Continuous statistics of the Lyα forest at 0 < z < 1.6:: the mean flux, flux distribution and autocorrelation from HST FOS spectra

We measure the amount of absorption in the Ly alpha forest at 0 < z < 1.6 in Hubble Space Telescope Faint Object Spectrograph spectra of 74 quasi-stellar objects (QSOs). Starting with a 334 QSO sample compiled by Bechtold et al., we selected 74 QSOs that have the highest signal-to-noise ratio and complete coverage of rest-frame wavelengths 1070 - 1170 angstrom. We measure the absorption from the flux in each pixel in units of the unabsorbed continuum level. We mask out regions of spectra that contain metal lines, or strong Ly alpha lines that are accompanied by other Lyman series line or metals at the same redshift, leaving Ly alpha absorption from the low-density intergalactic medium (IGM). At 0 < z < 1.6 we find that 79 per cent of the absorption is from the low-density IGM, 12 per cent from metals and 9 per cent from the strong HI lines, nearly identical to the percentages ( 78, 15 and 7) that we measured independently at z = 2 from spectra taken with the Kast spectrograph on the Lick 3-m. At z = 1 the low-density IGM absorbs 0.037 +/- 0.004 of the flux. The error includes some but not all of the uncertainty in the continuum level. The remaining part gives relative errors of approximately 0.21 when we report the mean absorption in eight independent redshift intervals, and 0.047 when we average over all redshifts. We find 1.46 times more absorption from the low-density IGM than comes from Ly alpha lines that Bechtold et al. listed in the same spectra. The amount of absorption increases with z and can be fit by a power law (1 + z)(alpha), with alpha = 1.01. If the absorption comes entirely from lines with fixed rest equivalent width, this result implies the number density of lines evolves like ( 1 + z)(0.01), or no change in the number of lines per unit redshift, consistent with the Janknecht et al. results on the distribution of lines. When we include similar measurements from higher redshifts, we need more degrees of freedom to fit the amount of absorption at 0 < z < 3.2. A power law with a break in slope, changing from index 1.5 at low z to 3.0 above z similar to 1.1 is a better but only marginally acceptable fit. We also calculate two other continuous statistics, the flux probability distribution function and the flux autocorrelation function that is non-zero out to v similar to 500 km s(-1) at 0.5 < z < 1.5.