A Bayesian Approach to Locating the Red Giant Branch Tip Magnitude (Part 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 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 3D view of the system. Further to the distributions thus obtained, we apply a satellite-specific prior on the satellite distances to weight the resulting distance posterior distributions, based on the halo density profile. Thus in a single publication, using a single method, a comprehensive coverage of the distances to the companion galaxies of M31 is presented, encompassing the dwarf spheroidals Andromedas I - III, V, IX-XXVII and XXX along with NGC147, NGC 185, M33 and M31 itself. Of these, the distances to Andromeda XXIV - XXVII and Andromeda XXX have never before been derived using the TRGB. Object distances are determined from high-resolution tip magnitude posterior distributions generated using the Markov Chain Monte Carlo (MCMC) technique and associated sampling of these distributions to take into account uncertainties in foreground extinction and the absolute magnitude of the TRGB as well as photometric errors. The distance PPDs obtained for each object both with, and without the aforementioned prior are made available to the reader in tabular form...