Mapping quasar light echoes in 3D with Ly{\alpha} forest tomography

The intense radiation emitted by luminous quasars dramatically alters the ionization state of their surrounding IGM. This so-called proximity effect extends out to tens of Mpc, and manifests as large coherent regions of enhanced Lyman-$\alpha$ (Ly$\alpha$) forest transmission in absorption spectra of background sightlines. Here we present a novel method based on Ly$\alpha$ forest tomography, which is capable of mapping these quasar `light echoes' in three dimensions. Using a dense grid (10-100) of faint ($m_r\approx24.7\,\mathrm{mag}$) background galaxies as absorption probes, one can measure the ionization state of the IGM in the vicinity of a foreground quasar, yielding detailed information about the quasar's radiative history and emission geometry. An end-to-end analysis - combining cosmological hydrodynamical simulations post-processed with a quasar emission model, realistic estimates of galaxy number densities, and instrument + telescope throughput - is conducted to explore the feasibility of detecting quasar light echoes. We present a new fully Bayesian statistical method that allows one to reconstruct quasar light echoes from thousands of individual low S/N transmission measurements. Armed with this machinery, we undertake an exhaustive parameter study and show that light echoes can be convincingly detected for luminous ($M_{1450} < -27.5\,\mathrm{mag}$ corresponding to $m_{1450} < 18.4\,\mathrm{mag}$ at $z\simeq 3.6$) quasars at redshifts $3<z_\mathrm{QSO}<5$, and that a relative precision better than $20\,\%$ on the quasar age can be achieved for individual objects, for the expected range of ages between 1 Myr and 100 Myr. The observational requirements are relatively modest - moderate resolution ($R\gtrsim750$) multi object spectroscopy at low $\rm{}S/N > 5$ is sufficient, requiring three hour integrations using existing instruments on 8m class telescopes.