MEASUREMENTS OF DA FOR A LARGE QSO SAMPLE AND DETERMINATION OF EVOLUTION OF LYMAN-ALPHA CLOUDS

We have measured D(A), the mean relative depression of quasar continuum between Lyalpha and Lybeta emission, for a large sample of quasars. We have carried out the measurements by simply adding the Lyalpha lines (excluding the lines in identified systems) together. The big advantage of this approach over the conventional method is that the continuum is fitted locally by employing high S/N and relatively high resolution spectra, and this leads to a more reliable estimate of the continuum level in the Lyalpha forest region. Also, the contamination of D(A) by metal lines is easily removed. Extending the method proposed by Zuo (1993) and Lu & Zuo (1993), we have determined gamma(int), the intrinsic evolutionary rate exponent of Lyalpha forest lines. For redshifts between 1.7 and 3.7, our best estimate is gamma(int) = 2.87 +/- 0.23 (for our Sample 2 QSOs). However, if we combine our measurements with the D(A) values determined for z(em) > 4 QSOs by Schneider, Schmidt, & Gunn (1989a, b, 1991), a better fit is obtained by adopting a broken power-law form with the break point at z = 3.11 and gamma1 = 2.82 for z < 3.11 and gamma2 = 5.07 for z > 3.11. Our method does not require line deblending and is quite robust to certain kinds of systematic errors in D(A) measurements. We have explored how a simple Lyalpha cloud mode in which all (baryonic) clouds are expanding and at the same time keeping roughly a r-2 density profile, combined with the evolution of the ionizing background, can be used to understand the observed D(A) evolution with redshift. This simple model offers a definite theory for the formation of absorption line profiles and leads to a line distribution eta(z, N) = AN-beta(1 + z)gammaint. We have calculated the line profiles for some impact parameter b(imp) and redshift z, and have found that they can be roughly approximated by Gaussian profiles with a b = 30 km s-1. This approximation is especially good for low-N lines and at low z.