We investigate the thermal and ionization history of Ly \alpha clouds photoionized by a time–dependent UV background , including nonequilibrium effects .
The results show that it is possible to obtain temperatures as low as T \sim 15000 K ( or , equivalently , Doppler parameters b \simeq 15 km s ^ { -1 } ) at z = 3 for cloud total densities n \sim 10 ^ { -4 } cm ^ { -3 } , if ( i ) the reionization epoch occurred at z _ { i } \sim 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 \times 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 .