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

Limits to the Gunn-Peterson effect due to neutral hydrogen have generally been obtained by modeling the observed Ly alpha forest as a superposition of absorption lines with Voigt profiles arising from clouds of photoionized gas, and a hypothesized uniform continuum arising from the intergalactic medium. However, owing to the formation of structure by gravitational instability, a photoionized intergalactic medium should be inhomogeneous on scales larger than the Jeans scale, and therefore the optical depth should fluctuate. Such a fluctuating continuum can always be modeled as a superposition of lines, but this decomposition does not necessarily have a direct physical meaning. We present a calculation of the evolution of the density in voids in a photoionized intergalactic medium, using the Zeldovich approximation and another analytical approximation which we argue should be more accurate in this regime. From this, we calculate the probability distribution of the Gunn-Peterson optical depth in terms of the amplitude of the primordial density fluctuations. Over most wavelengths in a quasar spectrum, the optical depth originates from gas in underdense regions, or voids. Individual absorption lines should be associated with overdense regions, which we do not treat here. This causes the median Gunn-Peterson absorption to be lower than the value for a uniform medium containing ah the baryons in the universe by a large factor, which increases as gravitational collapse proceeds. The Gunn-Peterson effect is the only known method to directly observe underdense matter in the universe, and it can be sensitive to the primordial fluctuations even in the nonlinear regime. In particular, in the He Pi Gunn-Peterson effect recently detected by Jakobsen et at, gaps in the absorption are a very sensitive probe to the most underdense voids. 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 Ly alpha clouds arise from gravitational collapse, their observations must be interpreted as the first detection of the fluctuating Gunn-Peterson effect, with a median value tau(GP) similar or equal to 0.06 at z = 4. If the linearly extrapolated rms density fluctuation at the Jeans scale for the photoionized gas were close to unity at this redshift (which is the case in typical low-density models with cold dark matter), then tau(GP) should be similar to 1/5 of the optical depth that would be produced by a uniform intergalactic medium. 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 et al., such models also predict correctly the number of Ly alpha absorption lines observed. For theories with much larger density fluctuations (such as standard cold dark matter), we argue that, given the observed number of lines with N-HI greater than or similar to 10(14) cm(-2) the Gunn-Peterson optical depth should be much lower than observed; this needs to be investigated in more detail using numerical simulations.