Two-point Separation Functions for Modeling Wide Binary Systems in Nearby Dwarf Galaxies

Abstract

<jats:title>Abstract</jats:title> <jats:p>We use a geometric method to derive (two-dimensional) separation functions among pairs of objects within populations of specified position function <jats:inline-formula> <jats:tex-math> <?CDATA ${dN}/d{\boldsymbol{R}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic">dN</mml:mi> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>d</mml:mi> <mml:mi mathvariant="bold-italic">R</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjac5b5fieqn1.gif" xlink:type="simple" /> </jats:inline-formula>. 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 subpopulations. 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 ≳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 inferred dark matter substructure on the smallest galactic scales.</jats:p>