The Statistics of Density Peaks and the Column Density Distribution of the Lyman - Alpha Forest

We develop a method to calculate the column density distribution of the Lyα forest for column densities in the range 10 − 10 cm. The Zel’dovich approximation, with appropriate smoothing, is used to compute the density and peculiar velocity fields. The effect of the latter on absorption profiles is discussed and it is shown to have little effect on the column density distribution. An approximation is introduced in which the column density distribution is related to a statistic of density peaks (involving its height and first and second derivatives along the line of sight) in real space. We show that the slope of the column density distribution is determined by the temperature-density relation as well as the power spectrum on scales 2 hMpc ∼ k < ∼ 20 hMpc . An expression relating the three is given. We find very good agreement between the column density distribution obtained by applying the Voigt-profile-fitting technique to the output of a full hydrodynamic simulation and that obtained using our approximate method for a test model. This formalism then is applied to study a group of CDM as well as CHDM models. We show that the amplitude of the column density distribution depends on the combination of parameters (Ωbh 2)2T 0 J −1 HI , which is not well-constrained by independent observations. The slope of the distribution, on the other hand, can be used to distinguish between different models: those with a smaller amplitude and a steeper slope of the power spectrum on small scales give rise to steeper distributions, for the Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 Center for Theoretical Physics, Laboratory for Nuclear Science, MIT Princeton University Observatory, Peyton Hall, Princeton, NJ 08544 Laboratory for Computational Astrophysics, National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL 61801 Present Address: NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510; e-mail: [email protected] Present Address: Department of Astronomy, University of California, Berkeley, CA 94720