Thermal instability and multi-phase interstellar medium in the first galaxies
We examine the linear stability and nonlinear growth of the thermal instability in isobarically contracting background gas with various metallicities and far-UV (FUV) field strengths. Such a background medium can be expected for protogalactic clouds and shocked gas with metallicity Z/Z{sub ⊙}>10{sup −4}. When the H{sub 2} cooling is suppressed by FUV fields (G{sub 0}>10{sup −3}) or the metallicity is high enough (Z/Z{sub ⊙}>10{sup −3}), the interstellar medium (ISM) is thermally unstable in the temperature range 100–7000 K owing to the cooling by C ii and O i fine-structure lines. In this case, a bi-phasic medium with a bimodal density probability distribution is formed as a consequence of the thermal instability. The characteristic scales of the thermal instability become smaller with increasing metallicity. Comparisons of the nonlinear simulations with different resolution indicates that the maximum scale of the thermal instability should be resolved with more than 60 cells to follow runaway cooling driven by the thermal instability. Under sufficiently weak FUV fields and with low metallicity, the density range of the thermal instability shrinks owing to the dominance of H{sub 2} cooling. As the FUV intensity is reduced, the bi-phasic structure becomes less remarkable and eventually disappears. Our basic results suggest that, in early galaxies, (i) fragmentation by the nonlinear growth of thermal instability could determine the mass spectrum of star clusters for Z/Z{sub ⊙}≲0.04, and (ii) a thermally bistable turbulent ISM like our galaxy becomes ubiquitous for Z/Z{sub ⊙}≳0.04, although the threshold metallicity depends on conditions such as thermal pressure, FUV strength, and redshift.