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 gas with various metallicities and FUV
field strengths. When the H2 cooling is suppressed by FUV fields (G_0>10^-3) or
the metallicity is high enough (Z/Zs>10^-3), the interstellar medium is
thermally unstable in the temperature range 100-7000 K owing to the cooling by
CII and OI 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 metallcity, the density range of the thermal instability
shrinks owing to dominance of H2 cooling. As the FUV intensity is reduced,
bi-phasic structure becomes less remarkable and disappears eventually. Our
basic results suggest that, in early galaxies, i) the thermal instability has
little effect for the medium with Z/Zs<10^-4, ii) fragmentation by the thermal
instability could determine mass spectrum of star clusters for 10^-4<Z/Zs<0.04,
and iii) thermally bistable turbulent interstellar medium like our galaxy
becomes ubiquitous for Z/Zs>0.04, although the threshold metallicity depends on
the conditions such as thermal pressure, FUV strength and redshift.
