Prospects for constraining quasar ages with fibre spectrographs: quasar-induced Ly α emission from the intergalactic medium

We present a theoretical framework for linking quasar properties, such as quasar age, to the surrounding Ly alpha emission intensity. In particular, we focus on a method for mapping the large-scale structure of Ly alpha emission intensity with galaxy spectra from wide-field spectroscopic surveys, e.g. the Subaru Prime Focus Spectrograph (PFS) or the Dark Energy Spectroscopic Instrument (DESI), and consider the quasar-induced Ly alpha emission from the intergalactic medium (IGM). To do this, we construct a theoretical model based on two physical processes: resonant scattering of quasar Ly alpha photons and fluorescence due to quasar ionizing photons, finding that the fluorescence contribution due to optically thick gas clouds is dominant. Taking into account the light-cone effect and assuming a typical quasar spectrum, we calculate the fluorescence contribution to the spectrum stacked within each bin of the separation angle from the quasar as a function of quasar age. Furthermore, we compute the quasar-Ly alpha emission cross-correlation and its SNR for the planned PFS survey. The predicted signal can only account for similar to 10 per cent of the measurements indicated from the BOSS and eBOSS surveys in the outer region of greater than or similar to 10 cMpc h(-1), and the predicted SNR is not sufficient to detect the quasar-induced contribution. However, we found that our model, combined with the contribution of star-forming galaxies, is not in conflict with these measurements. We discuss other possible contributions to the Ly alpha emission excess around quasars, the efficiency of using spectroscopic fibres, and the redshift dependence of our model.