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Properties of the Lyman Alpha Clouds from non-equilibrium Photoionization Models

We investigate the thermal and ionization history of Lyman alpha clouds photoionized by a time--dependent UV background, including non equilibrium effects. The results show that it is possible to obtain temperatures as low as T~15000 K (or, equivalently, Doppler parameters b~15 km/s) at z=3 for cloud total densities n~10^-4 cm^-3, if (i) the reionization epoch occurred at z_i~10, and (ii) the UV background has a factor 70-100 decrease at the HeII edge. A trend towards smaller b with increasing redshift is present in the redshift interval z=1-5. Higher densities lead to higher values of b and smaller hydrogen correction factors, n_{HII}/n_{HI}. The correction factors for helium are also given. For a hydrogen column density N_{HI}=3 10^{14} cm^{-2}, cloud sizes are larger than 100 kpc, consistent with recent observations of quasar pairs. Pressure confined models, instead, yield implausibly low cloud densities at low redshift, and too small sizes at intermediate redshift. The implications of the model are confronted with the available observational data.