The first measurement of the quasar lifetime distribution

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) similar or equal to 0.01 Myr - 1Gyr). However, the extent of the He II Ly alpha proximity zones in the absorption spectra of z(qso) similar to 3-4 quasars constitutes a unique probe, providing sensitivity to lifetimes up to similar 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 less than or similar to 1Myr ago, whereas others have been shining for greater than or similar to 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 lognormalQLD, we infer amean log(10)(tQ/Myr) = 0.22+0.22 -0.25 and standard deviation slog10tQ = 0.80+0.37 -0.27. Our results allow us to estimate the probability of detecting very young quasars with t(Q) <= 0.1Myr from their proximity zone sizes yielding p(=0.1Myr) = 0.19+0.11 -0.09, which is broadly consistent with recent determination at z similar to 6.