We examine the constraints on theories of galaxy formation that are obtained from observations of damped $\lya$ (DL) systems, assuming they are gaseous protodisks in dark matter halos. Using the Press-Schechter formalism, we find that the mixed dark matter model, with $\ohdm = 0.3$, $\ocdm = 0.65$, $\obaryon = 0.05$, and $h=0.5$, is ruled out because the number of galactic halos at $z\simeq 3$ is too small to account for the total gaseous mass in DL systems, even under the assumption that all the gas in collapsed halos has settled into disks of neutral gas. The standard CDM model can account for the gas in DL systems if the bias is $b\lsim 2$; the same is true for the CDM model with a cosmological constant, if $b\lsim 1.5$ for $Λ= 0.8$. However, one still needs to assume that a fraction $\gsim 0.4$ of the baryons in collapsed halos at $z\simeq 3$ is in the form of neutral gas in disks. We also calculate the column density distribution $f(\nhi)$ of the DL systems, in terms of the surface density profiles of disks and the distribution of their central column densities. It is shown that the form of $f(\nhi)$ at the high end of column density is a diagnostic for the nature of DL systems.

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