Inferring the distribution of the ionising photon escape fraction

Context. The escape fraction of ionising photons from galaxies (fesc) is a key parameter for understanding how intergalactic hydrogen became reionised, but it remains mostly unconstrained. Measurements have been limited to the average value in galaxy ensembles and to handfuls of individual detections. Aims. To help understand which mechanisms govern ionising photon escape, here we infer the distribution of fesc. Methods. We developed a hierarchical Bayesian inference technique to estimate the population distribution of fesc from the ratio of Lyman continuum to non-ionising UV flux measured from broadband photometry. We applied it to a sample of 148 z ≃ 3.5 star-forming galaxies from the VANDELS spectroscopic survey. Results. We explored four physically motivated distributions: constant, log-normal, exponential, and bimodal, and recovered ⟨fesc⟩≈5% for most models. We find the observations are best described by an exponential fesc distribution with scale factor $ \mu = 0.05^{+0.01}_{-0.02} $. This indicates most galaxies in our sample exhibit very low escape fractions, while predicting substantial ionising photon leakage for only a few galaxies, implying a range of optical depths in the interstellar medium and/or time variability in ionising photon escape. We rule out a bimodal distribution at high significance, indicating that a purely bimodal model of ionising photon escape (due to very strong sightline and/or time variability) is not favoured. We compare our recovered exponential distribution with the SPHINX simulations and find that, while the simulation also predicts an exponential distribution, it significantly underpredicts our inferred mean. The distribution of fesc can be a vital test for simulations in understanding ionising photon leakage, and is important to consider to gain a complete picture of reionisation.