2021MNRAS.505..649K

Understanding the growth of the supermassive black holes (SMBH) powering luminous quasars, their co-evolution with host galaxies, and impact on the surrounding intergalactic medium (IGM) depends sensitively on the duration of quasar accretion episodes. Unfortunately, this time-scale, known as the quasar lifetime, t_Q, is still uncertain by orders of magnitude (t_ Q_ ≃0.01 Myr - 1 Gyr). However, the extent of the He II Ly α proximity zones in the absorption spectra of z_qso ∼ 3-4 quasars constitutes a unique probe, providing sensitivity to lifetimes up to ∼30 Myr. Our recent analysis of 22 archival Hubble Space Telescope He II proximity zone spectra reveals a surprisingly broad range of emission time-scales, indicating that some quasars turned on <=1 Myr ago, whereas others have been shining for >=30 Myr. Determining the underlying quasar lifetime distribution (QLD) from proximity zone measurements is a challenging task owing to: (1) the limited sensitivity of individual measurements; (2) random sampling of the quasar light curves; (3) density fluctuations in the quasar environment; and (4) the inhomogeneous ionization state of He II in a reionizing IGM. We combine a seminumerical He II reionization model, hydrodynamical simulations post-processed with ionizing radiative transfer, and a novel statistical framework to infer the QLD from an ensemble of proximity zone measurements. Assuming a lognormal QLD, we infer a mean <log₁₀(t_ Q_/ Myr)>= 0.22^+0.22_–0.25 and standard deviation σ_ log_10t Q_ = 0.80^+0.37_–0.27. Our results allow us to estimate the probability of detecting very young quasars with t_Q <= 0.1 Myr from their proximity zone sizes yielding p (≤0.1 Myr) = 0.19^+0.11_–0.09, which is broadly consistent with recent determination at z ∼ 6.