Clustering properties and halo masses for central galaxies in the local
  Universe
  We investigate the clustering and dark matter halo mass for a sample of
$\sim$16,000 central galaxies selected from the SDSS/DR7 group catalog. We
select subsamples of central galaxies on three two-dimensional planes, each
formed by stellar mass ($M_{\star}$) and one of the other properties including
optical color (g-r) , surface stellar mass density ($\mu_{\star}$) and central
stellar velocity dispersion ($\sigma_{\star}$). For each subsample we measure
both the projected cross-correlation function ($w_{p}(r_{p})$) relative to a
reference galaxy sample, and an average mass of the host dark matter halos
($M_{halo}$) . For comparison we have also estimated the $w_{p}(r_{p})$ for the
full galaxy population and the subset of satellite galaxies. We find that, for
central galaxies, both $w_{p}(r_{p})$ and $M_{halo}$ show strongest dependence
on $M_{\star}$, and there is no clear dependence on other properties when
stellar mass is fixed. This result provides strong support to the
previously-adopted assumption that, for central galaxies, stellar mass is the
galaxy property that is best indicative of the host dark halo mass. The full
galaxy population and the subset of satellites show similar clustering
properties in all cases. However, they are similar to the centrals only at high
masses ($M_{\star} \geq 10^{11} M_{\odot}$). At low-mass ($M_{\star} \leq
10^{11} M_{\odot}$), the results are different: the $w_{p}(r_{p})$ increases
with both $\sigma$ and g-r when $M_{\star}$ is fixed, and depends very weakly
on $M_{\star}$ when $\sigma_{\star}$ or g-r is fixed. At fixed $M_{star}$, the
$\mu_{\star}$ shows weak correlations with clustering amplitude (and halo mass
for central galaxies). Our results suggest that it is necessary to consider
central and satellite galaxies separately when studying the link between
galaxies and dark matter halos. (Abridged)
