On the Luminosity Dependence of the Galaxy Pairwise Velocity Dispersion

We make predictions for the pairwise velocity dispersion (PVD) of galaxies with models that are constrained to match the projected correlation function and luminosity function of galaxies in the Two-Degree Field Galaxy Redshift Survey (2dFGRS). We use these data to constrain the halo occupation distribution (HOD) of 2dFGRS galaxies, then calculate the PVD by populating the halos of a large-volume, high-resolution N-body simulation. We examine the luminosity and scale dependence of the predicted PVD. At large scales the PVD is flat, but at r ∼ 2 h−1Mpc the dispersion rapidly rises as the dominant source of galaxy pairs transitions from two-halo pairs to pairs within a single halo. At small and large scales, r < 1 h−1Mpc and r & 3 h−1Mpc, we find that the PVD decreases with increasing galaxy luminosity. This result is mostly driven by the fraction of satellite galaxies fsat, which is well-constrained by the shape and amplitude of the correlation function. We find fsat ∼ 25% for galaxies fainter than L∗, while for brighter galaxies the satellite fraction rapidly declines, creating the decrease in the PVD with luminosity. At r = 1 h−1Mpc, the PVD has no dependence on luminosity because satellite galaxies dominate the statistics for both bright and faint objects. Recent measurements of the PVD in Fourier space using the “dispersion model” have reported a strong decline in PVD with increasing luminosity at k = 1 Mpc−1 h. We test this method with our HOD models, finding that the dispersion model roughly recovers the shape of PVD with scale, but that there is no consistent comparison between the PVD at a given k-scale and the true dispersion at a given value of r. This results in a luminosity dependence in k-space that is stronger than in configuration space. The luminosity dependence of the HOD results in Fourier space are consistent with those measured at k = 1 Mpc−1 h; thus the recent measurements of the PVD are fully explainable in the context of halo occupation models. The normalization of the PVD is lower than predicted by our fiducial model, and reproducing it requires a lower value of Ωm (∼ 0.2 instead of 0.3), a lower value of σ8 (∼ 0.7 instead of 0.9), or a significant bias between the velocity dispersion of galaxies and dark matter in massive halos. Subject headings: cosmology:theory — galaxies:halos — large scale structure of the universe