Constraints on Quasar Lifetimes and Beaming from the HeII Lyman-alpha Forest

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We show that comparisons of HeII Lyman-alpha forest lines of sight to nearby quasar populations can strongly constrain the lifetimes and emission geometry of quasars. By comparing the HeII and HI Lyman-alpha 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 HeII 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 degrees). A comparison to existing quasar surveys along two HeII Lyman-alpha 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.