Gravitational potential from small-scale clustering in action space: application to Gaia Data Release 2

Abstract

ABSTRACT Most measurements of mass in astronomy that use kinematics of stars or gas rely on assumptions of equilibrium that are often hard to verify. Instead, we develop a novel idea that uses the clustering in action space, as a probe of the underlying gravitational potential: the correct potential should maximize small-scale clustering in the action space. We provide a first-principle derivation of likelihood using the two-point correlation function in action space, and we test it against simulations of stellar streams. We then apply this method to the second data release of Gaia, and we use it to measure the radial force fraction fh and logarithmic slope α of the dark matter halo profile. We investigate stars within 9–11 kpc and 11.5–15 kpc from the Galactic Centre, and we find (fh, α) = (0.391 ± 0.009, 1.835 ± 0.092) and (0.351 ± 0.012, 1.687 ± 0.079), respectively. We also confirm that the set of parameters that maximize the likelihood function does correspond to the most clustering in the action space. The best-fitting circular velocity curve for the Milky Way potential is consistent with past measurements (although it is ∼5–10 per cent lower than previous methods that use masers or globular clusters). Our work provides a clear demonstration of the full statistical power that lies in the full phase space information, relieving the need for ad hoc assumptions such as virial equilibrium, circular motion or steam-finding algorithms.