MOND and IMF variations in early-type galaxies from $ATLAS^{3D}$
  MOdified Newtonian dynamics (MOND) represents a phenomenological alternative
to dark matter (DM) for the missing mass problem in galaxies and clusters of
galaxies. We analyze the central regions of a local sample of $\sim 220$
early-type galaxies from the $\rm ATLAS^{3D}$ survey, to see if the data can be
reproduced without recourse to DM. We estimate dynamical masses in the MOND
context through Jeans analysis, and compare to $\rm ATLAS^{3D}$ stellar masses
from stellar population synthesis. We find that the observed stellar
mass--velocity dispersion relation is steeper than expected assuming MOND with
a fixed stellar initial mass function (IMF) and a standard value for the
acceleration parameter $a_{\rm 0}$. Turning from the space of observables to
model space, a) fixing the IMF, a universal value for $a_{\rm 0}$ cannot be
fitted, while, b) fixing $a_{\rm 0}$ and leaving the IMF free to vary, we find
that it is "lighter" (Chabrier-like) for low-dispersion galaxies, and "heavier"
(Salpeter-like) for high dispersions. This MOND-based trend matches inferences
from Newtonian dynamics with DM, and from detailed analysis of spectral
absorption lines, adding to the converging lines of evidence for a
systematically-varying IMF.
