Pop III IMF

Michael L. NormanLaboratory 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 (Mcrit ~ 5x105 Ms) (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 Mc~100 Ms, 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 Mc, 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)

• 1st generation Pop III stars: role of sub-fragmentation and accretion

• 2nd generation Pop III: Variations on a theme– FUV, relic HII regions, shocked slabs

• Chemical feedback and 2nd 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~5x105 Ms at z~30 attract enough primordial gas to achieve significant baryonic core densities and temperatures

• H2 formation proceeds, and by z~20 cools core baryons to T~200K, n~104 cm-3, precipitating gravitational instability

• Collapse proceeds quasi-statically until n~108 cm-3, and dynamically at higher densities as core becomes fully molecular

• Collapsing core does not fragment, but forms a single massive star with MFS =O(100 Ms) 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 = 1010

Origin of mass scale: H2

• H2 cooling rate (per particle) becomes independent of density above n=104 cm-3 (“critical density”)

• 0-1 ro-vib. exitation temperature =590K– Tmin~200K

• Cloud core “loiters” at these conditions until a Jeans mass of gas accumulates

Evolution of cloud core

Abel, Bryan & Norman (2002)

Z=19+ 9 Myr+ 300 Kyr+ 30 Kyr+ 3 Kyr+ 1.5 Kyr+ 200 yr (z=18.18)

Gravitationally unstable

Gravitationally stable

G

cM s

SIS

3

97.0)( enc

encacc MM

Mt

Schaerer (2002)primordial stars

Shu

tms

If we bound MFS from below by tkh, get ~100 Ms

If we bound MFS from above by tms, get 600-1000 Ms

100 < MFS/Ms < 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 1012 cm-3

DM halo mass function (PS)

Pop III halos5x105 < Mhalo < 5x107

massrange

20-4000 Ms

)1( zT

)1(3/2 zMT virvir

)1( zT

)1(3/2 zMT virvir

Conclusions: cosmological evolution of characteristic fragmentation scale

• Pop III halos forming at higher redshifts have:– Higher mean temperature– Higher core H2 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 Mcloud >> Mc

• 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 accretesMstar=Mcore

Omukai & Nishi (1998)

density

temperature

0.6 pc 0.06 pc 1200 AU

collapsingrotating 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~1015 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)

accreted envelope entire ,/104 if

radiationby haltedaccretion ,/104 if3

3

yrMM

yrMM

acc

acc

Protostar growth with time-dependent accretion history

Omukai & Palla (2003)

In the absence of other effects, ABN02 star shouldgrow 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 H2, 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 Thresholdto Cool• H2 in photo-

dissociation equilibrium wrt FLW

• H2 cooling still effective for M>106 Msun

• Soft UVB delays, but does not suppress star formation

Machacek, Bryan & Abel 2001

FUVB delays collapse, and raises accretion rate (O’Shea & Norman 2006d)

Mvir

zcoll

FLW=10-24

FLW=10-23

FLW=10-22

FLW=5x10-23

10-2 Ms/yrAccretion rate increases with increasing FLW

Above Omukai-Palla critical accretion rateFinal 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(Xe)

Log(T)

Primordial 2nd Generation Objects• z ~ 11, Mdyn/ M = 4 x 107, Tvir=14,000 K

– well above minimum halo mass to form H2 in the presence of a SUV background (Machacek, Bryan & Abel 2001)

2 x 106 Msol of cold (200K) gas

– 100 x the amount that formed the 1st 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 H2 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)

4x105 yr

6x107 yr

2nd generation stars

• At Z=7x10-3 Zs, metal line cooling will dominate primordial gas cooling (Bromm & Loeb 2003)

• Assuming gas cools down to CMB temperature (47 K), then MJ~6 Ms 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 fSN host metal-producing SN

• Mergers with polluted halos form Pop II

• If fSN=0.1, Pop III halos from to z=0; Pop III stars dominate SF history

• If fSN=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

zthresholdPop III halo

Low massPop III halo

Enriched Pop III halo

Pop IIprotogalaxy

30 20 15 10

Slides in reserve

Turbulent AM transport

)(

)( rrr

rLF

Reynolds stress