Where is the molecular hydrogen in damped Ly alpha 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 H-2 column density distribution function f (N-H2) at z = 0. We show that it forms a natural extension to f (N-H I): the H-2 distribution exceeds f (N-H I) at N-H approximate to 10(22) cm(-2) and exhibits a power-law dropoff with slope similar to - 2.5. Approximately 97% of the H-2 mass density rho(H2) is in systems above N-H2 = 10(21) cm(-2). We derive a value rho(H2) = 1.1 x 10(7) h(70) M-. Mpc(-3), which is approximate to 25% the mass density of atomic hydrogen. Yet the redshift number density of H-2 above this N-H2 limit is only approximate to 3 x 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 > 10(21) cm(-2) absorber and the center of the galaxy hosting the H-2 gas is only 2.5 kpc. On the basis of arguments related to the Schmidt law, we argue that H-2 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.