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

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

1996-08-24

arxiv.org/abs/astro-ph/9608157v3

Astrophys.J. 486 (1997) 599

Astronomy and Astrophysics

Astrophysics

match accepted version; discussion added: the effect of the shape of the power spectrum on the slope of the column density dis

Scientific paper

10.1086/304539

We develop a method to calculate the column density distribution of the Lyman-alpha forest for column densities in the range $10^{12.5} - 10^{14.5} cm^{-2}$. 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 $2 h Mpc^{-1} < k < 20 h Mpc^{-1}$. 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 $(\Omega_b h^2)^2 T_0^{-0.7} J_{HI}^{-1}$, 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 range of column densities we study. Comparison with high resolution Keck data is made.

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