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

Limits to the Gunn-Peterson effect due to neutral hydrogen have genera lly been obtained by modeling the observed Ly alpha forest as a superp osition of absorption lines with Voigt profiles arising from clouds of photoionized gas, and a hypothesized uniform continuum arising from t he intergalactic medium. However, owing to the formation of structure by gravitational instability, a photoionized intergalactic medium shou ld be inhomogeneous on scales larger than the Jeans scale, and therefo re the optical depth should fluctuate. Such a fluctuating continuum ca n always be modeled as a superposition of lines, but this decompositio n does not necessarily have a direct physical meaning. We present a ca lculation of the evolution of the density in voids in a photoionized i ntergalactic medium, using the Zeldovich approximation and another ana lytical approximation which we argue should be more accurate in this r egime. From this, we calculate the probability distribution of the Gun n-Peterson optical depth in terms of the amplitude of the primordial d ensity fluctuations. Over most wavelengths in a quasar spectrum, the o ptical depth originates from gas in underdense regions, or voids. Indi vidual absorption lines should be associated with overdense regions, w hich we do not treat here. This causes the median Gunn-Peterson absorp tion to be lower than the value for a uniform medium containing ah the baryons in the universe by a large factor, which increases as gravita tional collapse proceeds. The Gunn-Peterson effect is the only known m ethod to directly observe underdense matter in the universe, and it ca n be sensitive to the primordial fluctuations even in the nonlinear re gime. In particular, in the He Pi Gunn-Peterson effect recently detect ed by Jakobsen et at, gaps in the absorption are a very sensitive prob e to the most underdense voids. We apply our calculations to the obser vations of the intensity distribution in a z = 4.11 quasar by Webb and coworkers. We show that if Ly alpha clouds arise from gravitational c ollapse, 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 de nsity fluctuation at the Jeans scale for the photoionized gas were clo se 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 pri mordial nucleosynthesis, and the intensity of the ionizing background derived from the proximity effect. From the numerical simulations of C en et al., such models also predict correctly the number of Ly alpha a bsorption lines observed. For theories with much larger density fluctu ations (such as standard cold dark matter), we argue that, given the o bserved 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 observe d; this needs to be investigated in more detail using numerical simula tions.