A BAYESIAN APPROACH TO LOCATING THE RED GIANT BRANCH TIP MAGNITUDE. II. DISTANCES TO THE SATELLITES OF M31

In "A Bayesian Approach to Locating the Red Giant Branch Tip Magnitude (Part I)," a new technique was introduced for obtaining distances using the tip of the red giant branch (TRGB) standard candle. Here we describe a useful complement to the technique with the potential to further reduce the uncertainty in our distance measurements by incorporating a matched-filter weighting scheme into the model likelihood calculations. In this scheme, stars are weighted according to their probability of being true object members. We then re-test our modified algorithm using random-realization artificial data to verify the validity of the generated posterior probability distributions (PPDs) and proceed to apply the algorithm to the satellite system of M31, culminating in a three-dimensional view of the system. Finally, a preliminary investigation into the satellite density distribution within the halo is made using the obtained distance distributions. For simplicity, this investigation assumes a single power law for the density as a function of radius, with the slope of this power law examined for several subsets of the entire satellite sample.