SPECTROSCOPY OF THE DOUBLE QUASARS Q1343- A NEW DETERMINATION OF THE SIZE OF LYMAN-ALPHA FOREST ABSORBERS(266A, Q1343+266B )

We have obtained spectroscopy of Q1343 + 266A, B, a pair of quasars at redshift z = 2.03 with a projected separation of 9''.5. This system i s well suited for probing the Ly alpha forest, since the two-component spectra show several Ly alpha lines in common and several others not. Using Bayesian statistics, under the idealization of uniform-radius s pherical absorbers, we find that the Ly alpha cloud radius at z approx imate to 1.8 lies in the range 40 h(-1) kpc < R < 280 h(-1) kpc with 9 8% confidence in a (Omega(0), Lambda(0)) = (1, 0) model universe, wher e h drop (H-0/100 km s(-1) Mpc(-1)). The median value of R is 90 h(-1) kpc. These numbers scale up by a factor 1.44 for (Omega(0), Lambda(0) ) = (0.1, 0) and by a factor 1.85 for (0.1, 0.9). Pressure-confined an d freely expanding Ly alpha cloud models in which the absorbers formed in a significantly more compressed state at z >> 2 are contradicted b y these new data, as are models involving stably confined gas concentr ations in photoionization equilibrium within minihalos of cold dark ma tter. The comoving density of Ly alpha forest objects at z similar to 2 is similar to 0.3 h (R/100 kpc)(-2) Mpc(-3) in a (1, 0) model univer se. This suggests a possible identification of Ly alpha clouds with th e unvirialized, collapsing progenitors of the faint, blue galaxies at z similar to 1.