Tracing the gas at redshift 1.7-3.5 with the Lyman-alpha forest: the FLO approach

[Abridged] We present FLO (From Lines to Over-densities), a new technique to reconstruct the hydrogen density field for the Lya forest lines observed in high resolution QSO spectra. The method is based on the hypothesis that the Lya lines arise in the low to intermediate density intergalactic gas and that the Jeans length is the typical size of the Lya absorbers. The reliability of FLO is tested against mock spectra obtained from cosmological simulations. The recovering algorithm gives satisfactory results in the range from the mean density to over-densities of ~30 and reproduces correctly the correlation function of the density field and the 1D power spectrum on scales between ~20 and 60 comoving Mpc. A sample of Lya forests from 22 high resolution QSO spectra is analysed, covering the redshift range 1.7<z<3.5. For each line of sight, we fit Voigt profiles to the lines of the Lya forest, providing the largest, homogeneous sample of fitted Lya lines ever studied. The line number density evolution with redshift follows a power-law relation: dn/dz=(166 +/- 4) [(1+z)/3.5]^{(2.8 +/- 0.2)} (1 sigma errors). The two-point correlation function of lines shows a signal up to separations of ~2 comoving Mpc; weak lines (log N(HI)<13.8) also show a significant clustering but on smaller scales (r<1.5 comoving Mpc). We estimate with FLO the hydrogen density field toward the 22 observed lines of sight. The redshift distribution of the average densities computed for each QSO is consistent with the cosmic mean hydrogen density in the analysed redshift range. The two-point correlation function and the 1D power spectrum of the delta field are estimated. The correlation function shows clustering signal up to ~4 comoving Mpc.