The Milky Way's circular velocity curve measured using element abundance gradients

Spectroscopic surveys now supply precise stellar label measurements such as element abundances for large samples of stars throughout the Milky Way. These element abundances are known to correlate with orbital actions or other dynamical invariants. We present a new data-driven method for empirically measuring the circular velocity curve of the Galaxy that uses element abundance gradients in the plane of radial kinematics. We use stellar surface abundances from the $\textit{APOGEE}$ survey combined with kinematic data from the $\textit{Gaia}$ mission. Our results confirm the ordered structure of the Milky Way disk in terms of average [Fe/H] and [Mg/Fe] abundance ratios, and suggest that $\langle$[Fe/H]$\rangle$ traces the radial position of stars in the disk, while $\langle$[Mg/Fe]$\rangle$ traces the orbital excursions around this radius. Our method uses the radial orbit structure in the Galaxy to enable an empirical measurement of the circular velocity curve, epicyclic and azimuthal frequencies, and kinematic gradients across the Milky Way disk. From these measurements, we infer a value of the circular velocity curve at the Solar radius of $v_{c,\odot} = 235.3^{+2.8}_{-3.7}$ km s$^{-1}$ using the most constraining abundance ratio, [Mg/Fe]. We also measure the radial and azimuthal frequencies for a circular orbit at the solar radius, $\kappa_{0,R_\odot}=36.9^{+0.8}_{-1.0}$ km s$^{-1}$ kpc$^{-1}$ and $\Omega_{0,R_\odot}=28.5_{-0.1}^{+0.4}$ km s$^{-1}$ kpc$^{-1}$, respectively. These values lead to an estimate of the Oort constants of $A = 16.5^{+0.1}_{-0.1}$ km s$^{-1}$ kpc$^{-1}$ and $B=-11.9^{+0.1}_{-0.3}$ km s$^{-1}$ kpc$^{-1}$. We measure the radial acceleration at the Solar radius to be $(\frac{\partial \Phi}{\partial R})_{\odot} = a_{R_\odot}=7.0^{+0.2}_{-0.1}$ pc Myr$^{-2}$.