A Distant Sample of Halo Wide Binaries from SDSS
  Samples of reliably identified halo wide binaries are scarce. If reasonably
free from selection effects and with a small degree of contamination by chance
alignments, these wide binaries become a powerful dynamical tool, having
provided one of the very few experiments capable of constraining the nature of
dark matter in the Milky Way halo. Currently, however, the best available
sample of halo wide binaries is confined to the solar neighborhood, and is
plagued by small number statistics at the widest separations. We present the
results of a program aimed to probe the wide binary population of the Galactic
halo at significantly larger distances, and which informs future searches that
could improve the statistics by orders of magnitude. Halo stars were taken from
the Sloan Digital Sky Survey after analysing the Galactic orbits of stars in
the reduced proper motion diagram. We then select candidate binaries by
searching for pairs with small differences in proper motion and small projected
separation on the sky. Using medium-resolution spectroscopy, a subsample of
candidates is validated via radial velocities, finding that about 68\% of
candidate pairs up to 20$^{\prime\prime}$ separation can be considered genuine
halo wide binaries, to the limits of the available data. Precise parallaxes
from \textit{Gaia} confirm that most of our selected pairs have their
components at the same distances, independently confirming the robustness of
our selection method. These results should prove valuable to guide the optimal
assembly of larger catalogs of halo wide binaries from upcoming large
databases, e.g., \textit{Gaia} and LSST.
