Objectives

The pipeline we’ve developed was able to generate probabilities for the photometric terms $P_{\text{CMD}}, P_{\text{dist}}$. The main objective is to now determine what a good cut or a sweet spot probability that we can ascribe to these probabilities that can accurately describe the properties of the target galaxy while having the least amount of contamination that predicted properties may not be skewed.

We will apply the Wolf equation that can describe the mass of these target galaxies accurately (given these objects are dispersion-supported, or held together by its own gravity without any significant tidal interactions) with the 2D projected half-light radius and velocity dispersion.

Results

Using a Boötes 1 as a test galaxy, we generate the photometric-only probabilities for sample stars. These stars then get binned into a probabilty cut between 10% and 90%, i.e., the first bin contains all stars with $P > 0.1%$ and the last bin contains all stars with $P > 0.9$. Then we throw those bins into emcee to calculate the velocity dispersions of each bin and compute the predicted galactic mass based on those dispersions in each bin.

Probability Cuts

We see that as each bin becomes more strict in terms of the probability cut, there are less sampled members, and thus we have larger errors on what the predicted mass could lie. According to Koposov et al., the true mass of Boötes 1 is somewhere in the ballpark of ${1.1}^{+1.3}_{-0.5} \times 10^{7} \text{M}_{\odot}$. Although it seems that the predicted mass for each bin lies above that specification, there is a likely chance that contaminants in the more “relaxed” cuts could be inflating the mass significantly. We plot the projected Wolf Equation mass with the uncertainties given the radial velocity measurement acquired by Koposov et al. in the last bin.

In order to find this sweet spot, we must reproduce this analysis with other galaxies like Palomar 13, Willman 1, and Segue 1 to determine the robustness of this method.

For now, this tweet best explains the current dilemma: