The Kinematic Properties of Milky Way Stellar Halo Populations
  In the $Gaia$ era stellar kinematics are extensively used to study Galactic
halo stellar populations, to search for halo structures, and to characterize
the interface between the halo and hot disc populations. We use distribution
function-based models of modern datasets with 6D phase space data to
qualitatively describe a variety of kinematic spaces commonly used in the study
of the Galactic halo. Furthermore, we quantitatively assess how well each
kinematic space can separate radially anisotropic from isotropic halo
populations. We find that scaled action space (the ``action diamond'') is
superior to other commonly used kinematic spaces at this task. We present a
new, easy to implement selection criterion for members of the
radially-anisotropic $Gaia$-Enceladus merger remnant, which we find achieves a
sample purity of 82 per cent in our models with respect to contamination from
the more isotropic halo. We compare this criterion to literature criteria,
finding that it produces the highest purity in the resulting samples, at the
expense of a modest reduction in completeness. We also show that selection
biases that underlie nearly all contemporary spectroscopic datasets can
noticeably impact the $E-L_{z}$ distribution of samples in a manner that may be
confused for real substructure. We conclude by providing recommendations for
how authors should use stellar kinematics in the future to study the Galactic
stellar halo.
