Constraints on the ultraviolet metagalactic emissivity using the Lyα forest

Numerical hydrodynamical simulations have proven a successful means of reproducing many of the statistical properties of the Lyalpha forest as measured in high redshift quasar spectra. The source of ionization of the intergalactic medium (IGM), however, remains unknown. We investigate how the Lyalpha forest may be used to probe the nature of the sources. We show that the attenuation of Lyman continuum photons by the IGM depends sensitively on the emissivity of the sources, permitting a strong constraint to be set on the required emissivity to match the measured values of the mean IGM Lyalpha optical depth. We find that, within the observational errors, quasi-stellar object (QSO) sources alone are able to account for the required ultraviolet (UV) background at z greater than or similar to 4. By contrast, the emissivity of Lyman-break galaxies (LBGs) must decline sharply with redshift, compared with the estimated emissivity at z approximate to 3, so as not to overproduce the UV background and drive the mean Lyalpha optical depth to values that are too low. We also investigate the effect of fluctuations in the UV background, as would arise if QSOs dominated. To this end, we derive the distribution function of the background radiation field produced by discrete sources in an infinite universe, including the effects of attenuation by an intervening absorbing medium. We show that, for z greater than or similar to 5, the fluctuations significantly boost the mean Lyalpha optical depth, and so increase the estimate for the mean ionization rate required to match the measured mean Lyalpha optical depths. The fluctuations will also result in large spatial correlations in the ionization level of the IGM. We show that the large mean Lyalpha optical depth measured at z approximate to 6 suggests such large correlations will be present if QSOs dominate the UV background. A secondary, smaller effect of the UV background fluctuations is a distortion of the pixel flux distribution. While the effect on the distribution may be too small to detect with existing telescopes, it may be measurable with the extremely large telescopes planned for the future. We also show that if QSOs dominate the UV background at z approximate to 6, then they will be sufficient in number to rejuvenate the ionization of a previously ionized IGM if it has not yet fully recombined.