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

In this thesis I present a new method for the statistical detection of binary stars via the novel Two-Point Separation Function, and apply this method to the detection of ultra-wide binary stars in Dwarf Spheroidal Galaxies (dSphs). dSphs are small, lowluminosity galaxies with extraordinarily high dynamical mass-to-light ratios (10-100 times those found in the solar neighbourhood [1]). Given that the galactic potential of these objects is dominated by the dark matter term, they provide an ideal testing ground for the survivability of ultra-wide binaries. As ultra-wide binaries are loosely bound, they are easily disrupted by the DM-dominated host tidal field, and the precise nature of that disruption is dependent on the form of the DM potential (in particular whether the potential is cored or cuspy and/or has clumpy substructure). As such, detection of ultra-wide binaries in dSphs can offer a window onto dark matter at the smallest scales. 

I present a derivation of the Two-Point Separation Function, a novel treatment of the analysis of pairwise separations between stars in dSph galaxies. The Two-Point Separation Function describes the separation density of pairs of stars given the surface density of their stellar positions. I derive the equations for obtaining analytical solutions for this separation density, and present examples of surface densities which yield analytically tractable densities, namely a Plummer profile, a uniform density, and a superposition thereof. I then show how these densities can be modified to include the separation density governing a population of binaries, and thus how a full fitting algorithm can be applied to constrain the parameters which govern the separation density of the binary population itself. 

I then present the results from a suite of fits to mock data sets which model 40 known Local Group dSphs. Each mock data set consists of a dSph population which follows a Plummer profile, a uniform foreground, and two distinct binary populations, one in the dSph and one in the foreground. For the dSph binaries, three separate binary separation distributions are tested: a single power law, a broken power law, and a truncated model. The results of these tests show a strong recovery of the binary parameters in both populations, with extremely good recovery of the indices of the power laws, the location of truncations or index changes, and perhaps most importantly the binary fraction itself, which has hitherto been entirely unconstrained in dSphs. 

I apply this method to an archival observation of the Ursa Minor dSph. The raw data is passed through a HST data reduction pipeline designed for resolved stellar photometry. Then, using Artificial Star Tests, I determine the spatially-dependent completeness of the sample, and the behaviour of selection effects. Finally, I attempt to remove galaxy contamination, i.e. sources which are misidentified as being stellar in nature when they are in fact small galaxies or small regions of larger galaxies. Two methods are used to isolate and mask the galaxies: the first depending on the RADXS parameter (a measure of the disagreement of the fitted Point Spread Function of a source and the actual brightness profile), and the second being a method which searches for contiguous chains of close sources. These methods remove all of the larger galaxies, but are unable to efficiently locate small galaxies which appear as two or three misidentified sources. 

The final data set for analysis contains some small galaxies which appear as small double or triple systems and thus, the results presented here for the binary fraction of Ursa Minor strictly constitute an upper bound. I find an upper bound for the detectable ultra-wide binary fraction in Ursa Minor of < 0.82±0.25% (which corresponds to an extrapolated true ultra-wide binary fraction of < 1.17±0.35%), with a separation density profile which exhibits a near-truncation at a scale of 0.15 parsecs. These represent the first statistically significant constraint on the fraction of ultra-wide binaries in a dSph, and the scale at which the truncation occurs is consistent with a cuspy dark matter potential.