Two-phase equilibrium and molecular hydrogen formation in damped Lyman-alpha systems

Molecular hydrogen is quite underabundant in damped Lyman-alpha systems at high redshift, when compared to the interstellar medium near the Sun. This has been interpreted as implying that the gas in damped Lyman-alpha systems is warm. like the nearby neutral intercloud medium, rather than cool, as in the clouds which give rise to most H I absorption in the Milky Way. Other lines of evidence suggest that the gas in damped Lyman-alpha systems -- in whole or part -- is actually cool; spectroscopy of neutral and ionized carbon, discussed here, shows that the damped Lyman-alpha systems observed at lower redshift z $<$ 2.3 are largely cool, while those seen at z $>$ 2.8 are warm (though not devoid of H2). To interpret the observations of carbon and hydrogen we constructed detailed numerical models of H2 formation under the conditions of two-phase thermal equilibrium, like those which account for conditions near the Sun, but with varying metallicity, dust-gas ratio, $etc$. We find that the low metallicity of damped Lyman-alpha systems is enough to suppress H2 formation by many orders of magnitude even in cool diffuse clouds, as long as the ambient optical/uv radiation field is not too small. For very low metallicity and under the most diffuse conditions, H2 formation will be dominated by slow gas-phase processes not involving grains, and a minimum molecular fraction in the range $10^{-8}-10^{-7}$ is expected.