Constraints on the Lyman continuum escape fraction for faint star forming galaxies

Star forming galaxies have long been considered the dominant sources of the cosmic ultraviolet background radiation at early epochs. However, observing and characterizing the galaxy population with significant ionizing emission has proven to be challenging. In particular, the fraction of ionizing radiation that escapes the local environment to the intergalactic medium is poorly known. We investigate the relation between the escape fraction and galaxy luminosity. We combine the deep ultraviolet observations of Hubble Ultra Deep Field (UVUDF) with the deep Multi Unit Spectroscopic Explorer (MUSE) observations of the same field, collecting a sample of 165 faint star forming galaxies in the $3 < z < 4$ redshift range with deep rest-frame observations of the Lyman continuum. In our sample, we do not find any galaxy with significant emission of LyC radiation. We bin the galaxies in various redshift and brightness intervals and stack their images. From stacked images we estimate the relative escape fraction upper limits as a function of the luminosity. Thanks to the depth of the sample we measure meaningful 1$σ$ upper limits of $f_{esc,rel} < 0.07, 0.2$ and 0.6 at $L \sim L_{\rm z=3}^{*}, 0.5L_{\rm z=3}^{*}$ and $0.1L_{\rm z=3}^{*}$, respectively. We use our estimates and theoretical predictions from the literature to study a possible dependence of the escape fraction on galaxy luminosity by modelling the ionizing background with different prescriptions of $f_{\rm esc} (M_{\rm UV})$. We show that the understanding of the luminosity dependence hinges on the ability to constrain the escape fraction down to $M_{\rm UV} \sim -18$ mag in the future.