Forecasting constraints on the mean free path of ionizing photons at z >= 5.4 from the Lyman-alpha forest flux autocorrelation function

Fluctuations in Lyman-alpha(Ly alpha) 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 (lambda(mfp)). The autocorrelation function of Ly alpha forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to lambda(mfp). Recent measurements at z similar to 6 suggest a rapid evolution of lambda(mfp) at z > 5.0 which would leave a signature in the evolution of the autocorrelation function. For this forecast, we model mock Ly alpha 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 lambda(mfp) = 9.0 cMpc at z = 6.0, we recover lambda(mfp) = 12(-3)(+6) cMpc. This precision is comparable to direct measurements of.mfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a similar to 40 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 alpha 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.