The relation in quasars has been probed only in a limited parameter space, namely, at ？ and ？ . Here we present a study of 26 quasars laying in the low-mass end of the relation, down to ？ . We selected quasars from the SDSS and HST-FOS archives, requiring modest (as derived through the virial paradigm). We imaged our sources in band from the Nordic Optical Telescope. The quasar host galaxies have been resolved in 25 out of 26 observed targets. Host galaxy luminosities and stellar masses are computed, under reasonable assumptions on their star formation histories. Combining these results with those from our previous studies, we manage to extend the sampled parameter space of the relation in quasars. The relation holds over 2 dex in both the parameters. For the first time, we are able to measure the slope of the relation in quasars. We find that it is consistent with the linear case (similarly to what observed in quiescent galaxies). We do not find any evidence of a population of massive black holes lying below the relation. 1. Introduction Massive black holes (BHs) are ubiquitously found in the centre of massive galaxies [1–3]. Their masses ( ) show strong correlations with large-scale properties of the host galaxies, namely, the stellar velocity dispersion ( , [4–7]), the luminosity, and mass of the spheroidal component ( , ; see [8–10]). These relations have been interpreted as the outcome of a joint evolution between BHs and their host galaxies [11–18]. In this scenario, the growth of BHs through accretion regulates the gas cooling in the outskirt of host galaxies through energy or momentum injection (feedback), thus quenching the formation of stars. Galaxy mergers may also play a role in this scenario, as gravitationally induced dynamical instabilities may trigger both star formation bursts and gas inflows fuelling the BH activity ([12, 19–21], see also [22]). The -host galaxy relations have been pinned down on an albeit small set of local, mostly quiescent galaxies. The sampled parameter space ranges over 3 dex in masses, from a few million to a few billion solar masses in terms of . Extending these studies beyond the local Universe is challenging. On one side, the influence radius of BHs, , that is, the radius where the gravitational potential is dominated by the singularity, is resolved only in very nearby objects (distances < few tens Mpc) with high values. For any other sources, indirect tracers of are required. The most commonly adopted indirect estimator of is based on the width of broad emission lines and the size of the broad line region
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