The Size and geometry of the Ly alpha clouds

Spectra of the QSO pair Q0307-195A,B have been obtained in the Ly-alpha Forest (3660 - 3930 A) and C IV (4720 - 4850 A) regions with a FWHM resolution between 0.7 and 0.5 A. 46 lines have been detected in the spectrum of object A while 36 in the spectrum of object B, of them 29 and 20 were identified as Ly-alpha absorptions respectively. The present observations have been supplemented with data of comparable quality on other 7 QSO pairs available in the literature to give an enlarged sample of 217 Ly-alpha lines with rest equivalent width W_o > 0.3 A. The analysis of the hits (i.e. when an absorption line appears in both QSO spectra) and misses (i.e. when a line is seen in any of the QSO spectra, but no line is seen in the other), carried out with an improved statistical approach, indicates that the absorbers have typically a large size (h = H_0/100 km/s/Mpc, q_0 = 0.5): R = 362 h^{-1} kpc, with 95 % confidence limits 298< R <426 h^{-1} kpc and R = 412 h^{-1} kpc, with 95 % confidence limits 333< R <514 h^{-1} kpc for the radius in idealized spherical and disc geometries, respectively. The present data do not allow to establish any correlation of the typical inferred size with the proper separation or with the redshift of the pairs. The correlation between the observed equivalent widths of the absorbers in the adjacent lines of sight becomes poorer and poorer with increasing proper separation. A disc geometry with a column density profile N(r) \propto (r/R_0)^{-gamma}, gamma=4, is found to reasonably reproduce the data with R_0 ~ 100-200 h^{-1} kpc, but also spherical clouds with the same column density profile and a power-law distribution of radii may give a satisfactory representation of the observations.