QSOs sigposting cluster size halos as gravitational lenses: halo mass, projected mass density profile and concentration at $z\sim 0.7$

Abstract

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, $0.2<z<1.0$, on the SMGs observed by Herschel at $1.2<z<4.0$. Two different methodologies were successfully applied: the traditional cross-correlation function approach and the Davis-Peebles estimator through stacking technique. The second one was found to be more robust for analysing the strong lensing regime ($<20-30$ arcsec in our case) and provides the possibility to take into account the positional errors of the sources in our samples. From the halo modelling of the cross-correlation function, the halo mass where the QSOs acting as lenses are located was estimated to be greater than ${\log }_{10}(M_{min}/M_{\odot })>13.6_{-0.4}^{+0.9}$, also confirmed by the mass density profile analysis ($M_{200c}\sim 10^{14}{M}_{\odot }$). These mass values indicate that we are observing the lensing effect of a cluster size halo signposted by the QSOs, as in previous studies of the magnification bias. 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 is in good agreement with a Navarro-Frank-White (NFW) profile. We also attempt an estimation of the halo mass and the concentration parameters, obtaining $M_{NFW}=1.0_{-0.2}^{+0.4}\times 10^{14}{M}_{\odot }$ and $C=3.5_{-0.3}^{+0.5}$. This concentration value is rather low and it would indicate that the cluster halos around these QSOs are unrelaxed. However, higher concentration values still provides a compatible fit to the data.

30 pages, 8 figures, JCAP accepted