= Ionized gas density from an absorption distribution
{title2=$\Omega_g=\frac{H_0\mu_Hm_H}{c\rho_{\mathrm{crit},0}}\int\frac{N}{x_{\rm HI}}f_X(N,z)\,dN$}
A neutral-hydrogen <column density> $N$ traces total hydrogen column $N/x_{\rm HI}$ only after specifying its neutral fraction $x_{\rm HI}$. Integrating the latter against the distribution per <absorption distance> gives the comoving gas <mass density> in the displayed expression. The factor $\mu_H$ includes helium if desired. In <photoionization equilibrium> for optically thin, almost fully ionized hydrogen, $x_{\rm HI}\simeq\alpha(T)n_H/\Gamma$, so gas density, <temperature>, <photoionization rate> and absorber size are required. An observed distribution alone does not fix the total baryon inventory.
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