Simulations of Early Structure Formation: Primordial Gas Clouds

Abstract

We use cosmological simulations to study the origin of primordial star-forming clouds in a ÃCDM universe, by following the formation of dark matter halos and the cooling of gas within them. To model the physics of chemically pristine gas, we employ a nonequilibrium treatment of the chemistry of nine species (e À , H, H + , He, He + , He ++ , H 2 , H þ 2 , H À ) and include cooling by molecular hydrogen. By considering cosmological volumes, we are able to study the statistical properties of primordial halos, and the high resolution of our simulations enables us to examine these objects in detail. In particular, we explore the hierarchical growth of bound structures forming at redshifts z % 25 30 with total masses in the range %10 5 10 6 M . We find that when the amount of molecular hydrogen in these objects reaches a critical level, cooling by rotational line emission is efficient, and dense clumps of cold gas form. We identify these '' gas clouds '' as sites for primordial star formation. In our simulations, the threshold for gas cloud formation by molecular cooling corresponds to a critical halo mass of %5 Â 10 5 h À1 M , in agreement with earlier estimates, but with a weak dependence on redshift in the range z > 16. The complex interplay between the gravitational formation of dark halos and the thermodynamic and chemical evolution of the gas clouds compromises analytic estimates of the critical H 2 fraction. Dynamical heating from mass accretion and mergers opposes relatively inefficient cooling by molecular hydrogen, delaying the production of star-forming clouds in rapidly growing halos. We also investigate the effect of photodissociating ultraviolet radiation on the formation of primordial gas clouds. We consider two extreme cases, first by including a uniform radiation field in the optically thin limit and second by accounting for the maximum effect of gas self-shielding in virialized regions. For radiation with Lyman-Werner band flux J > 10 À23 ergs s À1 cm À2 Hz À1 sr À1 , hydrogen molecules are rapidly dissociated, rendering gas cooling inefficient. In both the cases we consider, the overall effect can be described by computing an equilibrium H 2 abundance for the radiation flux and defining an effective shielding factor. Based on our numerical results, we develop a semianalytic model of the formation of the first stars and demonstrate how it can be coupled with large N-body simulations to predict the star formation rate in the early universe.

Revised rate coefficients for H2 and H− destruction by realistic stellar spectra

“…We refer the reader to Abel et al (1997) for a derivation of the same, where the authors derive the photodissociation rate constant κ27 ∼ 1.1 × 10 8 s −1 , for a given value of an un-normalised flux (F in units of erg/s/Hz/cm 2 ). Thus, for our definition of J21, κ di = 4π10 −21 κ27 = 1.38 × 10 −12 s −1 (see Yoshida et al 2003). Thus Eq.…”

“…At temperature below ∼ 8000 K, primordial gas in the early Universe cools most efficiently via molecular hydrogen to temperatures of ≈ few 100 K at which point the Jeans mass can be exceeded and gravitational runaway collapse of gas can proceed (e.g. Omukai & Nishi 1998;Abel et al 2002;Yoshida et al 2003). This channel of cooling is of importance for the formation of the first stars (Population III, or Pop III) in mini-haloes at z 10, which kick-start the metal enrichment of the inter-galactic medium and inter-stellar medium (e.g.…”

The astrophysics of early galaxy formation

“…Such simulations performed in the context of ΛCDM cosmologies have shown that the first stars (the so-called 'Population III') in the universe formed out of metal-free gas in dark matter minihalos of mass above a few ×10 5 M ⊙ (Abel et al 2000;Fuller & Couchman 2000;Yoshida et al 2003;Reed Abel et al 2002;Bromm et al 2002;see Bromm &Larson 2004 andFerrara 2005 for recent reviews). In Kuhlen & Madau (2005) we used a modified version of enzo, an adaptive mesh refinement (AMR), grid-based hybrid (hydro+N-body) code developed by Bryan & Norman (see http://cosmos.ucsd.edu/enzo/) to solve the cosmological hydrodynamics equations and study the cooling and collapse of primordial gas in the first baryonic structures.…”

“…For T vir ∼ < a few thousand kelvins the virialization shock is not ionizing, the free electrons left over from recombination are depleted in the denser regions, and the production of H 2 stalls at a temperature-dependent asymptotic molecular fraction x H2 ≈ 10 −8 T 1.5 vir ln(1 + t/t rec ), where t rec is the hydrogen recombination time-scale (Tegmark et al 1997). A typical H 2 fraction in excess of 200 times the primordial value is therefore produced after the collapse of structures with virial temperatures of order 10 3 K. This is large enough to efficiently cool the gas and allow it to collapse within a Hubble time unless significant heating occurs during this phase (Abel et al 2000;Yoshida et al 2003). Fig.…”

“…Gas condensation in the first baryonic objects is possible through the formation of H 2 molecules, which cool via roto-vibrational transitions down to temperatures of a few hundred kelvins. In the absence of a UV photodissociating flux and of ionizing Xray radiation, three-dimensional simulations of early structure formation show that the fraction of cold, dense gas available for accretion onto seed black holes or star formation exceeds 20% for halos more massive than 10 6 M ⊙ already at redshifts 20 (Machacek et al 2003;Yoshida et al 2003).…”