The M_BH - M_star relation for X-ray obscured, red QSOs at 1.2< z <2.6

We present near-infrared spectra, obtained with SINFONI and XShooter observations at ESO VLT, of nine dusty, red QSOs at 1.2<z<2.6. The sources are hard X-ray detected, characterized by cold absorption (N_H>10^{21} - 10^{22} cm^{-2}) and show a broad Ha component in the NIR spectra. We complement this sample with twelve additional sources taken from the literature with similar properties resulting in a total sample of 21 X-ray obscured, intermediate type (1.8-1.9), dusty reddened QSOs. From the broad Ha line we have computed the BH masses through the virial formula and derived Eddington ratios. Moreover, from optical/IR multi-component SED fitting we have derived the stellar mass of their host galaxies and their SFRs. We find that most of the sources in our sample are hosted in starburst and main sequence star-forming galaxies with Eddington ratios lambda>0.1. We find a strong trend with the BH mass i.e. less massive objects are scattered below and above the local relation while the most massive ones are mainly located above it. We also studied the evolution of these sources on the M_BH-M_star plane compared to a sample of optically blue type--1 QSOs and we find that obscured red QSOs show a ratio of M_BH to M_star that increases with redshift which is consistent with or slightly lower than what has been found for blue QSOs. These sources may represent the blow-out phase at the end of the rapid BH growth and immediately preceding the classical blue QSOs typically sampled in optical surveys. They in fact show evidence of outflows in the ionized gas component, but their BH has already fully formed.