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  1. Abstract

    The total mass of the Local Group (LG) is a fundamental quantity that enables interpreting the orbits of its constituent galaxies and placing the LG in a cosmological context. One of the few methods that allows inferring the total mass directly is the “Timing Argument,” which models the relative orbit of the Milky Way (MW) and M31 in equilibrium. The MW itself is not in equilibrium, a byproduct of its merger history and including the recent pericentric passage of the Large Magellanic Cloud (LMC), and recent work has found that the MW disk is moving with a lower bound “travel velocity” of ∼32 km s−1with respect to the outer stellar halo. Previous Timing Argument measurements have attempted to account for this nonequilibrium state, but have been restricted to theoretical predictions for the impact of the LMC specifically. In this paper, we quantify the impact of a travel velocity on recovered LG mass estimates using several different compilations of recent kinematic measurements of M31. We find that incorporating the measured value of the travel velocity lowers the inferred LG mass by 10%–12% compared to a static MW halo. Measurements of the travel velocity with more distant tracers could yield even larger values, which would further decrease the inferred LG mass. Therefore, the newly measured travel velocity directly implies a lower LG mass than from a model with a static MW halo and must be considered in future dynamical studies of the Local Volume.

     
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  2. Abstract

    We use a geometric method to derive (two-dimensional) separation functions among pairs of objects within populations of specified position functiondN/dR. 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.

     
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