The physical properties of the Lyα forest at z>1.5

Combining a new, increased data set of eight quasi-stellar objects (QSOs) covering the Lyalpha forest at redshifts 1.5 < z < 3.6 from VLT/UVES observations with previously published results, we have investigated the properties of the Lyalpha forest at 1.5 < z < 4. With the six QSOs covering the Lyalpha forest at 1 5 < z < 2 5, we have extended previous studies in this redshift range. In particular, we have concentrated on the evolution of the line number density and the clustering of the Lyalpha forest at z less than or equal to 2.5, where the Lyalpha forest starts to show some inhomogeneity from sightline to sightline. We have fitted Voigt profiles to the Lyalpha absorption lines as in previous studies, and have, for two QSOs with z(em) similar to 2.4, fitted Lyalpha and higher order of Lyman lines down to 3050 Angstrom simultaneously. This latter approach has been taken in order to study the Lyalpha forest at z similar to 2.2 and the higher H I column density Lyalpha forest in the Lybeta forest region. For a given N-H I range, the Lyalpha forest at 1.5 < z < 4 shows the monotonic evolution, which is governed mainly by the Hubble expansion at this redshift range. In general, the Lyalpha forest line number density (dn/dz) is best approximated with dn/dz = 6.1(1 + z)(2.47+/-0.18) for the H I column density N-H I = 10(13.64-17) cm(-2) at 1.5 < z < 4. When the results at 0 < z < 1.5 from Hubble Space Telescope (HST) observations are combined, the slow-down in the number density evolution occurs at z < 1.5. For higher column density clouds at N-H I > 10(14) cm(2), there is a variation in the line number density from sightline to sightline at z < 2.5. This variation is stronger for higher column density systems, probably due to more gravitationally evolved structures at lower z. The mean H I opacity <(tau)over bar>(H I) is (τ) over bar (H I)(z) = 0.0032(1 + z)(3.37+/-0.20) at 1.5 < z < 4. HST observations show evidence for slower evolution of (τ) over bar (H I) at z < 1. For N-H I = 10(12.5-15) cm(-2), the differential column density distribution function, f(N-H I), can be best fitted by f(N-H I) ∝ N-H I(-beta) with beta approximate to 1.5 for 1.5 < z < 4. When combined with HST observations, the exponent beta increases as z decreases at 0 < z < 4 for N-H I = 10(13-17) cm(-2). The correlation strength of the step optical depth correlation function shows the strong evolution from z = 3.3 to [z] = 2.1, although there is a large scatter along different sightlines. The analyses of the Lyalpha forest at z similar to 2.2 are, in general, in good agreement with those of the Lyalpha forest.