2011ApJ...735..117F

We show that comparisons of He II Lyα forest lines of sight to nearby quasar populations can strongly constrain the lifetimes and emission geometry of quasars. By comparing the He II and H I Lyα forests along a particular line of sight, one can trace fluctuations in the hardness of the radiation field (which are driven by fluctuations in the He II ionization rate). Because this high-energy background is highly variable–thanks to the rarity of the bright quasars that dominate it and the relatively short attenuation lengths of these photons–it is straightforward to associate features in the radiation field with their source quasars. Here we quantify how finite lifetimes and beamed emission geometries affect these expectations. Finite lifetimes induce a time delay that displaces the observed radiation peak relative to the quasar. For beamed emission, geometry dictates that sources invisible to the observer can still create a peak in the radiation field. We show that both these models produce substantial populations of "bare" peaks (without an associated quasar) for reasonable parameter values (lifetimes ∼10⁶-10⁸ yr and beaming angles ≲ 90°). A comparison to existing quasar surveys along two He II Lyα forest lines of sight rules out isotropic emission and infinite lifetime at high confidence; they can be accommodated either by moderate beaming or lifetimes ∼10⁷-10⁸ yr. We also show that the distribution of radial displacements between peaks and their quasars can unambiguously distinguish these two models, although larger statistical samples are needed.