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

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 sub(crit), primordial gas cools more efficiently by fine-structure lines of [C II] (157.74 km), [O I] (63.18 km, 145.5 km), [Si II] (34.8 km), and [Fe II] (25.99 km, 35.35 km) than by H I or H sub(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 sub(crit) as the point when the total cooling rate by metals plus H sub(2) equals the adiabatic compressional heating. We explore two metallicity scenarios: (1) a single metallicity for all heavy elements and (2) individual metallicities (Z sub(C), Z sub(O), Z sub(Si), and Z sub(Fe)) from theoretical supernova yields. For dense gas (n,10 super(3) cm super(-3)) with metals in relative solar abundances, fragmentation occurs at Z sub(crit) - 10 super(-3.5) Z sub( ). However, for lower density gas (n = 1-100 cm super(-3)), particularly in halos enriched in Si, O, and Fe, we find Z sub(crit) - 0.1%-1% Z sub( ). 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 sub(2) rotational states (J = 2 and J = 3). Primordial clouds of 10 super(8) M sub( )at 200 K are detectable in redshifted fine-structure lines, with far-infrared fluxes between 10 super(-22) and 10 super(-21) W m super(-2). For metallicities Z sub(O) - 10 super(-3) and molecular fractions f super(H2) - 10 super(-3), the fine-structure emission lines of [O I], [Si II], and [Fe II] could be 10 super(2)-1 0 super(3) times stronger than the H sub(2) rotational lines at 28.22 km (J= 2 1 0) and 17.03 km (J = 3 1 1).