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Lyman continuum leakage in faint star-forming galaxies at redshift z=3-3.5 probed by gamma-ray bursts

We present the observations of Lyman continuum (LyC) emission in the afterglow spectra of GRB 191004B at $z=3.5055$, together with those of the other two previously known LyC-emitting long gamma-ray bursts (LGRB) (GRB 050908 at $z=3.3467$, and GRB 060607A at $z=3.0749$), to determine their LyC escape fraction and compare their properties. From the afterglow spectrum of GRB 191004B we determine a neutral hydrogen column density at the LGRB redshift of $\log(N_{\rm HI}/cm^{-2})= 17.2 \pm 0.15$, and negligible extinction ($A_{\rm V}=0.03 \pm 0.02$ mag). The only metal absorption lines detected are CIV and SiIV. In contrast to GRB 050908 and GRB 060607A, the host galaxy of GRB 191004B displays significant Ly$α$ emission. From its Ly$α$ emission and the non-detection of Balmer emission lines we constrain its star-formation rate (SFR) to $1 \leq$ SFR $\leq 4.7$ M$_{\odot}\ yr^{-1}$. We fit the Ly$α$ emission with a shell model and find parameters values consistent with the observed ones. The absolute LyC escape fractions we find for GRB 191004B, GRB 050908 and GRB 060607A are of $0.35^{+0.10}_{-0.11}$, $0.08^{+0.05}_{-0.04}$ and $0.20^{+0.05}_{-0.05}$, respectively. We compare the LyC escape fraction of LGRBs to the values of other LyC emitters found from the literature, showing that LGRB afterglows can be powerful tools to study LyC escape for faint high-redshift star-forming galaxies. Indeed we could push LyC leakage studies to much higher absolute magnitudes. The host galaxies of the three LGRB presented here have all $M_{\rm 1600} > -19.5$ mag, with the GRB 060607A host at $M_{\rm 1600} > -16$ mag. LGRB hosts may therefore be particularly suitable for exploring the ionizing escape fraction in galaxies that are too faint or distant for conventional techniques. Furthermore the time investment is very small compared to galaxy studies. [Abridged]