Pop III IMF Michael L. Norman Laboratory for Computational Astrophysics UC San Diego (with thanks to Andrea Ferrara & Mario Livio)

General Comments Definition: Pop III = zero metallicity IMF not observationally constrained at this time –We don’t observe Pop III stars directly –Interpretation of “fossil evidence” highly uncertain Must rely on theory/simulations (yikes!) –Robust prediction: first stars were massive –But not all Pop III stars may form this way

Why do we care? Fate of Pop III depends sensitively on mass IMF controls early radiative and chemical evolution of the universe, and the population of seed black holes Figure courtesy Alex Heger

Defining the Pop III IMF What is the statistical ensemble? First stars are believed to form in isolation, one per low mass halo (M crit ~ 5x10 5 M s ) (Abel, Bryan & Norman 2002) –Simply not enough cool baryons to form 2 cores High z IMF may be strongly peaked about the characteristic mass scale M c ~100 M s, with dispersion reflecting halo properties (O’Shea & Norman 2006b) If some more massive halos at lower z remain pristine (chemical feedback), Pop III clusters may form with a broader, but still top-heavy IMF (Larson 1998) Primordial stars formed through secondary processes (shocked slabs, relic HII regions), may have lower M c, and a broader dispersion It is highly likely n(M)=n(M,z) My proposal: ensemble is the entire Pop III era

Topics Characteristic fragmentation mass scale of “first star” halos –Origin (old) –cosmological evolution (new) 1 st generation Pop III stars: role of sub- fragmentation and accretion 2 nd generation Pop III: Variations on a theme –FUV, relic HII regions, shocked slabs Chemical feedback and 2 nd generation stars The rise and fall of Pop III: a schematic

Formation of the first stars (Abel et al, Bromm et al.) DM halos of M~5x10 5 M s at z~30 attract enough primordial gas to achieve significant baryonic core densities and temperatures H 2 formation proceeds, and by z~20 cools core baryons to T~200K, n~10 4 cm -3, precipitating gravitational instability Collapse proceeds quasi-statically until n~10 8 cm -3, and dynamically at higher densities as core becomes fully molecular Collapsing core does not fragment, but forms a single massive star with M FS =O(100 M s ) as inferred by its accretion rate These results are numerically converged

Pop III Star formation: the current paradigm From Abel, Bryan and Norman 2002, Science, 295, 93 Range of resolved scales = 10 10

Origin of mass scale: H 2 H 2 cooling rate (per particle) becomes independent of density above n=10 4 cm -3 (“critical density”) 0-1 ro-vib. exitation temperature =590K –T min ~200K Cloud core “loiters” at these conditions until a Jeans mass of gas accumulates

Evolution of cloud core Abel, Bryan & Norman (2002) Z= Myr Kyr + 30 Kyr + 3 Kyr Kyr yr (z=18.18) Gravitationally unstable Gravitationally stable

Schaerer (2002) primordial stars Shu t ms If we bound M FS from below by t kh, get ~100 M s If we bound M FS from above by t ms, get M s 100 < M FS /M s < 1000 (neglecting feedback)

Cosmological Evolution of Characteristic Mass Scale (O’Shea & Norman (2006b)) The Issue –How representative are these results? –Are Pop III halos forming at different redshifts different? The Simulations –12 simulations (4 random realizations) x (3 box sizes) –Run to core collapse –Analyzed when central density had reached cm -3 DM halo mass function (PS) Pop III halos 5x10 5 < M halo < 5x10 7

mass range M s

Conclusions: cosmological evolution of characteristic fragmentation scale Pop III halos forming at higher redshifts have: –Higher mean temperature –Higher core H 2 fraction –Lower core temperature, and hence –Lower accretion rates The first Pop III stars to form may be less massive than those forming later Pop III epoch may start modestly and build to a crescendo Or it might be the other way around…..

Fragmentation and Accretion Turbulent fragmentation and competitive accretion both seem to account for present day IMF Both rely on M cloud >> M c Could these mechanisms operate in high mass primordial halos? –If so, might expect a Pop III IMF with shape like present-day IMF, but shifted to high mass (Larson 1998) –Can massive primordial halos from? What about good-old gravitational fragmentation? (Hoyle 1953) –CAUTION!

