Modeling the HeII Transverse Proximity Effect: Constraints on Quasar Lifetime and Obscuration

The HeII transverse proximity effect - enhanced HeII Ly{\alpha} transmission in a background sightline caused by the ionizing radiation of a foreground quasar - offers a unique opportunity to probe the emission properties of quasars, in particular the emission geometry (obscuration, beaming) and the quasar lifetime. Building on the foreground quasar survey published in Schmidt+2017, we present a detailed model of the HeII transverse proximity effect, specifically designed to include light travel time effects, finite quasar ages, and quasar obscuration. We post-process outputs from a cosmological hydrodynamical simulation with a fluctuating HeII UV background model, plus the added effect of the radiation from a single bright foreground quasar. We vary the age $t_\mathrm{age}$ and obscured sky fractions $\Omega_\mathrm{obsc}$ of the foreground quasar, and explore the resulting effect on the HeII transverse proximity effect signal. Fluctuations in IGM density and the UV background, as well as the unknown orientation of the foreground quasar, result in a large variance of the HeII Ly{\alpha} transmission along the background sightline. We develop a fully Bayesian statistical formalism to compare far UV HeII Ly{\alpha} transmission spectra of the background quasars to our models, and extract joint constraints on $t_\mathrm{age}$ and $\Omega_\mathrm{obsc}$ for the six Schmidt+2017 foreground quasars with the highest implied HeII photoionization rates. Our analysis suggests a bimodal distribution of quasar emission properties, whereby one foreground quasar, associated with a strong HeII transmission spike, is relatively old $(22\,\mathrm{Myr})$ and unobscured $\Omega_\mathrm{obsc}<35\%$, whereas three others are either younger than $(10\,\mathrm{Myr})$ or highly obscured $(\Omega_\mathrm{obsc}>70\%)$.