Lyα-Lyman continuum connection in 3.5 ≤ z ≤ 4.3 star-forming galaxies from the VUDS survey

Context. To identify the galaxies responsible for the reionization of the Universe, we must rely on the investigation of the Lyman continuum (LyC) properties of z <= 5 star-forming galaxies, where we can still directly observe their ionizing radiation. Aims. The aim of this work is to explore the correlation between the LyC emission and some of the proposed indirect indicators of LyC radiation at z similar to 4 such as a bright Ly alpha emission and a compact UV continuum size. Methods. We selected a sample of 201 star-forming galaxies from the Vimos Ultra Deep Survey (VUDS) at 3 : 5 <= z <= 4 : 3 in the COSMOS, ECDFS, and VVDS-2h fields, including only those with reliable spectroscopic redshifts, a clean spectrum in the LyC range and clearly not contaminated by bright nearby sources in the same slit. For all galaxies we measured the Ly alpha EW, the Ly alpha velocity shift with respect to the systemic redshift, the Ly alpha spatial extension and the UV continuum effective radius. We then selected different sub-samples according to the properties predicted to be good LyC emission indicators: in particular we created sub-samples of galaxies with EW(Ly alpha) >= 70 angstrom, Ly alpha(ext) <= 5.7 kpc, r(UV) <= 0.30 kpc and vertical bar Delta(nu Ly alpha)vertical bar <= 200 km s(-1). We stacked all the galaxies in each sub-sample and measured the flux density ratio (f(lambda)(895)/f(lambda)(1470)), that we considered to be a proxy for LyC emission. We then compared these ratios to those obtained for the complementary samples. Finally, to estimate the statistical contamination from lower redshift inter-lopers in our samples, we performed dedicated Monte Carlo simulations using an ultradeep U-band image of the ECDFS field. Results. We find that the stacks of galaxies which are UV compact (r(UV) <= 0.30 kpc) and have bright Ly alpha emission (EW(Ly alpha) >= 70 angstrom), have much higher LyC fluxes compared to the rest of the galaxy population. These parameters appear to be good indicators of LyC radiation in agreement with theoretical studies and previous observational works. In addition we find that galaxies with a low Ly alpha spatial extent (Ly alpha(ext) <= 5.7 kpc) have higher LyC flux compared to the rest of the population. Such a correlation had never been analysed before and seems even stronger than the correlation with high EW(Ly alpha) and small r(UV). These results assume that the stacks from all sub-samples present the same statistical contamination from lower redshift interlopers. If we subtract a statistical contamination from low redshift interlopers obtained with the simulations from the flux density ratios (f (lambda)(895)/f(lambda)(1470)) of the significant sub-samples we find that these samples contain real LyC leaking flux with a very high probability, although the true average escape fractions are very uncertain. Conclusions. Our work indicates that galaxies with very high EW(Ly alpha), small Ly ff ext and small rUV are very likely the best candidates to show Lyman continuum radiation at z <= 4 and could therefore be the galaxies that have contributed most to reionisation.