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 ${0.08}_{-0.02}^{0.05}{M}_{\odot }\,{\mathrm{pc}}^{-3}$, which is close to estimates from recent Jeans analyses. Given the accounting of the baryon budget from McKee et al., we obtain a local dark matter density of $-{0.004}_{-0.02}^{0.05}\,{M}_{\odot }\,{\mathrm{pc}}^{-3}$, which is slightly below other modern estimates but consistent within the current uncertainties of our method. The error bars are currently about five times larger than kinematical estimates, but should improve in the future for this novel dynamical method. 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 that is within a ∼kpc of the Sun. We find that current measurements of binary pulsar accelerations lead to large uncertainties in the slope of the rotation curve. We give a fitting function for the vertical acceleration az: az = − α1z; ${\mathrm{log}}_{10}({\alpha }_{1}/{\mathrm{Gyr}}^{-2})={3.69}_{-0.12}^{0.19}$. By analyzing interacting simulations of the Milky Way, we find that large asymmetric variations in daz/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 measurements toward lines-of-sight near pulsars, to test theories of gravity and constrain dark matter sub-structure.