The effects of an ionizing background on the H I column density distribution in the local universe

Using data on the H I column density distribution in the local universe, f(N-H I) in this paper we show how to determine g(N-H), the distribution of the total gas (H I+H II) column density. A simple power-law fitted to f(N-H I) fails due to bendings in the distributions when N-H (I) < 10(20) cm(-2) and H is no longer fully neutral. If an ultraviolet background is responsible for the gas ionization and g(N-H) ∝ N-H(-alpha), we find the values of alpha and of the intensity of the background radiation that are compatible with the present data. The best-fitting values of alpha, however, depend upon the scaling law of the gas volume densities with N-H and cannot be determined unambiguously. We examine in detail two models: one in which the average gas volume density decreases steadily with N-H, and another in which it stays constant at low column densities. The former model leads to a steep power-law fit for g(N-H) with alpha similar or equal to 3.3 +/- 0.4, and requires an ultraviolet flux larger than what the quasi-stellar objects (QSOs) alone produce at z = 0. For the latter, a similar or equal to 1.5 +/- 0.1 and a lower ionizing flux is required. The ambiguities concerning the modeling and the resulting steep or shallow N-H distribution can be resolved only if new 21 cm observations and QSOs Lyman limit absorbers searches provide more data in the H I-H II transition region at low redshifts. Using the best fit obtained for higher redshift data, we outline two possible scenarios for the evolution of gaseous structures, compatible with the available data at z similar to 0.