On the effect of the ionizing background on the Lyα forest autocorrelation function

An analytical framework is presented to understand the effects of a fluctuating intensity of the cosmic ionizing background on the correlations of the Ly alpha forest transmission fraction measured in quasar spectra. In the absence of intensity fluctuations, the Ly alpha power spectrum should have the expected cold dark matter power spectrum with redshift distortions in the linear regime, with a bias factor b(delta) and a redshift distortion parameter beta that depend on redshift but are independent of scale. The intensity fluctuations introduce a scale dependence in both b(delta) and beta, but keeping their product b(delta)beta fixed. Observations of the Ly alpha correlations and cross-correlations with radiation sources like those being done at present in the Baryon Oscillation Spectroscopic Survey of Sloan Digital Sky Survey third generation have the potential to measure this scale dependence, which reflects the biasing properties of the sources and absorbers of the ionizing background. We also compute a second term affecting the Ly alpha spectrum, due to shot noise in the sources of radiation. This term is very large if luminous quasars are assumed to produce the ionizing background and to emit isotropically with a constant luminosity, but should be reduced by a contribution from galaxies, and by the finite lifetime and anisotropic emission of quasars.