1 Introduction

The evolution of the Lyman forest is governed by two main factors: the Hubble expansion and the the metagalactic UV background. At high redshift the expansion, which tends to increase the ionisation of the matter, and the UV background, increasing or non-decreasing with decreasing redshift, work in the same direction and cause a steep evolution of the number of lines with z. At low redshift, the UV background starts to decrease with decreasing redshift, due to the reduced number of ionising sources, and this effect counteracts the Hubble expansion. As a result the evolution of the number of lines slows down.

In a recent study of the evolution of the Lyman forest Kim et al. (2001) have shown that the number of Ly$\alpha$ lines per unit redshift, ${\rm d}N/{\rm d}z$, is well described by a double power-law with a break at $z\sim 1$. For column densities in the interval $N_H{\sc i} = 10^{13.64-16} \ {\rm cm}^{-2}$, ${\rm d}N/{\rm d}z \propto (1+z)^{2.19 \pm 0.27}$ at 1.5 <z < 4, while ${\rm d}N/{\rm d}z \propto (1+z)^{0.16 \pm 0.16}$ at z<1 (Weymann et al. 1998).

Recent numerical simulations have been remarkably successful in reproducing the observed evolution (see, for example Davé et al. 1999; Machacek et al. 2000), leaving little doubt about the general interpretation of the phenomenon. However the same simulations predict the break in the ${\rm d}N/{\rm d}z$ power-law at a redshift $z \sim 1.8$ which appears too high in the light of the new results of Kim et al. (2001). This suggests that the UV background implemented in the simulations is not completely correct: QSOs have been considered as the main source of ionising photons, and, since their space density drops below $z\sim 2$, so does the UV background. However, galaxies can produce a non-negligible ionising flux too, perhaps more significant than previously assumed, as shown by recent measurements by Steidel et al. (2001). The galaxy contribution can keep the UV background relatively high until at $z\sim 1$ the global star formation rate in the Universe quickly decreases, determining the change in the number density of lines.

In this paper we recompute the contribution of QSOs and galaxies to the UV background following the recipes of Madau (1991, 1992), Haardt & Madau (1996) and Madau et al. (1998) (Sect. 2). In Sect. 3 the results are compared with constraints on the UV background derived from the proximity effect and the H$\alpha$ emission of high galactic latitude clouds. In Sect. 4 the evolution of the number of Ly$\alpha$ lines per unit redshift is computed according to a simple analytical model for different relative contributions of galaxies and QSOs. In Sect. 5 we summarise the results and discuss some consequences of them in terms of present and future observations.

All the computations are carried out for two flat cosmologies: an Einstein-De Sitter cosmology ( $\Omega _{\rm m}=1$, $\Omega_\Lambda=0$) and a $\Lambda$ cosmology ( $\Omega_{\rm m}=0.3,\Omega_\Lambda=0.7$). We have adopted H₀=70 kms^-1 Mpc^-1 (Freedman et al. 2001) throughout and scaled to this value the data derived from the literature.