# Time-dependent behaviour of quasar proximity zones at $z \sim 6$

## TL;DR

This study uses radiative transfer simulations and a semi-analytic model to analyze the time-dependent behavior of quasar proximity zones at redshift around 6, providing insights into quasar activity timescales and growth of supermassive black holes.

## Contribution

It introduces a semi-analytic model that captures the equilibrium and non-equilibrium behavior of proximity zones and links quasar variability to observed zone sizes.

## Key findings

- Simulated proximity zone sizes match observations well.
- Large luminosity variations on timescales less than 10^4 years are unlikely.
- Proximity zones can be explained by steady emission models without requiring rapid variability.

## Abstract

Since the discovery of $z\sim 6$ quasars two decades ago, studies of their Ly$\alpha$-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 timescales 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 timescales from $\sim10^3$ to $10^8$ years. The sizes of the simulated proximity zones, as quantified by the distance at which the smoothed Ly$\alpha$ transmission drops below 10% (denoted $R_p$), are in excellent agreement with observations, with the exception of a handful of particularly small zones that have been attributed to extremely short $\lesssim 10^4$ year 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 $\lesssim10^5$ year timescales is imprinted on the distribution of observed proximity zone sizes. We show that large variations in the ionizing luminosity of quasars on timescales of $\lesssim10^4$ years are disfavored based on the good agreement between the observed distribution of $R_p$ and our model prediction based on "lightbulb" (i.e. steady constant emission) light curves.