Time-dependent behaviour of quasar proximity zones at z ∼ 6

ABSTRACT Since the discovery of z ∼ 6 quasars two decades ago, studies of their Ly α-transparent proximity zones have largely focused on their utility as a probe of cosmic reionization. But even when in a highly ionized intergalactic medium, these zones provide a rich laboratory for determining the time-scales that govern quasar activity and the concomitant growth of their supermassive black holes. In this work, we use a suite of 1D radiative transfer simulations of quasar proximity zones to explore their time-dependent behaviour for activity time-scales from ∼103 to 108 yr. The sizes of the simulated proximity zones, as quantified by the distance at which the smoothed Ly α transmission drops below 10 per cent (denoted Rp), are in excellent agreement with observations, with the exception of a handful of particularly small zones that have been attributed to extremely short ≲104 lifetimes. We develop a physically motivated semi-analytic model of proximity zones which captures the bulk of their equilibrium and non-equilibrium behaviour, and use this model to investigate how quasar variability on ≲105 yr time-scales is imprinted on the distribution of observed proximity zone sizes. We show that large variations in the ionizing luminosity of quasars on time-scales of ≲104 yr are disfavoured based on the good agreement between the observed distribution of Rp and our model prediction based on ‘lightbulb’ (i.e. steady constant emission) light curves.