ABSTRACT
Under the assumption that galaxies and quasi-stellar objects (QSOs) dominate the metagalactic ultraviolet (UV) background, it is shown that at high redshifts, fluctuations in the UV background are dominated by QSO shot noise and have an autocorrelation length of a few to several comoving Mpcs, depending on the bright end of the QSO luminosity function. The correlations create long-range spatial coherence in the neutral hydrogen fraction. Using a semi-analytic model, it is demonstrated that the coherence may account for the broad distribution in effective optical depths measured in the Lyα forest spectra of background QSOs, for line-of-sight segments of comoving length $50\, h^{-1}$ Mpc at redshifts 5 < z < 6. Capturing the fluctuations in a numerical simulation requires a comoving box size of ∼1 Gpc, although a box half this size may be adequate if sufficient random realizations of the QSO population are performed.
The luminosity function of high-redshift quasi-stellar objects. A combined analysis of GOODS and SDSS