Damped lyman-alpha systems versus cold + hot dark matter

Although the cold + hot dark matter (CHDM) cosmology provides perhaps the best fit of any model to all the available data at the current epoch (z = 0), CHDM produces structure at relatively low redshifts and thus is very sensitive to the observed numbers of massive objects at high redshifts. Damped Lyα systems are abundant in quasar absorption spectra and provide possibly the most significant evidence for early structure formation, and thus a stringent constraint on CHDM. Using the numbers of halos in N-body simulations to normalize Press-Schechter estimates of the number densities of protogalaxies as a function of redshift, we find that CHDM with OMEGAc_/OMEGAnu_/OMEGAb_ = 0. 6/0. 3/0. 1 is compatible with the damped Lyα data only at 3 damped Lyα data. The situation is uncertain because there is very little data for z > 3. The predictions of CHDM are quite sensitive to the hot (neutrino) fraction, and we find that OMEGAc_/OMEGAnu_/OMEGAb_ = 0. 725/0. 20/0. 075 (and possibly even OMEGAc_/OMEGAnu_/OMEGAb_ = 0. 675/0. 25/0. 075) is compatible with the z > 3 data. With one massive neutrino species, using OMEGAnu_ = 0. 20 instead of 0. 30 corresponds to lowering the neutrino mass from 7. 0 to 4. 7 eV, for H₀_ = 50 km s^-1^ Mpc^-1^ and T - 2. 726 K. In CHDM, the higher redshift damped Lyα systems are predicted to have lower masses (~3 x 10¹0^ Mₛun_ at z = 3), a prediction which can be checked by measuring the velocity widths of the associated metal-line systems. Predictions for high-z objects crucially depend on the effects of limited resolution and the finite box size in N-body simulations or on the parameters of the Press-Schechter approximation, if it is used. By analyzing our numerical simulations with vastly different resolutions and box sizes as well as those of Ma & Bertschinger (1994), we show that for the CHDM models with OMEGAnu_ = 0. 2-0. 3 the Press-Schechter approximation should be used with Gaussian filter with δc_ = 1. 5 if halos are defined with the mean overdensity larger than 200. If one tries to recover the total mass of a collapsed halo, a better value for the collapse parameter is δc_ = 1. 40. We argue that nonlinear effects due to waves both longer and shorter than those considered in numerical simulations could probably result in δc_ as low as δc_ = 1. 3.