Galaxy cluster mass density profile derived using the submillimetre galaxies magnification bias

Context. The magnification bias is a gravitational lensing e ffect that produces an increase or decrease in the detection probability of background sources near the position of a lense. The special properties of the submillimetre galaxies (SMGs; steep source number counts, high redshift, and a very low cross-contamination with respect to the optical band) makes them the optimal background sample for magnification bias studies. Aims. We want to study the average mass density profile of tens to hundreds of clusters of galaxies acting as lenses that produce a magnification bias on the SMGs, and to estimate their associated masses and concentrations for di fferent richness ranges. The cluster richness is defined as R = L-200/L-* with L-200 as the total r-band luminosity within the radius r(200). Methods. The background sample is composed of SMGs observed by Herschel with 1.2 < z < 4.0 (mean redshift at similar to 2.3) while the foreground sample is made up of galaxy clusters extracted from the Sloan Digital Sky Survey III with photometric redshifts of 0.05 < z < 0.8 (mean redshift at similar to 0.38). Measurements are obtained by stacking the SMG-cluster pairs to estimate the cross-correlation function using the Davis-Peebles estimator. This methodology allows us to derive the mass density profile for a wide range of angular scales, similar to 2-250 arcsec or similar to 10-1300 kpc for z = 0.38, with a high radial resolution, and in particular to study the inner part of the dark matter halo (<100 kpc). In addition, we also divide the cluster sample into five bins of richness and we analyse the estimated cross-correlation data using di fferent combinations of the most common theoretical mass density profiles. Results. It is impossible to fit the data with a single mass density profile at all scales: in the inner part there is a clear excess in the mass density profile with respect to the outer part that we interpret as the galactic halo of the big central galaxy. As for the outer part, the estimated average masses increase with richness from M-200c = 5.8 x 10(13) M-circle dot to M-200c = 51.5 x 10(13) M-circle dot (M-200c = 7.1 x 10(13) M-circle dot for the total sample). With respect to the concentration parameter, its average also increases with richness from C = 0 .74 to C = 1 .74 (C = 1 .72 for the total sample). In the small-scale regions, the obtained average masses fluctuate around M-200c = 3-4 x 10(13) M-circle dot with average concentration values of around C similar to 4. Conclusions. The total average masses are in perfect agreement with the mass-richness relationship estimated from the cluster catalogue. In the bins of lowest richness, the central galactic halo constitutes similar to 40% of the total mass of the cluster and its relevance decreases for higher richness values. While the estimated average concentration values of the central galactic halos are in agreement with traditional mass-concentration relationships, we find low concentrations for the outer part. Moreover, the concentrations decrease for lower richness values, probably indicating that the group of galaxies cannot be considered to be relaxed systems. Finally, we notice a systematic lack of signal at the transition between the dominance of the cluster halo and the central galactic halo (similar to 100 kpc). This feature is also present in previous studies using di fferent catalogues and /or methodologies, but is never discussed.