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 Ly-alpha 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) proportional to N exp (1-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. We present a theoretical analysis of how the 'proximity effect' influences a W-limited sample of Ly-alpha 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 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 about 2-4.