C⁺/H_<b>2</b>gas in star-forming clouds and galaxies

Abstract

We present analytic theory for the total column density of singly ionized carbon (C+) in the optically thick photon dominated regions (PDRs) of far-UV irradiated (star-forming) molecular clouds. We derive a simple formula for the C+ column as a function of the cloud (hydrogen) density, the far-UV field intensity, and metallicity, encompassing the wide range of galaxy conditions. When assuming the typical relation between UV and density in the cold neutral medium, the C+ column becomes a function of the metallicity alone. We verify our analysis with detailed numerical PDR models. For optically thick gas, most of the C+ column is mixed with hydrogen that is primarily molecular (H&lt;inf&gt;2&lt;/inf&gt;), and this ‘C+/H&lt;inf&gt;2&lt;/inf&gt;’ gas layer accounts for almost all of the ‘CO-dark’ molecular gas in PDRs. The C+/H&lt;inf&gt;2&lt;/inf&gt; column density is limited by dust shielding and is inversely proportional to the metallicity down to ∼0.1 solar. At lower metallicities, H&lt;inf&gt;2&lt;/inf&gt; line blocking dominates and the C+/H&lt;inf&gt;2&lt;/inf&gt; column saturates. Applying our theory to CO surveys in low-redshift spirals, we estimate the fraction of C+/H&lt;inf&gt;2&lt;/inf&gt; gas out of the total molecular gas to be typically ∼0.4. At redshifts 1 &lt; &lt;it&gt;z&lt;/it&gt; &lt; 3 in massive disc galaxies the C+/H&lt;inf&gt;2&lt;/inf&gt; gas represents a very small fraction of the total molecular gas (&amp;lsim; 0.16). This small fraction at high redshifts is due to the high gas surface densities when compared to local galaxies.