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VLT/X-shooter spectroscopy of the afterglow of the Swift GRB 130606A: Chemical abundances and reionisation at $z\sim6$

The reionisation of the Universe is thought to have ended around z~6, as inferred from spectroscopy of distant bright background sources, such as quasars (QSO) and gamma-ray burst (GRB) afterglows. Furthermore, spectroscopy of a GRB afterglow provides insight in its host galaxy, which is often too dim and distant to study otherwise. We present the high S/N VLT/X-shooter spectrum of GRB130606A at z=5.913. We aim to measure the degree of ionisation of the IGM between 5.02<z<5.84 and to study the chemical abundance pattern and dust content of its host galaxy. We measured the flux decrement due to absorption at Ly$α$, $β$ and $γ$ wavelength regions. The hydrogen and metal absorption lines formed in the host galaxy were fitted with Voigt profiles to obtain column densities. Our measurements of the Ly$α$-forest optical depth are consistent with previous measurements of QSOs, but have a much smaller uncertainty. The analysis of the red damping wing yields a neutral fraction $x_{HI}<0.05$ (3$σ$). We obtain column density measurements of several elements. The ionisation corrections due to the GRB is estimated to be negligible (<0.03 dex), but larger corrections may apply due to the pre-existing radiation field (up to 0.4 dex based on sub-DLA studies). Our measurements confirm that the Universe is already predominantly ionised over the redshift range probed in this work, but was slightly more neutral at z>5.6. GRBs are useful probes of the ionisation state of the IGM in the early Universe, but because of internal scatter we need a larger statistical sample to draw robust conclusions. The high [Si/Fe] in the host can be due to dust depletion, alpha-element enhancement, or a combination of both. The very high value of [Al/Fe]=2.40+/-0.78 might connected to the stellar population history. We estimate the host metallicity to be -1.7<[M/H]<-0.9 (2%-13% of solar). (trunc.)