Stochastic Absorption of the Light of Background Sources due to Intergalactic Neutral Hydrogen I. Testing different line-number evolution models via the cosmic flux decrement
[Abridged] We test the accuracy of different models of the attenuation of light due to resonant scattering by intergalactic neutral hydrogen by comparing their predictions of the evolution of the mean cosmic flux decrement, D_A, to measurements of this quantity based on observations. To this end, we use data available in the literature and our own measurements of the cosmic flux decrement for 25 quasars in the redshift range 2.71 < z < 5.41 taken from the SDSS Data Release 5. In order to perform the measurements of D_A, we fit a power-law to the continuum redward of the Lya emission line, and extrapolate this fit to region blueward of it, where the flux is severely affected by absorption due to intervening HI absorbers. We compute, using numerical simulations, the redshift evolution of D_A accounting for the presence of Lya Forest absorbers and Lyman limit systems randomly distributed along the line-of-sight, and compute its intrinsic scatter at the 1-, 2-, and 3-sigma level due to fluctuations in the absorber properties (column density, Doppler parameter, redshift) along different lines-of-sight. The numerical simulations consist of Monte Carlo realizations of distributions of the absorber properties constrained from observations. The results from the models considered here confirm our theoretical expectation that the distribution of D_A at any given redshift be well described by a lognormal distribution function. This implies that the effective optical depth, usually defined as the negative logarithm of the average flux, 1 - D_A, is very accurately Gaussian distributed, in contrast to previous studies. This result is independent to the form of the input distribution functions, and rather insensitive to the presence of high-column density absorbers, such as the Lyman limit systems.