New constraints on the average escape fraction of Lyman continuum
  radiation in z~4 galaxies from the VIMOS Ultra Deep Survey (VUDS)
  Determining the average fraction of Lyman continuum (LyC) photons escaping
high redshift galaxies is essential for understanding how reionization
proceeded in the z>6 Universe. We want to measure the LyC signal from a sample
of sources in the Chandra Deep Field South (CDFS) and COSMOS fields for which
ultra-deep VIMOS spectroscopy as well as multi-wavelength Hubble Space
Telescope (HST) imaging are available.
  We select a sample of 46 galaxies at $z\sim 4$ from the VIMOS Ultra Deep
Survey (VUDS) database, such that the VUDS spectra contain the LyC part of the
spectra, that is, the rest-frame range $880-910\AA$. Taking advantage of the
HST imaging, we apply a careful cleaning procedure and reject all the sources
showing nearby clumps with different colours, that could potentially be
lower-redshift interlopers. After this procedure, the sample is reduced to 33
galaxies. We measure the ratio between ionizing flux (LyC at $895\AA$) and
non-ionizing emission (at $\sim 1500 \AA$) for all individual sources. We also
produce a normalized stacked spectrum of all sources. Assuming an intrinsic
average $L_{\nu}(1470)/L_{\nu}(895)$ of 3, we estimate the individual and
average relative escape fraction. We do not detect ionizing radiation from any
individual source, although we identify a possible LyC emitter with very high
Ly$\alpha$ equivalent width (EW). From the stacked spectrum and assuming a mean
transmissivity for the sample, we measure a relative escape fraction
$f_{esc}^{rel}=0.09\pm0.04$. We also look for correlations between the limits
in the LyC flux and source properties and find a tentative correlation between
LyC flux and the EW of the Ly$\alpha$ emission line.
  Our results imply that the LyC flux emitted by $V=25-26$ star-forming
galaxies at z$\sim$4 is at most very modest, in agreement with previous upper
limits from studies based on broad and narrow band imaging.
