We measure the amount of absorption in the \lyaf at 0 < z < 1.6 in Hubble Space Telescope Faint Object Spectrograph spectra of 74 QSOs .
Starting with a 334 QSO sample compiled by Bechtold et al . 2002 , we selected 74 QSOs that have the highest signal to noise and complete coverage of rest frame wavelengths 1070 –1170 Å .
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 .
At 0 < z < 1.6 we find that 79 % of the absorption is from the low density intergalactic medium , 12 % from metals and 9 % from the strong H I 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 intergalactic medium absorbs 0.037 \pm 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 intergalactic medium than comes from Ly \alpha lines that Bechtold et al . 2002 listed in the same spectra .
The amount of absorption increases with z and can be fit by a power law in ( 1 + z ) with index 1.01 .
This corresponds to no change in the number of lines , of fixed rest frame equivalent widths , per unit redshift , consistent with the Janknecht et al . 2006 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 \sim 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 \sim 500 km s ^ { -1 } at 0.5 < z < 1.5 .