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(crit), primordial gas cools more efficiently by fine-structure lines of [C (II)] (157.74 mu m), [O (I)] (63.18 mu m, 145.5 mu m), [Si (II)] (34.8 mu m), and [Fe (II)] (25.99 mu m, 35.35 mu 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 Zcrit 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(-3)) with metals in relative solar abundances, fragmentation occurs at Z(crit) approximate to 10(-3.5) Z circle dot. However, for lower density gas (n = 1 - 100 cm(-3)), particularly in halos enriched in Si, O, and Fe, we find Z(crit) approximate to 0: 1% - 1% Z circle dot. 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 = 2 and J = 3). Primordial clouds of 10(8) M circle dot at 200 K are detectable in redshifted fine-structure lines, with far-infrared fluxes between 10(-22) and 10(-21) Wm(-2). For metallicities Z(O) approximate to 10(-3) and molecular fractions f(H2) approximate to 10(-3), 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 mu m (J = 2 -> 0) and 17.03 mu m (J = 3 -> 1).