Galaxy-galaxy and galaxy-cluster lensing with the SDSS and FIRST surveys

We perform a galaxy-galaxy lensing study by correlating the shapes of $\sim$2.7 $\times$ 10$^5$ galaxies selected from the VLA FIRST radio survey with the positions of $\sim$38.5 million SDSS galaxies, $\sim$132000 BCGs and $\sim$78000 SDSS galaxies that are also detected in the VLA FIRST survey. The measurements are conducted on angular scales ${\theta}$ $\lesssim$ 1200 arcsec. On scales ${\theta}$ $\lesssim$ 200 arcsec we find that the measurements are corrupted by residual systematic effects associated with the instrumental beam of the VLA data. Using simulations we show that we can successfully apply a correction for these effects. Using the three lens samples (the SDSS DR10 sample, the BCG sample and the SDSS-FIRST matched object sample) we measure a tangential shear signal that is inconsistent with zero at the 10${\sigma}$, 3.8${\sigma}$ and 9${\sigma}$ level respectively. Fitting an NFW model to the detected signals we find that the ensemble mass profile of the BCG sample agrees with the values in the literature. However, the mass profiles of the SDSS DR10 and the SDSS-FIRST matched object samples are found to be shallower and steeper than results in the literature respectively. The best-fitting Virial masses for the SDSS DR10, BCG and SDSS-FIRST matched samples, derived using an NFW model and allowing for a varying concentration factor, are M$^{SDSS-DR10}_{200}$ = (1.2 $\pm$ 0.4) $\times$ 10$^{12}$M$_{\odot}$, M$^{BCG}_{200}$ = (1.4 $\pm$ 1.3) $\times$ 10$^{13}$M$_{\odot}$ and M$^{SDSS-FIRST}_{200}$ = 8.0 $\pm$ 4.2 $\times$ 10$^{13}$M$_{\odot}$ respectively. These results are in good agreement (within $\sim$2${\sigma}$) with values in the literature. Our findings suggest that for galaxies to be both bright in the radio and in the optical they must be embedded in very dense environment on scales R $\lesssim$ 1Mpc.