http://arxiv.org/abs/1603.02300
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. 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$_2$), and this “C$^+$/H$_2$” gas layer accounts for almost all of the `CO-dark’ molecular gas in PDRs. The C$^+$/H$_2$ column density is limited by dust shielding and is inversely proportional to the metallicity down to $\sim$0.1 solar. At lower metallicities, H$_2$ line blocking dominates and the C$^+$/H$_2$ column saturates. Applying our theory to CO surveys in low redshift spirals we estimate the fraction of C$^+$/H$_2$ gas out of the total molecular gas to be typically $\sim$0.4. At redshifts $1<z<3$ in massive disk galaxies the C$^+$/H$_2$ gas represents a very small fraction of the total molecular gas ($<0.16$). This small fraction at high redshifts is due to the high gas surface densities when compared to local galaxies.
R. Nordon and A. Sternberg
Wed, 9 Mar 16
15/71
Comments: 13 pages, 12 figures. Comments are welcomed
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