QSOs acting as gravitational lenses: halo mass and projected mass density profile at $z\sim0.7$
Magnification bias is a gravitational lensing effect that is normally overlooked because it is considered sub-optimal in comparison with the lensing shear. Thanks to the demonstrated optimal characteristics of the sub-millimetre galaxies (SMGs) for lensing analysis, in this work we were able to measure the magnification bias produced by a sample of QSOs acting as lenses, $0.2 13.6_{-0.4}^{+0.9}$, also confirmed by the mass density profile analysis ($M_{NFW}=1.6_{-0.5}^{+2.1}\times10^{14} M_\odot$). These mass values indicate that we are observing the lensing effect of a cluster size halo signposted by the QSOs. Moreover, we were able to estimate the lensing convergence, $\kappa(\theta)$, for our magnification bias measurements down to a few kpcs. The derived mass density profile shows a core in its centre and it is compatible with a Navarro-Frank-White (NFW) profile. The core radius, $r_c=30_{-10}^{+14}$ kpc, was estimated using a cored Singular Isothermal Sphere profile that fits even better the data. In addition, we were not able to detect any baryonic/stellar component at very small scales. Both results could indicate the effect of a strong baryonic feedback produced by the active galactic nuclei in the centre of the QSOs responsible of the removal of the expected cusp.