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$\sigma$ 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.
