  As the second paper of a series on studying galaxy-galaxy lensing signals
using the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we present our
measurement and modelling of the lensing signals around groups of galaxies. We
divide the groups into four halo mass bins, and measure the signals around four
different halo-center tracers: brightest central galaxy (BCG),
luminosity-weighted center, number-weighted center and X-ray peak position. For
X-ray and SDSS DR7 cross identified groups, we further split the groups into
low and high X-ray emission subsamples, both of which are assigned with two
halo-center tracers, BCGs and X-ray peak positions. The galaxy-galaxy lensing
signals show that BCGs, among the four candidates, are the best halo-center
tracers. We model the lensing signals using a combination of four
contributions: off-centered NFW host halo profile, sub-halo contribution,
stellar contribution, and projected 2-halo term. We sample the posterior of 5
parameters i.e., halo mass, concentration, off-centering distance, sub halo
mass, and fraction of subhalos via a MCMC package using the galaxy-galaxy
lensing signals. After taking into account the sampling effects (e.g. Eddington
bias), we found the best fit halo masses obtained from lensing signals are
quite consistent with those obtained in the group catalog based on an abundance
matching method, except in the lowest mass bin. Subject headings: (cosmology:)
gravitational lensing, galaxies: clusters: general
