Optical spectroscopy of high-redshift BL Lac objects

BL Lac objects (BLLs) are defined by the presence of very weak (typically $<$ 5 Å) or even absent spectral lines. This makes determining their distance particularly challenging, especially at high redshift, where the sources are fainter and the host galaxy contribution in the optical band becomes negligible. Yet measuring their distance is crucial for deriving and modelling their luminosity, notably in the gamma-ray band, where BLLs dominate the extragalactic sky. In this work, we re-examine the reported high-redshift (z $>$ 0.6) BLLs, many of which are commonly cited in the literature despite appearing questionable. We present new spectra for 52 objects obtained with the 10.4 m GTC. For 16 of them we propose a new redshift or provide a spectroscopic lower limit, while for 14 sources we confirm previously published values. In 22 cases the spectra remain featureless, even with high S/N observations. These objects are likely to lie at 0.3 $<$ z $<$ 1.4 ; the lack of host-galaxy features sets a lower limit to their distance, while the absence of intervening absorption systems argues against substantially higher redshifts. We compare our findings with the previous robustly established cases of BLLs at z $>$ 0.6 that meet our selection criteria.