The redshift-space two-point correlation functions of galaxies and groups in the Nearby Optical Galaxy sample

We use the two-point correlation function in redshift space, $\xi(s)$, to study the clustering of the galaxies and groups of the Nearby Optical Galaxy (NOG) sample, which is a nearly all-sky, complete, magnitude-limited sample of $\sim$7000 bright and nearby optical galaxies. The correlation function of galaxies is well described by a power law, $\xi(s)=(s/s_0)^{-\gamma}$, with slope $\gamma\sim1.5$ and $s_0\sim6.4 h^{-1}$Mpc (on scales $2.7 - 12 h^{-1}$Mpc), in agreement with previous results of several redshift surveys of optical galaxies. We confirm the existence of morphological segregation between early- and late-type galaxies and, in particular, we find a gradual decreasing of the strength of clustering from the S0 galaxies to the late-type spirals, on intermediate scales. Furthermore, luminous galaxies turn out to be more clustered than dim galaxies. The luminosity segregation, which is significant for both early- and late-type objects, starts to become appreciable only for galaxies brighter than $M_B\sim -19.5 + 5 \log h$ ($\sim 0.6 L^*$) and is independent on scale. The NOG group correlation functions are characterized by $s_0$-values ranging from $\sim 8 h^{-1}$ Mpc (for groups with at least three members) to $\sim10 h^{-1}$ Mpc (for groups with at least five members). The degree of group clustering depends on the physical properties of groups. Specifically, groups with greater velocity dispersions, sizes and masses tend to be more clustered than those with lower values of these quantities.