We have analyzed the properties of low column density Ly \alpha forest clouds ( 12.8 \leq \log N _ { HI } \leq 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 } \leq 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 .