Additional observations and analysis of the Lyman-alpha absorption lines toward the QSO pair Q0107-025A,B

We present further analysis and discussion of the properties of the absorption lines in the QSO pair Q0107-025A,B (z(em) = 0.956, 0.952; angular separation 1.'29) based upon spectroscopy obtained with the Faint Object Spectrograph (FOS) of the Hubble Space Telescope (HST). We also present observations of the pair at shorter wavelengths taken with the HST Goddard High Resolution Spectrograph lower-solution grating, as well as Multiple Mirror Telescope spectra obtained with the intent of looking for metal-line counterparts to the Lyman-alpha absorption systems. The most interesting feature revealed by the GHRS spectra is a weak Lyman limit system with a redshift of z(LLS) = 0.3997. The Lyman limit system itself is seen only in Q0107-025B, but corresponding Ly alpha lines can be seen in the FOS spectra of both Q0107-025A and B indicating that lower column density gas extends out to greater distances than higher column density gas. From a sample of 5 sigma lines with W-0 > 0.32 Angstrom detected in the FOS spectra, we count five systems (including a probable system) common to both spectra with velocity differences less than 150 km s(-1) and six systems that are not in common to both spectra in the redshift range 0.48 < z < 0.89. From the presence of common absorption, we obtain lower limits on the radius of the absorbers of 140-160 h(-1) kpc [h = H-0/(100 km s(-1) Mpc(-1)) q(0) = 0.5]. Using a simple maximum-likelihood analysis, we estimate a characteristic radius of 505 h(-1) kpc assuming spherical absorbers, with confidence lower and upper limits of 345 < R < 1520 h(-1) kpc. For disklike absorbers, we derive a most probable radius of 715 h(-1) kpc and 95% confidence limits of 470 < R < 2310 h(-1) kpc. We also present a new statistical technique to test the relative likelihood of three geometric models. In particular, we consider spherical absorbers, with and without a distribution in size, as well as filamentary and disklike absorbers. Spherical absorbers with uniform radius can be ruled out since they cannot simultaneously reproduce the large equivalent width coincidences and anticoincidences observed. The model that best reproduce the equivalent width distribution of the observed coincident and anticoincident systems corresponds to randomly inclined disks with characteristic radius 915 h(-1) kpc and 95% confidence interval 560 < R < 1270 h(-1) kpc. Our results are in agreement with recent cosmological simulations that produce Ly alpha forest absorbers in the form of filaments and sheets with coherence lengths as great as 1 Mpc.