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

Abstract

Context. The magnification bias on the submillimetre galaxies (SMGs) is a gravitational lensing effect, where the SMGs are used as background lensed galaxies. This effect can be used to investigate the mass density profiles of different types of foreground lenses. Aims. 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. Methods. The background SMG sample consists of objects observed by Herschel with 1.2 < z < 4.0 (mean redshift at ∼2.2). The foreground samples are QSOs with spectroscopic redshifts 0.2 < z < 1.0 (mean redshift at ∼0.7) and massive galaxies with also spectroscopic redshifts 0.2 < z < 1.0 (mean redshift at ∼0.3). 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. The advantage of such an approach is that it allows us to study the mass density profile over a wide range of angular scales, from ∼2 to ∼250 arcsec, including the inner part of the dark-matter halo (≲100 kpc). 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. Results. The measurements are correctly fitted after splitting the available angular scales into an inner and an outer part using two independent mass density profiles, one for each region. In particular, for the QSOs, we obtain masses of log10(M/M⊙) = 13.51 ± 0.04 and of log10(M/M⊙) = 13.44 ± 0.17 for the inner and outer parts, respectively. The estimated masses for the galaxy sample are log10(M/M⊙) = 13.32 ± 0.08 and log10(M/M⊙) = 12.78 ± 0.21 for the inner and outer parts, respectively. The concentrations for the inner part are much higher than those for the outer region for both samples: C = 6.85 ± 0.34 (inner) and C = 0.36 ± 0.18 (outer) for the QSOs and C = 8.23 ± 0.77 (inner) and C = 1.21 ± 1.01 (outer) for the galaxies. Conclusions. In both samples, the inner part has an excess in the mass density profile with respect to the outer part for both QSOs and galaxy samples. We obtain similar values for the central mass with both samples, and they are also 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. We believe this to be related to the probability of galactic interactions and/or the different evolutionary stages.