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We use ultra-deep ultraviolet VLT/VIMOS intermediate-band and VLT/FORS1narrow-band imaging in the GOODS Southern field to derive limits on thedistribution of the escape fraction (f_esc) of ionizing radiation for L >~L*(z=3) Lyman Break Galaxies (LBGs) at redshift 3.4--4.5. Only one LBG, atredshift z=3.795, is detected in its Lyman continuum (LyC; S/N~5.5), thehighest redshift galaxy currently known with a direct detection. Itsultraviolet morphology is quite compact (R_eff=0.8, kpc physical). Three out ofseven AGN are also detected in their LyC, including one at redshift z=3.951 andz850 = 26.1. From stacked data (LBGs) we set an upper limit to the averagef_esc in the range 5%--20%, depending on the how the data are selected (e.g.,by magnitude and/or redshift). We undertake extensive Monte Carlo simulationsthat take into account intergalactic attenuation, stellar population synthesismodels, dust extinction and photometric noise in order to explore the momentsof the distribution of the escaping radiation. Various distributions(exponential, log-normal and Gaussian) are explored. We find that the medianf_esc is lower than ~6% with an 84% percentile limit not larger than 20%. Ifthis result remains valid for fainter LBGs down to current observationallimits, then the LBG population might be not sufficient to account for theentire photoionization budget at the redshifts considered here, with the exactdetails dependent upon the assumed ionizing background and QSO contributionthereto. It is possible that f_esc depends on the UV luminosity of thegalaxies, with fainter galaxies having higher f_esc, and estimates of f_escfrom a sample of faint LBG from the HUDF (i775<28.5) are in broad quantitativeagreement with such a scenario.

The Great Observatories Origins Deep Survey: Constraints on the Lyman Continuum Escape Fraction Distribution of Lyman--Break Galaxies at 3.4