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.