3 Warm or cool gas in damped Lyman-$\alpha$ systems? - Observations of C I and C II

In Tables 1 and 2 we have gathered information on the neutral and ionized carbon lines available in the literature. For each source we show the observed column densities, and the metallicity derived from zinc, which is believed to be (at most) only lightly depleted (Pettini et al. 1994; Vladilo et al. 2000). From the metallicity we derive a quantity N(C II)$_{\rm m}$ which is meant to represent the maximum amount of carbon available in the gas phase, i.e. it is the column density of carbon assuming that carbon and zinc have the same metallicity and depletion. Comparison with the measured C II column densities shows that carbon is not lacking, with the notable exception of PHL957. N(C II)$_{\rm m}$ is used as a surrogate where measured values of N(C II) are unavailable at low redshift in Table 1.

The ratio N(C II)/N(C I) is much larger for the sources at high zin Table 2, above 13 000-30 000, consistent only with an origin in overwhelmingly warm gas: the fraction of cool gas must be of order a few percent at most. At lower redshift, two of the measured ratios, and that inferred for the source 1756+237, are below 1000, consistent with cool neutral gas in the stable region of the two-phase equilibrium, at thermal pressures $P/k = 3000 {-} 4000 ~{\rm cm}^{-3}$ K, and densities $n({\rm H}) = 10 {-} 70 ~{\rm cm}^{-3}$. The data for PHL957 are also consistent with stable cool gas at $n({\rm H}) \la 10~{\rm cm}^{-3}$, $p/k \la 2500~{\rm cm}^{-3}$ K, while 1331+170 is in the marginally unstable region at $n({\rm H}) = 10~{\rm cm}^{-3}$, $p/k = 2800~{\rm cm}^{-3}$ K. For the systems at lower redshift, there must be a very large proportion of cool gas, though we cannot say exactly how much.

The N(C II*)/N(C II) ratios are noticeably smaller at high redshift in Table 2, and would presumably be smaller still by a factor 2 or more, were it not for the cosmic background radiation, which has a noticeable effect (only) above z = 2.5 in warm gas (see Fig. 4). The N(C II*)/N(C II) ratios observed at lower redshift, in presumably cool gas, are 50-100% higher than in the models. This could be explained by an enhanced ISRF (Fig. 5, bottom left panel) or by some depletion of carbon for PHL957, where the metallicity of carbon is (uniquely) very low compared to that of Zn, and N(C II*)/N(C II) is rather large.

To summarize, comparison of the tabulated observational results with the calculated properties of carbon in two-phase media shows quite unambiguously that the observed gas has a substantial contribution from cool gas at lower redshift but is very largely warm at z > 2.8. Whether this shift from cool to warm gas is systematic or coincidental remains to be explored. Norman & Spaans (1997) predicted that multi-phase equilibrium, cool gas and substantial quantities of ${\rm H}_2$ would occur in protogalactic disks only when the metallicity had increased to 0.03-0.1 Solar, somewhere in the interval 1 < z < 2.