Redshift measurement of Fermi blazars for the Cherenkov telescope array

International audienceBlazars are active galactic nuclei, and the most numerous High Energy (HE) and Very High Energy (VHE) γ-ray emitters. Their optical emission is often dominated by non-thermal, and, in the case of BL Lacs, featureless continuum radiation. This makes the determination of their redshift extremely difficult. Indeed, as of today only about 50% of γ-ray blazars have a measured spectroscopic redshift. The knowledge of redshift is fundamental because it allows the precise modeling of the VHE emission and also of its interaction with the extragalactic background light (EBL). The beginning of the Cherenkov Telescope Array (CTA) operations in the near future will allow the detection of several hundreds of new blazars. Using the Fermi catalogue of sources above 50 GeV (2FHL), we performed simulations which indicate that a significant fraction of the 2FHL blazars detectable by CTA will not have a measured redshift. As a matter of fact, the organization of observing campaigns to measure the redshift of these blazars has been recognized as a necessary support for the AGN Key Science Project of CTA. We are planning such an observing campaign. In order to optimize our chances of success, we will perform preliminary deep imaging observations aimed at detecting or setting upper limits to the host galaxy. We will then take spectra of the candidates with the brightest host galaxies. Taking advantage of the recent success of an X-shooter GTO observing campaign, these observations will be different with respect to previous ones due to the use of higher resolution spectrographs and of 8 meter class telescopes. We are starting to submit proposals for these observations. In this paper we briefly describe how candidates are selected and the corresponding observation program