Gravitational Potential from small-scale clustering in action space:
  Application to Gaia DR2
  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
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 test it against simulations of stellar streams. We then apply this
method to the 2nd data release of Gaia, and use it to measure the radial force
fraction $f_h$ and logarithmic slope $\alpha$ of dark matter halo profile. We
investigate stars within 9-11 kpc and 11.5-15 kpc from Galactic centre, and
find $(f_h,\alpha)= (0.391\pm 0.009, 1.835\pm 0.092) $ and $(0.351\pm
0.012,1.687\pm 0.079)$, respectively. We also confirm that the set of
parameters that maximize the likelihood function do correspond to the most
clustering in the action space. The best-fit circular velocity curve for Milky
Way potential is consistent with past measurements (although it is $\sim$
5-10\% 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 {\it ad hoc}
assumptions such as virial equilibrium, circular motion, or steam-finding
algorithms.
