Testing Modified Newtonian dynamics through statistics of velocity
  dispersion profiles in the inner regions of elliptical galaxies
  Modified Newtonian dynamics (MOND) provides a paradigm alternative to dark
matter 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 early-type galaxies, but it remains unclear
whether MOND can fit the various empirical properties of early-type galaxies.
As a way of rigorously testing MOND in elliptical galaxies we calculate the
MOND-predicted velocity dispersion profiles (VDPs) in the inner regions of
$\sim 2000$ nearly round SDSS elliptical galaxies under a variety of
assumptions on VD anisotropy, and then compare the predicted distribution of
VDP slopes with the observed distribution in 11 ATLAS3d galaxies selected with
essentially the same criteria. We find that the MOND model parameterised 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.
