A measurement of the Galactic plane mass density from binary pulsar
  accelerations
  We use compiled high-precision pulsar timing measurements to directly measure
the Galactic acceleration of binary pulsars relative to the Solar System
barycenter. Given the vertical accelerations, we use the Poisson equation to
derive the Oort limit, i.e., the total volume mass density in the Galactic
mid-plane. Our best-fitting model gives an Oort limit of $0.08^{0.05}_{-0.02}
M_{\odot}/\rm pc^{3}$, which is close to estimates from recent Jeans analyses.
Given the accounting of the baryon budget from McKee et al. (2015), we obtain a
local dark matter density of $-0.004^{0.05}_{-0.02}~M_{\odot}/\rm pc^{3}$,
which is slightly below other modern estimates but consistent within the
current uncertainties of our method. While this first measurement of the Oort
limit (and other Galactic parameters) has error bars that are currently several
times larger than kinematical estimates, they should improve in the future. We
also constrain the oblateness of the potential, finding it consistent with that
expected from the disk and inconsistent with a potential dominated by a
spherical halo, as is appropriate for our sample which is within a $\sim$ kpc
of the Sun. We find that the slope of the rotation curve is not constrained by
current measurements of binary pulsar accelerations. We give a fitting function
for the vertical acceleration $a_{z}$: $a_{z} = -\alpha_{1}z$; $\log_{10}
(\alpha_{1}/{\rm Gyr}^{-2})=3.69^{0.19}_{-0.12}$. By analyzing interacting
simulations of the Milky Way, we find that large asymmetric variations in
$da_{z}/dz$ as a function of vertical height may be a signature of
sub-structure. We end by discussing the power of combining constraints from
pulsar timing and high-precision radial velocity (RV) measurements towards
lines-of-sight near pulsars, to test theories of gravity and constrain dark
matter sub-structure.
