Clustering of K-band selected local galaxies

We present detailed clustering analysis of a large K-band selected local galaxy sample, which is constructed from the 2MASS and the SDSS and consists of $82,486$ galaxies with $10<K<13.5$ and $0.01<z<0.1$. The two-point correlation function of the magnitude-limited sample in real space at small scales is well described by a power law $\xi (r)=(r\mathrm{/}6.44\pm 0.23{)}^{-1.81\pm 0.02}$. The pairwise velocity dispersion is derived from the anisotropic two-point correlation function and find the dispersion ${\sigma }_{12}=685\pm 17\text{kms}$ if its scale invariance is assumed, which is larger than values measured in optical bands selected galaxy samples. We further investigate the dependence of the two-point correlation function and the ${\sigma }_{12}$ on the $g-r$ color and the $K$-band luminosity, obtain similar results to previous works in optical bands. Comparing a mock galaxy sample with our real data indicates that the semi-analytical model can not mimic the ${\sigma }_{12}$ in observation albeit it can approximate the two-point correlation function within measurement uncertainties.