The first measurement of the quasar lifetime distribution

ABSTRACT 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, tQ, is still uncertain by orders of magnitude (t ₐ 0. 01\, Myr - 1\, Gyr). However, the extent of the He ii Ly α proximity zones in the absorption spectra of zqso ∼ 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 ₐ / Myr) = 0. 22^+0. 22-₀. ₂₅ and standard deviation ₋₎₆₁₀t ₐ = 0. 80^+0. 37-₀. ₂₇. Our results allow us to estimate the probability of detecting very young quasars with tQ ≤ 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.