We show that comparisons of He ii Ly \alpha 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 Ly \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 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 \sim 10 ^ { 6 } – 10 ^ { 8 } \mbox { yr } and beaming angles \lesssim 90 \arcdeg ) .
A comparison to existing quasar surveys along two He ii Ly \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 \sim 10 ^ { 7 } – 10 ^ { 8 } \mbox { 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 .