ages” 2. Thermal equilibrium matter-CBR until z ≈160 : independent of z e.g. globular clusters 3. Thermal decoupling, Growth of Cosmic Structure During the Dark Ages

1. Recombination z ≈1200, start of “dark ages” 2. Thermal equilibrium matter-CBR until z ≈160 : independent of z e.g. globular clusters 3. Thermal decoupling, 4. “First Light” 5. Reionization, e.g. galaxies

Madau (2002) Evolution of the Protostar : Radius

Initial condition

m* = 0.04 M

r* = 14 R (Ripamonti et al. 02) Evolution of the Protostar : Radius Comparison with Stahler et al. (1986), Omukai & Palla (2001)

Initial condition Photosphere

m* = 0.04 M Accretion Shock r* = 14 R (Ripamonti et al. 02) Main Sequence (Schaerer 2002) Evolution of the Protostar : Radius Comparison with Stahler et al. (1986), Omukai & Palla (2001)

Initial condition

m* = 0.04 M

r* = 14 R (Ripamonti et al. 02) Evolution of the Protostar : Radius Comparison with Stahler et al. (1986), Omukai & Palla (2001)

Initial condition

m* = 0.04 M

r* = 14 R (Ripamonti et al. 02) Evolution of the Protostar : Radius Comparison with Stahler et al. (1986), Omukai & Palla (2001)

Initial condition

m* = 0.04 M

r* = 14 R (Ripamonti et al. 02) Evolution of the Protostar : Radius Comparison with Stahler et al. (1986), Omukai & Palla (2001)

Initial condition

m* = 0.04 M

r* = 14 R (Ripamonti et al. 02) Evolution of the Protostar : Radius Comparison with Stahler et al. (1986), Omukai & Palla (2001)

Initial condition

m* = 0.04 M

r* = 14 R (Ripamonti et al. 02)

Protostar is large (~100 R) until it is older than tKelvin Contraction to Main Sequence Accretion along Main Sequence Redshift dependence of IMF: Pop III.1

Redshift dependence of K’

O’Shea & Norman (2007) K’ increases from ~0.37 at z=30 to ~4.3 at z=20.

For PopIII.1 stars ->m*= 40M to 900M Redshift dependence of IMF: Pop III.1

Redshift dependence of K’

O’Shea & Norman (2007) K’ increases from ~0.37 at z=30 to ~4.3 at z=20.

For PopIII.1 stars ->m*= 40M to 900M

However, maybe Pop III.1 stars no longer exist by z=20 because of stellar feedback from previous stars.

Overview of Physical Scales

AV=200 M82 SSCs (McCrady & Graham 2007) A8μm=8.1 23 -2 NH=4.2x10 cm -2 Σ=4800 M pc

AV=7.5 A8μm=0.30 22 -2 NH=1.6x10 cm -2 Σ=180 M pc

AV=1.4 21 -2 NH=3.0x10 cm -2 Σ=34 M pc Overview of Physical Scales

SSCs in dwarf irregulars (K. Johnson, Kobulnicky, J. Turner et al.)

AV=200 A8μm=8.1 23 -2 NH=4.2x10 cm -2 Σ=4800 M pc

AV=7.5 A8μm=0.30 22 -2 NH=1.6x10 cm -2 Σ=180 M pc

AV=1.4 21 -2 NH=3.0x10 cm -2 Σ=34 M pc Overview of Physical Scales

SSCs in dwarf irregulars (K. Johnson, Kobulnicky, J. Turner et al.)

AV=200 A8μm=8.1 23 -2 NH=4.2x10 cm -2 Σ=4800 M pc

AV=7.5 A8μm=0.30 22 -2 NH=1.6x10 cm -2 Pop III.1 (K’=1) core Σ=180 M pc

AV=1.4 21 -2 NH=3.0x10 cm -2 Σ=34 M pc Overview of Physical Scales

SSCs in dwarf irregulars (K. Johnson, Kobulnicky, J. Turner et al.)

AV=200 A8μm=8.1 23 -2 NH=4.2x10 cm -2 Σ=4800 M pc

AV=7.5 A8μm=0.30 22 -2 NH=1.6x10 cm -2 Σ=180 M pc

AV=1.4 21 -2 NH=3.0x10 cm -2 Σ=34 M pc Overview of Physical Scales

SSCs in dwarf irregulars (K. Johnson, Kobulnicky, J. Turner et al.)

AV=200 A8μm=8.1 N =4.2x1023cm-2 5 -3 H nH~2x10 cm -2 Σ=4800 M pc 5 tff~1x10 yr

AV=7.5 A8μm=0.30 22 -2 NH=1.6x10 cm -2 Σ=180 M pc

AV=1.4 21 -2 NH=3.0x10 cm -2 Σ=34 M pc