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Abstract

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 time- scale, often referred to as the quasar lifetime, is still uncertain by orders of magnitude (t_Q ̃eq 0.01 Myr - 1 Gyr). Absorption spectra of quasars exhibiting transmission in the He II Ly α forest provide a unique opportunity to make precise measurements of the quasar lifetime. Indeed, the size of a quasar's He II proximity zone, the region near the quasar 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 II proximity zones in the Hubble Space Telescope (HST) spectra of six z ̃ 4 quasars to theoretical models generated by post-processing 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 the surrounding IGM. We measure lifetimes 0.63^{+0.82}_{-0.40} Myr and 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\rangle = 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.