Testing Dark Matter and Modifications to Gravity using Local Milky Way
  Observables
  Galactic rotation curves are often considered the first robust evidence for
the existence of dark matter. However, even in the presence of a dark matter
halo, other galactic-scale observations, such as the Baryonic Tully-Fisher
Relation and the Radial Acceleration Relation, remain challenging to explain.
This has motivated long-distance, infrared modifications to gravity as an
alternative to the dark matter hypothesis as well as various DM theories with
similar phenomenology. In general, the standard lore has been that any model
that reduces to the phenomenology of MOdified Newtonian Dynamics (MOND) on
galactic scales explains essentially all galaxy-scale observables. We present a
framework to test precisely this statement using local Milky Way observables,
including the vertical acceleration field, the rotation curve, the baryonic
surface density, and the stellar disk profile. We focus on models that predict
scalar amplifications of gravity, i.e., models that increase the magnitude but
do not change the direction of the gravitational acceleration. We find that
models of this type are disfavored relative to a simple dark matter halo model
because the Milky Way data requires a substantial amplification of the radial
acceleration with little amplification of the vertical acceleration. We
conclude that models which result in a MOND-like force struggle to
simultaneously explain both the rotational velocity and vertical motion of
nearby stars in the Milky Way.
