The Lyman-Alpha Forest in the Lensed Quasar Q0957+561 and the Characteristic Dimension of the Absorbing Clouds

Far-ultraviolet spectra of the gravitational lens components Q0957+561 A and 9 were obtained with the Hubble Space Telescope Faint Object Spectrograph (FOS) at five equally spaced epochs, one every two weeks. We confirm the flux variability of the quasar's Lyman-alpha and 0 VI emission lines reported by Dolan et al. (1995) in IUE spectra. The fluxes in these lines vary on a time scale of weeks in the observer's rest frame, independently of each other and of the surrounding continuum. The individual spectra of each image were co-added to investigate the properties of the Lyman-alpha forest along the two lines of sight to the quasar. Absorption lines having equivalent width W > 0.3 A in the observer's frame not previously identified by Michalitsianos et al. (1997) as interstellar lines, metal lines, or higher order Lyman lines were taken to be Ly-alpha forest lines. The existence of each line in this consistently selected set was then verified by its presence in two archival FOS spectra with -1.5 times higher signal to noise than our co-added spectra. Ly-alpha forest lines with W > 0.3 A appear at 41 distinct wavelengths in the spectra of the two images. one absorption line in the spectrum of image A has no counterpart in the spectrum of image B and one line in image B has no counterpart in image A. Based on the separation of the lines of sight over the redshift range searched for Ly-forest lines, the density of the absorbing clouds in the direction of Q0957+561 must change significantly over a distance R = 160 (+120, -70)/ h(sub 50) kpc in the simplified model where the absorbers are treated as spherical clouds and the characteristic dimension, R, is the radius. (We adopt H(sub 0) = 50 h(sub 50) km/s/ kpc, q(sub 0) = 1/2, and lambda = 0 throughout the paper.) The 95% confidence interval on R extends from (50 - 950)/h(sub 50) kpc We show in the Appendix that the fraction of Ly-alpha forest lines that appear in only one spectrum can be expressed as a rapidly converging power series in 1/r, where r the ratio of the radius of the cloud to the separation of the two lines of sight at the redshift of the cloud. This power series can be rewritten to give r in terms of the fraction of Ly-forest wavelengths that appear in the spectrum of only one image. A simple linear approximation to the solution that everywhere agrees with the power series solution to better than 0.8% for r > 2 is derived in the Appendix.