Distance estimation of gamma-ray-emitting BL Lac objects from imaging observations

Aims. The direct redshift determination of BL Lac objects is highly challenging as the emission in the optical and near-infrared bands is largely dominated by the non-thermal emission from the relativistic jet, which points very close to our line of sight. Therefore, the optical spectra of BL Lac objects often show no spectral lines from the host galaxy. In this work, we aim to overcome this difficulty by attempting to detect the host galaxy and derive redshift constraints based on assumptions on the galaxy magnitude ('imaging redshifts'). Methods. Imaging redshifts were derived by obtaining deep optical images under good seeing conditions, making it possible to detect the host galaxy as a weak extension of the point-like source. We then derived the imaging redshift by using the host galaxy as a standard candle, employing two different methods. Results. We determine the imaging redshift for 9 out of 17 blazars that we observed as part of this programme. The redshift range of these targets is 0.28-0.60, and the two methods used to derive the redshift give very consistent results within the uncertainties. We also performed a detailed comparison of the imaging redshifts with those obtained using other methods, such as direct spectroscopic constraints or looking for groups of galaxies close to the blazar. We show that the constraints from the different methods are consistent and that combining the three constraints narrows down the redshift. For example, in the case of J2156.0+1818, which is the most distant source for which we detect the host galaxy, the redshift range is narrowed to 0.63 < z < 0.71. This makes the source interesting for future studies of extragalactic background light in the Cherenkov Telescope Array Observatory era.