GRB hosts through cosmic time - VLT/X-Shooter emission-line spectroscopy of 96 GRB-selected galaxies at 0.1 < z < 3.6

[Abridged] We present data and initial results from VLT/X-Shooter emission-line spectroscopy of 96 GRB-selected galaxies at 0.1<z<3.6, the largest sample of GRB host spectroscopy available to date. Most of our GRBs were detected by Swift and 76% are at 0.5<z<2.5 with a median z~1.6. Based on Balmer and/or forbidden lines of oxygen, nitrogen, and neon, we measure systemic redshifts, star formation rates (SFRs), visual attenuations, oxygen abundances (12+log(O/H)), and emission-line widths. We find a strong change of the typical physical properties of GRB hosts with redshift. The median SFR, for example, increases from ~0.6 M_sun/yr at z~0.6 up to ~15 M_sun/yr at z~2. A higher ratio of [OIII]/[OII] at higher redshifts leads to an increasing distance of GRB-selected galaxies to the locus of local galaxies in the BPT diagram. Oxygen abundances of the galaxies are distributed between 12+log(O/H)=7.9 and 12+log(O/H)=9.0 with a median of 12+log(O/H)~8.5. The fraction of GRB-selected galaxies with super-solar metallicities is around 20% at z<1 in the adopted metallicity scale. This is significantly less than the fraction of star formation in similar galaxies, illustrating that GRBs are scarce in high-metallicity environments. At z~3, sensitivity limits us to probing only the most luminous GRB hosts for which we derive metallicities of Z ~< 0.5 Z_sun. Together with a high incidence of galaxies with similar metallicity in our sample at z~1.5, this indicates that the metallicity dependence observed at low redshift will not be dominant at z~3.