The redshift evolution of Lyman-$\alpha$ absorbers

We present a model for the Lyman-alpha absorbers that treats all objects (from the low-density forest clouds to the dense damped systems) in a unified description. This approach is consistent with an earlier model of galaxies (luminosity function, metallicity) but also with the known description of the density field in the small-scale non-linear regime. We consider two cosmological models: a critical universe $\Omega=1$ with a CDM power-spectrum, and an open CDM universe with $\Omega_0=0.3$, $\Lambda=0$. We reproduce the available data on column density distribution as a function of redshift, the value of the main new parameter, the background ionizing UV flux, being consistent with the observed limits. This allows a quantitatively trustable analytical description of the opacity, mass, size, velocity dispersion and metallicity of these absorbers, over a range of column densities spanning 10 orders of magnitude. Moreover, together with an earlier model of galaxy formation this draws a unified picture of the redshift evolution of structures in the universe, from underdense clouds to massive high density galaxies, from weak to very deep potential wells