Two-Point Separation Functions for Modeling Wide Binary Systems in
  Nearby Dwarf Galaxies
  We use a geometric method to derive (two-dimensional) separation functions
amongst pairs of objects within populations of specified position function
$\mathrm{d} N/\mathrm{d} \vec{R}$. We present analytic solutions for separation
functions corresponding to a uniform surface density within a circular field, a
Plummer sphere (viewed in projection), and the mixture thereof -- including
contributions from binary objects within both sub-populations. These results
enable inferences about binary object populations via direct modeling of object
position and pair separation data, without resorting to standard estimators of
the two-point correlation function. Analyzing mock data sets designed to mimic
known dwarf spheroidal galaxies, we demonstrate the ability to recover input
properties including the number of wide binary star systems and, in cases where
the number of resolved binary pairs is assumed to be $\gtrsim$ a few hundred,
characteristic features (e.g., steepening and/or truncation) of their
separation function. Combined with forthcoming observational capabilities, this
methodology opens a window onto the formation and/or survival of wide binary
populations in dwarf galaxies, and offers a novel probe of dark matter
substructure on the smallest galactic scales.
