The Redshift Evolution of the Lyman $\alpha$ Forest

We have analyzed the properties of low column density Lyman alpha forest clouds (12.8 < log N_HI < 16.0) toward 5 QSOs at different redshifts, using high signal-to-noise data from the HIRES spectrograph on the Keck I 10-m telescope. The results are used to study the evolution of these clouds in the interval 2.1 < z < 3.5. We find: 1) The differential density distribution of forest clouds, f(N_HI), fits an empirical power law with a typical slope of -1.35 to -1.55 for clouds with N_HI < 10^14.3 cm^-2 and changes extremely slowly with redshift over this N_HI range. 2) The deviation of f(N_HI) from this power-law distribution at higher column densities depends on redshift: for higher redshifts, the departure from a power-law distribution occurs at higher N_HI, which means that higher column density clouds rapidly disappear with decreasing redshift. This may be consistent with an invariant shape for the different column density distributions, but with a shift to a lower column density normalization for systems at different redshifts driven by the overall expansion of the universe. 3) The line widths of the forest clouds increase as redshift decreases. 4) The correlation strength of the forest clouds seems to increase as redshift decreases. We discuss these results in terms of the evolution of the IGM comparing the results to models and analytic descriptions of the evolution of structure in the gas