The first measurement of the quasar lifetime distribution

Abstract

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 ($t_{\rm Q} \simeq 0.01\, {\rm Myr} - 1\, {\rm Gyr}$). 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 $\langle {\rm log}_{10}(t_{\rm Q} / {\rm Myr})\rangle = 0.22^{+0.22}_{-0.25}$ and standard deviation $\sigma _{{\rm log}_{10}t_{\rm Q}} = 0.80^{+0.37}_{-0.27}$. Our results allow us to estimate the probability of detecting very young quasars with tQ ≤ 0.1 Myr from their proximity zone sizes yielding $p ({\le}0.1\, {\rm Myr}) = 0.19^{+0.11}_{-0.09}$, which is broadly consistent with recent determination at z ∼ 6.