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Fluctuations in Lyman-α (Ly α) forest transmission towards high-z quasars are partially sourced from spatial fluctuations in the ultraviolet background, the level of which are set by the mean free path of ionizing photons (λmfp). The autocorrelation function of Ly α forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to λmfp. Recent measurements at z ∼ 6 suggest a rapid evolution of λmfp at z > 5.0 which would leave a signature in the evolution of the autocorrelation function. For this forecast, we model mock Ly α forest data with properties similar to the XQR-30 extended data set at 5.4 ≤ z ≤ 6.0. At each z, we investigate 100 mock data sets and an ideal case where mock data matches model values of the autocorrelation function. For ideal data with λmfp = 9.0 cMpc at z = 6.0, we recover $\lambda _{\text{mfp}}=12^{+6}_{-3}$ cMpc. This precision is comparable to direct measurements of λmfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a $\sim 40~{{\ \rm per\ cent}}$ reduction in the error bars over all z. The distribution of mock values of the autocorrelation function in this work is highly non-Gaussian for high-z, which should caution work with other statistics of the high-z Ly α forest against making this assumption. We use a rigorous statistical method to pass an inference test, however future work on non-Gaussian methods will enable higher precision measurements.

 

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.