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THE GUNN-PETERSON EFFECT FROM UNDERDENSE REGIONS IN A PHOTOIONIZED INTERGALACTIC MEDIUM

We use the Zel'dovich approximation and another analytical approximation to calculate the evolution under gravitational instability of the underdense regions of a photoionized intergalactic medium (IGM). We find that over most of the spectrum of a quasar, the optical depth to $\lya$ scattering originates from gas in underdense regions, or voids. This causes the ratio of the median Gunn-Peterson (GP) absorption to the value for a uniform medium containing all the baryons in the universe to be very small, and to decrease as gravitational collapse proceeds. We apply our calculations to the observations of the intensity distribution in a $z=4.11$ quasar by Webb and coworkers. We show that if $\lya$ clouds arise from gravitational collapse, their observations must be interpreted as the first detection of the (fluctuating) GP effect, with a median value $τ_{GP}\simeq 0.06$ at $z=4$. For typical low-density ($Ω\sim 0.4$) cosmological models, this is consistent with the predicted baryon density from primordial nucleosynthesis, and the intensity of the ionizing background derived from the proximity effect. From the numerical simulations of Cen \etal, such models also predict correctly the number of $\lya$ absorption lines observed.