Where Is the Molecular Hydrogen in Damped Lyα Absorbers?

We show in this paper why molecular millimeter absorption line searches in DLAs have been unsuccessful. We use CO emission-line maps of local galaxies to derive the H₂ column density distribution function f(N_H2) at z=0. We show that it forms a natural extension to f(N_HI): the H₂ distribution exceeds f(N_HI) at N_H~10²²cm^-2 and exhibits a power-law dropoff with slope ~-2.5. Approximately 97% of the H₂ mass density ρ_H2 is in systems above N_H2=10²¹ cm^-2. We derive a value ρ_H2=1.1×10⁷ h₇₀ M_solar Mpc^-3, which is ~25% the mass density of atomic hydrogen. Yet the redshift number density of H₂ above this N_H2 limit is only ~3×10^-4, a factor 150 lower than that for H I in DLAs at z=0. Furthermore, we show that the median impact parameter between a N_H2>10²¹ cm^-2 absorber and the center of the galaxy hosting the H₂ gas is only 2.5 kpc. On the basis of arguments related to the Schmidt law, we argue that H₂ gas above this column density limit is associated with a large fraction of the integral star formation rate density. Even allowing for an increased molecular mass density at higher redshifts, the derived cross sections indicate that it is very unlikely to identify the bulk of the molecular gas in present quasar absorption lines samples. We discuss the prospects for identifying this molecular mass in future surveys.