An Equilibrium Model of the Galaxy Determined by Element Abundance Gradients

Abstract We present a method to determine the gravitational potential of the Milky Way from measurements of the locations, velocities, and element abundances of stars in the Galactic disk. The method relies on the assumption that the Galaxy is axisymmetric and stationary and that element abundance ratios such as [Fe/H] and [Mg/Fe] are smooth functions of three isolating integrals of motion. We use Fisher Information theory to predict the efficacy of individual abundance ratios to constrain the potential. We also use N -body simulations to test the extent by which secular evolution in the disk introduces statistical and systematic errors into the analysis. We apply our method to a sample of stars from Gaia Data Release 3 and the APOGEE survey and infer the vertical force profile at the position of the Sun and the rotation curve in the midplane and find good agreement with previously published results. The residuals of the model show corrugations in [Fe/H] as a function of L z , the angular momentum component along the spin axis of the Galaxy. Using the correspondence between L z and Galactocentric cylindrical radius, we show that these features line up with the four spiral arms closest to the Sun.