THE QUASAR PROXIMITY EFFECT IN AN EQUIVALENT-WIDTH-LIMITED SAMPLE OF THE LYMAN-ALPHA FOREST

We have obtained a simple analytical approximation to the relationship between a rest-frame equivalent-width distribution for Lyalpha forest absorption lines, N(W), and an H I column density distribution of the observed cloud number, N(N). Assuming a simple power-law form for N(N) is-proportional-to N1-beta, it is shown that beta = 1.4 turns out to agree fairly well with the observed form of N(W) in a broad range of column densities, 10(13) cm-2 less than or similar to N less than or similar to 5 x 10(16) cm-2, which corresponds to equivalent-width range W = 0.06-0.7 angstrom. We present a theoretical analysis of how the ''proximity effect'' influences a W-limited sample of Lyalpha forest lines. It is shown that this influence is considerably smaller than has been found before for a N-limited sample, for which an approximate value of beta (almost-equal-to 1.7) was assumed rather than derived as has been done, for a W-limited sample, in the present paper. As a result, available observational data appear to be still consistent with the conjecture that the observed population of QSOs is the major source of the UV background at redshifts z almost-equal-to 2-4.