Stellar mass versus velocity dispersion as tracers of the lensing signal around bulge-dominated galaxies

We present the results of a weak gravitational lensing analysis to determine whether the stellar mass or else the velocity dispersion is more closely related to the amplitude of the lensing signal around galaxies, hence to the projected distribution of dark matter. The lensing signal on smaller scales than the virial radius corresponds most closely to the lensing velocity dispersion in the case of a singular isothermal profile, but is also sensitive on larger scales to the clustering of the haloes. We have selected over 4000 lens galaxies at a redshift z < 0.2 with concentrated (or bulge-dominated) surface brightness profiles from the similar to 300 square degree overlap between the Red-sequence Cluster Survey 2 (RCS2) and the data release 7 (DR7) of the Sloan Digital Sky Survey (SDSS). We consider both the spectroscopic velocity dispersion and a model velocity dispersion (a combination of the stellar mass, the size, and the Sersic index of a galaxy). Comparing the model and spectroscopic velocity dispersion we find that they correlate well for galaxies with concentrated brightness profiles. We find that the stellar mass and the spectroscopic velocity dispersion trace the amplitude of the lensing signal on small scales equally well. The model velocity dispersion, however, does significantly worse. A possible explanation is that the halo properties that determine the small-scale lensing signal - mainly the total mass - also depend on the structural parameters of galaxies, such as the effective radius and Sersic index, but we lack data for a definitive conclusion.