Redshift evolution of the Lyman-alpha forest

The Lyman-alpha forest becomes denser and more opaque towards higher cosmological redshift, for a fixed absorption selection over the ordinary post-reionization range. The incidence is often parametrized as $d\mathcal{N}/dz=A(1+z{)}^{\gamma }$, with the index depending on the column density threshold and epoch. The evolution flattens at low redshift as the declining cosmic ionizing background partly offsets dilution of the intergalactic medium. For optically thin gas at fixed overdensity, photoionization equilibrium gives approximately $n_{\mathrm{HI}}\propto \alpha (T)(1+z{)}^6/\Gamma$, illustrating why density, temperature and ionizing radiation all matter.