Statistics of matter distribution from halo dynamics

The galaxy-background correlation function at short distances is explored by means of the observed disk dynamics of spiral galaxies. Using both the sample of galaxies and the analytical method for dark-to-luminous mass decomposition from optical rotation curves presented by Persic and Salucci, individual sizes and mean densities are worked out for 42 extended halos (taken to be η = 10 times as massive as their respective disks) as functions of both the intensity and the gradient of the central velocity field. The statistics for the expected density enhancements within given distances from galactic centers shows simple properties which strongly tie galaxy-background and galaxy-galaxy correlation functions. In particular, we find that: (a) the two-point galaxy-background correlation function is in agreement with its galaxy-galaxy counterpart (slope γ = 1.76 +/- 0.03; clustering length r_0_ = (7.1 +/- 0.7)[η/10)gamma-2^(1/{OMEGA}_0_)]^1/γ^ h^-1^_50_ Mpc); (b) the three-point and four-point correlation functions fit the so-called hierarchical clustering expression; (c) the constants Q (for the three-point function) and R-a_ and R_b_ (for the four-point function) are found to be Q = 0.46 +/- 0.04 and R_a_ + 0.35 R_b_ = 0.19 +/- 0.05, in agreement with BBGKY hierarchy predictions. The main consideration which naturally follows is that on the scale of galaxies the statistics of matter seems to be highlighted with equal effectiveness by both the luminous point-object distribution and the dark- matter properties underlying the halo-influenced disk dynamics.