Quasi-stellar objects and galaxy mass density profiles derived using the submillimetre galaxies magnification bias

In this work, we want to exploit the magnification bias of the SMGs using two different foreground samples, quasi-stellar objects (QSOs) and galaxies. Our aim is to study and compare their mass density profiles and estimate their masses and concentrations. The background SMG sample consists of objects observed by \textit{Herschel} with 1.2<z<4.0. The foreground samples are QSOs and massive galaxies with spectroscopic redshifts between 0.2 and 1.0. The cross-correlation measurements are estimated with the Davis-Peebles estimator by stacking the SMG-QSO and SMG-galaxy pairs for the two analysed cases, respectively. This approach allows us to study the mass density profile from $\sim2$ to $\sim250$ arcsec. Moreover, the analysis is carried out by combining two of the most common theoretical mass density profiles in order to fit the cross-correlation measurements. The measurements are correctly fitted after splitting the available angular scales into an inner and an outer part using independent mass density profiles for each region. For the QSOs, we obtain masses and concentrations of $\log_{10}(M/M_{\odot})=13.51\pm0.04; C=6.85\pm0.34$ for the inner part and $\log_{10}(M/M_{\odot})=13.44\pm0.17; C=0.36\pm0.18$ for outer parts. For the galaxy sample are $\log_{10}(M/M_{\odot})=13.32\pm0.08; C=8.23\pm0.77$ and $\log_{10}(M/M_{\odot})=12.78\pm0.21; C=1.21\pm1.01$ for the inner and outer parts, respectively. In both samples, the inner part has an excess in the mass density profile and much higher concentration with respect to the outer part. We obtain similar values for the central mass with both samples, in agreement with those of galaxy clusters results. However, the estimated masses for the outer region and the concentrations of the inner region both vary with lens sample. This could be related to the probability of galactic interactions and/or the different evolutionary stages.