Measuring the radiative histories of high-redshift QSOs with the transverse proximity effect

Since the photons that stream from QSOs alter the ionization state of the gas they traverse, any changes to a QSO's luminosity will produce outward-propagating ionization gradients in the surrounding intergalactic gas. This paper shows that at redshift zsimilar to3, the gradients will alter the gas's Lyalpha absorption opacity enough to produce a detectable signature in the spectra of faint background galaxies. By obtaining noisy (signal-to-noise ratio similar to4) low-resolution (similar to7 Angstrom) spectra of several dozen background galaxies in an Rsimilar to20' field surrounding an isotropically radiating 18th magnitude QSO at z=3, it should be possible to detect any order-of-magnitude changes to the QSO's luminosity over the previous 50-100 Myr and to measure the time t(Q) since the onset of the QSO's current luminous outburst with an accuracy of similar to5 Myr for t(Q)less than or similar to50 Myr. Smaller fields of view are acceptable for shorter QSO lifetimes. The major uncertainty, aside from cosmic variance, will be the shape and orientation of the QSO's ionization cone. This can be determined from the data if the number of background sources is increased by a factor of a few. The method will then provide a direct test of unification models for active galactic nuclei.