Ionizing radiation fluctuations and large-scale structure in the Lyα forest

We investigate the large-scale inhomogeneities of the hydrogen-ionizing radiation field in the universe at redshift z = 3. Using a ray-tracing algorithm, we simulate a model in which quasars are the dominant sources of radiation. We make use of large-scale N-body simulations of a Lambda cold dark matter universe and include such effects as finite quasar lifetimes and output on the light cone, which affects the shape of quasar light echoes. We create Lyalpha forest spectra that would be generated in the presence of such a fluctuating radiation field, finding that the power spectrum of the Lyalpha forest can be suppressed by as much as 15% for modes with k = 0.05-1 h Mpc(-1). This relatively small effect may have consequences for high-precision measurements of the Lyalpha power spectrum on larger scales than have yet been published. We also investigate a second probe of the ionizing radiation fluctuations, the cross-correlation of quasar positions and the Lyalpha forest. For both quasar lifetimes that we simulate (10(7) and 10(8) yr), we expect to see a strong decrease in the Lyalpha absorption close to other quasars ( the "foreground'' proximity effect). We then use data from the Sloan Digital Sky Survey First Data Release to make an observational determination of this statistic. We find no sign of our predicted lack of absorption, but instead increased absorption close to quasars. If the bursts of radiation from quasars last on average less than 106 yr, then we would not expect to be able to see the foreground effect. However, the strength of the absorption itself seems to be indicative of rare objects and hence much longer total times of emission per quasar. Variability of quasars in bursts with timescales of between 10(4) and 10(6) yr could reconcile these two facts.