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1.3. Gunn-Peterson Effect

Consider radiation emitted at some frequency nue that lies blueward of Lyalpha by a source at redshift ze, and observed at Earth at frequency nuo = nue (1 + ze)-1. At a redshift z such that (1 + z) = (1 + ze) nualpha / nue, the emitted photons pass through the local Lyalpha resonance as they propagates towards us through a smoothly distributed sea of neutral hydrogen atoms, and are scattered off the line-of-sight with a cross-section (neglecting stimulated emission) of

Equation 11 (11)

where f = 0.4162 is the upward oscillator strength for the transition, phi is the line profile function [with normalization integ phi(nu) dnu = 1], c is the speed of light, and e and me are the electron charge and mass, respectively. The total optical depth for resonant scattering at the observed frequency is given by the line integral of this cross-section times the neutral hydrogen proper density nHI(z),

Equation 12 (12)

where dl /dz = c H0-1 (1 + z)-1 [OmegaM (1 + z)3 + OmegaK (1 + z)2 + OmegaLambda]-1/2 is the proper line element in a Friedmann-Robertson-Walker metric, and OmegaM, OmegaLambda, and OmegaK = 1 - OmegaM - OmegaLambda are the matter, vacuum, and curvature contribution to the present density parameter. As the scattering cross-section is sharply peaked around nualpha, we can write

Equation 13 (13)

In an Einstein-de Sitter (OmegaM = 1, OmegaLambda = 0) Universe, this becomes

Equation 14 (14)

The same expression for the opacity is also valid in the case of optically thin (to Lyalpha scattering) discrete clouds as long as nHI is replaced with the average neutral density of individual clouds times their volume filling factor.

In an expanding Universe homogeneously filled with neutral hydrogen, the above equations apply to all parts of the source spectrum to the blue of Lyalpha. An absorption trough should then be detected in the level of the rest-frame UV continuum of the quasar; this is the so-called ``Gunn-Peterson effect''. Between the discrete absorption lines of the Lyalpha forest clouds, quasar spectra do not show a pronounced Gunn-Peterson absorption trough. The current upper limit at ze approx 5 is tauGP < 0.1 in the region of minimum opacity, implying from equation (14) a neutral fraction of nHI / nbarH < 10-6 h. Even if 99% of all the cosmic baryons fragment at these epochs into structures that can be identified with quasar absorption systems, with only 1% remaining in a smoothly distributed component, the implication is a diffuse IGM which is ionized to better than 1 part in 104.

In modern interpretations of the IGM, it is difficult to use the Gunn-Peterson effect to quantify the amount of ionizing radiation that is necessary to keep the neutral hydrogen absorption below the detection limits. This is because, in hierarchical clustering scenarios for the formation of cosmic structures (the Cold Dark Matter model being the most studied example), the accumulation of matter in overdense regions under the influence of gravity reduces the optical depth for Lyalpha scattering considerably below the average in most of the volume of the Universe, and regions of minimum opacity occur in the most underdense areas (expanding `cosmic minivoids').

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