Statistical redshift of the very-high-energy blazar S5 0716+714

Context. Blazars are the most numerous class of very-high-energy (VHE; E > 100 GeV) gamma-ray emitters. At present, measured redshifts are available only for about 80% of the VHE gamma-ray sources; this is mainly due to the di fficulty in measuring reliable redshifts from their nearly featureless continuum optical spectra. Aims. As the VHE sky is still vastly unexplored, VHE blazars are unique objects. High-energy spectra from blazars are used for extragalactic background light studies, to investigate topics related to cosmology or fundamental physics, and to find the source luminosity. This allows one to study the properties of the host galaxy, its black hole, and the gamma-ray emission mechanisms. All of these studies require suitable estimations of the blazar distance, which has motivated the use of novel approaches when measuring the redshift of faint optical lines in their spectra is very uncertain. Methods. We present the new optical spectroscopic observations of S5 0716 +714 and its environment taken on December 20, 2019, with the Gemini GMOS North telescope. Results. We do not find any absorption lines in the blazar spectrum; however, we were able to get the redshifts of 21 other galaxies in the field, 15 of which form a group at z = 0.2304 +/- 0.0013. Performing a population study of galaxies, we found that S5 0716 +714 belongs to this group with a probability >99%.