The lifetime of quasars is fundamental for understanding the growth of supermassive black holes, and is an important ingredient in models of the reionization of the intergalactic medium (IGM). However, despite various attempts to determine quasar lifetimes, current estimates from a variety of methods are uncertain by orders of magnitude. This work combines cosmological hydrodynamical simulations and 1D radiative transfer to investigate the structure and evolution of the He II Lyα proximity zones around quasars at z ≃ 3 − 4. We show that the time evolution in the proximity zone can be described by a simple analytical model for the approach of the He II fraction x HeII (t) to ionization equilibrium, and use this picture to illustrate how the transmission profile depends on the quasar lifetime, quasar UV luminosity, and the ionization state of Helium in the ambient IGM (i.e. the average He II fraction, or equivalently the metagalactic He II ionizing background). A significant degeneracy exists between the lifetime and the average He II fraction, however the latter can be determined from measurements of the He II Lyα optical depth far from quasars, allowing the lifetime to be measured. We advocate stacking existing He II quasar spectra at z ∼ 3, and show that the shape of this average proximity zone profile is sensitive to lifetimes as long as ∼ 30 Myr. At higher redshift z ∼ 4 where the He II fraction is poorly constrained, degeneracies will make it challenging to determine these parameters independently. Our analytical model for He II proximity zones should also provide a useful description of the properties of H I proximity zones around quasars at z ≃ 6 − 7.

The duration of quasar accretion episodes is a key quantity for distinguishing between models for the formation and growth of supermassive black holes, the evolution of quasars, and their potential feedback effects on their host galaxies. However, this critical timescale, often referred to as the quasar lifetime, is still uncertain by orders of magnitude (t Q 0.01 Myr − 1 Gyr). Absorption spectra of quasars exhibiting transmission in the He Lyα forest provide a unique opportunity to make precise measurements of the quasar lifetime. Indeed, the size of a quasar's He proximity zone, the region near the quasar itself where its own radiation dramatically alters the ionization state of the surrounding intergalactic medium (IGM), depends sensitively on its lifetime for t Q 30 Myr, comparable to the expected e-folding time-scale for SMBH growth t S = 45 Myr. In this study we compare the sizes of He proximity zones in the Hubble Space Telescope (HST) spectra of six z 4 quasars to theoretical models generated by postprocessing cosmological hydrodynamical simulations with a 1D radiative transfer algorithm. We introduce a Bayesian statistical method to infer the lifetimes of individual quasars which allows us to fully marginalize over the unknown ionization state of He in the surrounding IGM. We measure lifetimes t Q = 0.63 +0.82 −0.40 Myr and t Q = 5.75 +4.72 −2.74 Myr for two objects. For the other four quasars large redshift uncertainties undermine our sensitivity allowing us to only place upper or lower limits. However a joint analysis of these four systems yields a measurement of their average lifetime of t Q = 1.17 +1.77 −0.84 Myr. We discuss our short ∼ 1 Myr inferred lifetimes in the context of other quasar lifetime constraints and the growth of SMBHs.

Despite decades of effort, the timing and duration of He II reionization and the properties of the quasars believed to drive it, are still not well constrained. We present a new method to study both via the thermal proximity effect -the heating of the intergalactic medium (IGM) around quasars when their radiation doubly ionizes helium. We post-process hydrodynamical simulations with 1D radiative transfer and study how the thermal proximity effect depends on He II fraction, x HeII,0 , which prevailed in the IGM before the quasar turned on, and the quasar lifetime t Q . We find that the amplitude of the temperature boost in the quasar environment depends on x HeII,0 , with a characteristic value of ∆T ≃ 10 4 K for x HeII,0 = 1.0, whereas the size of the thermal proximity zone is sensitive to t Q ,with typical sizes of ≃ 100 cMpc for t Q = 10 8 yr. This temperature boost increases the thermal broadening of H I absorption lines near the quasar. We introduce a new Bayesian statistical method based on measuring the Lyα forest power spectrum as a function of distance from the quasar, and demonstrate that the thermal proximity effect should be easily detectable. For a mock dataset of 50 quasars at z ≃ 4, we predict that one can measure x HeII,0 to an (absolute) precision ≈ 0.04, and t Q to a precision of ≈ 0.1 dex. By applying our formalism to existing high-resolution Lyα forest spectra, one should be able to reconstruct the He II reionization history,providing a global census of hard photons in the high-z universe.

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 (tQ ≃ 0.01 Myr − 1 Gyr). However, the extent of the He ii Lyα 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 timescales, 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 semi-numerical 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 $\langle {\rm log}_{10}\left( t_{\rm Q} / {\rm Myr} \right)\rangle = 0.22^{+0.22}_{-0.25}$ 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 $p \left( \le 0.1\, {\rm Myr}\right) = 0.19^{+0.11}_{-0.09}$, which is broadly consistent with recent determination at z ∼ 6.