In order to investigate the origin of the excess of strong MgII systems towards GRB afterglows as compared to QSO sightlines, we have measured the incidence of MgII absorbers towards a third class of objects: the Blazars. This class includes the BL Lac object population for which a tentative excess of MgII systems had already been reported. We observed with FORS1 at the ESO-VLT 42 Blazars with an emission redshift 0.8<z_em<1.9, to which we added the three high z northern objects belonging to the 1Jy BL Lac sample. We detect 32 MgII absorbers in the redshift range 0.35-1.45, leading to an excess in the incidence of MgII absorbers compared to that measured towards QSOs by a factor ~2, detected at 3 sigma. The amplitude of the effect is similar to that found along GRB sightlines. Our analysis provides a new piece of evidence that the observed incidence of MgII absorbers might depend on the type of background source. In front of Blazars, the excess is apparent for both strong (w_ r(2796) > 1.0 A) and weaker (0.3 < w_r(2796) < 1.0 A) MgII systems. The dependence on velocity separation with respect to the background Blazars indicates, at the ~1.5 sigma level, a potential excess for beta = v/c ~0.1. We show that biases involving dust extinction or gravitational amplification are not likely to notably affect the incidence of MgII systems towards Blazars. Finally we discuss the physical conditions required for these absorbers to be gas entrained by the powerful Blazar jets. More realistic numerical modelling of jet-ambient gas interaction is required to reach any firm conclusions as well as repeat observations at high spectral resolution of strong MgII absorbers towards Blazars in both high and low states.
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