The Characteristic Dimension of Lyman-Alpha Forest Clouds Toward Q0957+561

Far-ultraviolet spectra of the gravitational lens components Q0957+561 A and B were obtained with the Hubble Space Telescope Faint Object Spectrograph to investigate the characteristic dimension of Lyman-alpha forest clouds in the direction of the quasar. If one makes the usual assumption that the absorbing structures are spherical clouds with a single radius, that radius can be found analytically from the ratio of Lyman-alpha lines in only one line of sight to the number in both. A simple power series approximation to this solution, accurate everywhere to better than 1%, will be presented. Absorption lines in Q0957+561 having equivalent width greater than 0.3 A in the observer's frame not previously identified 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 approximately 1.5 times higher signal to noise than our spectra. Ly-alpha forest lines 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-alpha forest lines, the density of the absorbing clouds in the direction of Q0957+561 must change significantly over a radius R = 160 (+120, -70) h (sup -1) (sub 50) kpc (H (sub 0) 50 h (sub 50) km s (sup -1) kpc (sup -1), q (sub 0) = 1/2). The 95% confidence interval on R extends from (50 950) h (sup -1) (sub 50) kpc.