TESTING GRAVITY WITH MOTION OF SATELLITES AROUND GALAXIES: NEWTONIAN GRAVITY AGAINST MODIFIED NEWTONIAN DYNAMICS

The motion of satellite galaxies around normal galaxies at distances 50–500 kpc provides a sensitive test for theories. We study the surface density and velocities of satellites around isolated red galaxies in the Sloan Digital Sky Survey. We find that the surface number density of satellites declines with the projected distance as a power law with the slope −1.5 to 2. The rms velocities gradually decline: observations exclude constant velocities at a ∼10σ level. We show that observational data strongly favor the standard model; all three major statistics of satellites—the number-density profile, the line-of-sight velocity dispersion, and the distribution function of the velocities—agree remarkably well with the predictions of the standard cosmological model. Thus, the success of the standard model extends to scales (50–500) kpc, much lower than what was previously considered. Modified Newtonian dynamics (MOND) fails on these scales for models which assume any single power-law number-density profile of satellites and any constant velocity anisotropy by predicting nearly constant rms velocities of satellites. Satellite data can be fit by fine-tuned models, which require (1) specific non-power-law density profile, (2) very radial orbits at large distances (velocity anisotropy β = 0.60.7 at R = 200–300 kpc), and (3) 2–2.5 times more stellar mass than what is found in the galaxies. The external gravity force—a necessary component for MOND—makes the situation even worse. We argue that a combination of satellite data and observational constraints on stellar masses make these models very problematic.