Testing modified Newtonian dynamics through statistics of velocity dispersion profiles in the inner regions of elliptical galaxies

Modified Newtonian dynamics (MOND) proposed by Milgrom provides a paradigm alternative to dark matter (DM) that has been successful in fitting and predicting the rich phenomenology of rotating disc galaxies. There have also been attempts to test MOND in dispersion-supported spheroidal early-type galaxies, but it remains unclear whether MOND can fit the various empirical properties of early-type galaxies for the whole ranges of mass and radius. As a way of rigorously testing MOND in elliptical galaxies we calculate the MOND-predicted velocity dispersion profiles (VDPs) in the inner regions of ∼2000 nearly round Sloan Digital Sky Survey elliptical galaxies under a variety of assumptions on velocity dispersion (VD) anisotropy, and then compare the predicted distribution of VDP slopes with the observed distribution in 11 ATLAS^3D galaxies selected with essentially the same criteria. We find that the MOND model parametrized with an interpolating function that works well for rotating galaxies can also reproduce the observed distribution of VDP slopes based only on the observed stellar mass distribution without DM or any other galaxy-to-galaxy varying factor. This is remarkable in view that Newtonian dynamics with DM requires a specific amount and/or profile of DM for each galaxy in order to reproduce the observed distribution of VDP slopes. When we analyse non-round galaxy samples using the MOND-based spherical Jeans equation, we do not find any systematic difference in the mean property of the VDP slope distribution compared with the nearly round sample. However, in line with previous studies of MOND through individual analyses of elliptical galaxies, varying MOND interpolating function or VD anisotropy can lead to systematic change in the VDP slope distribution, indicating that a statistical analysis of VDPs can be used to constrain specific MOND models with an accurate measurement of VDP slopes or a prior constraint on VD anisotropy.