Abstract
Understanding the growth of the supermassive black holes powering luminous
quasars, their co-evolution with host galaxies, and impact on the surrounding
intergalactic medium depends sensitively on the duration of quasar accretion
episodes. Unfortunately, this time-scale, known as the quasar lifetime, $t_\rm
Q$, is still uncertain by orders of magnitude ($t_Q0.01~\rm
Myr-1~Gyr$). However, the extent of the He II Ly$\alpha$ proximity zones
in the absorption spectra of $z_qso\sim3-4$ quasars constitutes a unique
probe, providing sensitivity to lifetimes up to $30$ Myr. Our recent
analysis of $22$ archival 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 log-normal QLD, we infer a
mean $log_10łeft(t_Q/\rm
Myr\right)\rangle=0.22^+0.22_-0.25$ and standard deviation $\sigma_\rm
log_10t_Q=0.80^+0.37_-0.27$. Our results allow us to estimate the
probability of detecting young quasars with $t_Qłeq0.1$ Myr from their
proximity zone sizes yielding $płeft(0.1~\rm
Myr\right)=0.19^+0.11_-0.09$, which is broadly consistent with recent
determination at $z6$.
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