0-D free-fall models Omukai (2001) Not dynamically self-consistent

1-D hydrodynamical models Spherical symmetric –no fragmentation Dynamically self- consistent –Rate chemistry, EOS, radiative transfer entire massive envelope eventually accretes  M star =M core Omukai & Nishi (1998)

density temperature 0.6 pc0.06 pc1200 AU collapsing rotating core disk ABN02

Fragmentation and Accretion Yes, both happen But, in low mass halos at least, only one central fragment forms, which then accretes Angular momentum important on small scales, but no centrifugal barrier found to n~10 15 cm -3 Disk not an accretion disk per se, but a rotating, collapsing core Could possibly fragment into a binary Evidence of turbulent transport of AM and AM “segregation” (O’Shea & Norman 2006c)

Accretion rate may determine the final stellar mass ( Omukai & Palla 2003 )

Protostar growth with time- dependent accretion history Omukai & Palla (2003) In the absence of other effects, ABN02 star should grow to ~600 Ms

Effects of Rotation (Tan & McKee 2004) Collapse becomes supersonic when core becomes fully molecular Assuming gas conserves AM inside sonic radius, TM04 argue that an accretion will form Most of the mass is accreted via this disk Eddington limited accretion is bypassed Protostellar evolution similar to OP03 subcritical case (all mass is accreted)

Variations on a Theme 1. Effect of FUV Background The issue: –FUV photons from first stars easily escape primordial halos, building up soft UV background –will photo-dissociate H 2, inhibiting cooling and hence Pop III star formation (Dekel & Rees 1987; Haiman, Rees & Loeb 1997; Haiman, Abel & Rees 2000) Solomon process Does negative feedback quench star formation in low mass halos?

Mass Threshold to Cool H 2 in photo- dissociation equilibrium wrt F LW H 2 cooling still effective for M>10 6 M sun Soft UVB delays, but does not suppress star formation Machacek, Bryan & Abel 2001

FUVB delays collapse, and raises accretion rate (O’Shea & Norman 2006d) M vir z coll F LW = F LW = F LW = F LW =5x M s /yr Accretion rate increases with increasing F LW Above Omukai-Palla critical accretion rate Final mass may be smaller

Variations on a Theme 2. Pop III star formation in a relic HII region (O’Shea et al. 2005) 100 kpc (com) Log(T) Log(X e )

Log(T)

Primordial 2 nd Generation Objects z ~ 11, M dyn / M  = 4 x 10 7, T vir =14,000 K –well above minimum halo mass to form H 2 in the presence of a SUV background (Machacek, Bryan & Abel 2001)  2 x 10 6 M sol of cold (200K) gas –100 x the amount that formed the 1 st star due to abundant electrons –Will it form a star 100x as massive (SMS)? –Will it form a cluster of Pop III stars? IMF? AMR simulations with more levels can answer these questions (O’Shea & Norman, in prep)

Variations on a Theme 3. Pop III star formation in SN shells (Uehara & Inutsuka 2000; Mackey, Bromm & Hernquist 2003) Blast waves in primordial halos will sweep up shells of gas which from H 2 and HD Gas cools below 100 K due to HD Shell fragments due to gravitational instability Mass scale: brown dwarfs Uehara & Inutsuka (2000)

Chemical Feedback from Pop III (O’Shea & Norman 2006c, poster) 4x10 5 yr 6x10 7 yr

2 nd generation stars At Z=7x10 -3 Z s, metal line cooling will dominate primordial gas cooling (Bromm & Loeb 2003) Assuming gas cools down to CMB temperature (47 K), then M J ~6 M s for our core density. This is resolution-dependent and hence an upper limit. Expect extreme Pop II to have a universal IMF shifted slightly to higher mass IMF will depend of properties of molecular cloud turbulence (Padoan & Nordlund 2002), which we can (and will) quantify

Evolution of Pop III Halo fraction (Schneider et al. 2006) Procedure: construct merger tree from N-body simulation Assume fraction f SN host metal-producing SN Mergers with polluted halos form Pop II If f SN =0.1, Pop III halos from to z=0; Pop III stars dominate SF history If f SN =1, Pop III halos continue to form at negative feedback threshold; Pop II stars dominate SF history

Rise and Fall of Pop III: A schematic z threshold Pop III halo Low mass Pop III halo Enriched Pop III halo Pop II protogalaxy

Slides in reserve

Turbulent AM transport Reynolds stress