Critical Metallicity and Fine‐Structure Emission of Primordial Gas Enriched by the First Stars

Abstract

The influence of the first stars on the formation of second-generation objects at high redshift may be determined, in part, by their metal enrichment of surrounding gas. At a critical metallicity, Z crit , primordial gas cools more efficiently by fine-structure lines of [C ii] (157.74 m), [O i] (63.18 m, 145.5 m), [Si ii] (34.8 m), and [Fe ii] (25.99 m, 35.35 m) than by H i or H 2 emission.This cooling may alter the process of fragmentation into smaller units. We study the time-dependent cooling of primordial gas enriched by heavy elements from early massive stars, particularly O, Si, and Fe. We define Z crit as the point when the total cooling rate by metals plus H 2 equals the adiabatic compressional heating. We explore two metallicity scenarios: (1) a single metallicity for all heavy elements and (2) individual metallicities (Z C , Z O , Z Si , and Z Fe ) from theoretical supernova yields. For dense gas (n ! 10 3 cm À3 ) with metals in relative solar abundances, fragmentation occurs at Z crit % 10 À3:5 Z . However, for lower density gas (n ¼ 1 100 cm À3 ), particularly in halos enriched in Si, O, and Fe, we find Z crit % 0:1% 1% Z . The critical metallicity approaches a minimum value at high n set by efficient LTE cooling, with thermalized level populations of fine-structure states and H 2 rotational states (J ¼ 2 and J ¼ 3). Primordial clouds of 10 8 M at 200 K are detectable in redshifted fine-structure lines, with far-infrared fluxes between 10 À22 and 10 À21 W m À2 . For metallicities Z O % 10 À3 and molecular fractions f H 2 % 10 À3 , the fine-structure emission lines of [O i], [Si ii], and [Fe ii] could be 10 2 -10 3 times stronger than the H 2 rotational lines at 28.22 m (J ¼ 2 ! 0) and 17.03 m (J ¼ 3 ! 1).

Formation of supermassive black holes

“…Enriched halos have a more efficient cooling, which in turn favors fragmentation and star formation over the efficient collection of gas conducive to MBH formation. It has been suggested that efficient gas collapse probably occurs only in massive halos with virial temperatures T vir ∼ > 10 4 K under metal-free conditions where the formation of H 2 is inhibited (Bromm and Loeb, 2003), or for gas enriched below the critical metallicity threshold for fragmentation (Santoro and Shull, 2006). For these systems the tenuous gas cools down by atomic hydrogen only until it reaches Tgas ∼ 4000 K. At this point the cooling function of the atomic hydrogen drops by a few orders of magnitude, and contraction proceeds nearly adiabatically.…”

“…The second condition implies that at low density H 2 is dissociated and does not contribute to cooling. The third condition ensures that gas can fragment and form low-mass stars only if the gas density is above a certain threshold, n crit,Z (which depends on the metallicity, see Santoro and Shull, 2006): this causes only the highest density regions of a proto-galactic disc (see section 2.3) to be prone to star formation.…”

A Practical Guide to the Massive Black Hole Cosmic History

“…Devecchi and Volonteri [83] showed that runaway collapse is a viable route for seed BH formation in mildly metal polluted (Z < 10 −3 Z ), efficient hydrogen cooling (T v > 10 4 K) halos at high redshift. Their scenario is similar to the direct collapse mechanism discussed above, with the difference that the mass accumulated in the central parsec overcomes the density threshold (function of the metallicity, see [84]) at which fragmentation and star formation occur efficiently. The most massive stars in the resulting compact cluster undergo runaway collisions forming a VMS of several thousand solar masses, leaving behind a seed BH remnant of ∼1000-2000 M .…”

ROBO: a model and a code for studying the interstellar medium

“…Many gas and dust components are taken into account, among which we recall the molecular hydrogen and the metal coolants (Santoro & Shull 2006;Maio et al 2007) or HD (McGreer & Bryan 2008). To track the evolution of these components, the ISM model and robo take various physical processes into account that may affect the behavior of the whole system.…”