Spatial Correlations in the Helium-Ionizing Background

After quasars ionize intergalactic HeII at z~3, a large radiation field builds up above the HeII ionization edge. Unlike the background responsible for HI ionizations, this field should be highly variable, thanks to the scarcity of bright quasars and the relatively short attenuation lengths (~50 Mpc) of these high-energy photons. Recent observations of the HeII and HI Lyman-alpha forests show that this background does indeed vary strongly, with substantial fluctuations on scales as small as ~2 Mpc. Here we show that such spatial fluctuation scales are naturally expected in any model in which the sources are as rare as bright quasars, so long as the attenuation length is relatively small. The correlation length itself is comparable to the attenuation length (~10 Mpc) for the most plausible physical scenarios, but we find order-of-magnitude fluctuations on all scales smaller than ~6 Mpc. Moreover, aliasing along the one-dimensional skewers probed by the HeII and HI Lyman-alpha forests exaggerates these variations, so that order-of-magnitude fluctuations should be observed on all scales smaller than ~20 Mpc. Complex radiative transfer is therefore not required to explain the observed fluctuations, at least at the level of current data.