Physics and Astronomy Masters Talk

Charles Bonfield

“Hierarchical Bayesian Modeling of Galaxy Group Velocity Dispersions for the Complete, Volume-Limited ECO Catalog”

We present a new approach for probing the mass function of dark matter halos using galaxy group observables. Traditionally, similar efforts that utilize line-of-sight velocities rely upon estimated group velocity dispersions as proxies for halo masses. For groups with few observed members (N), these estimates are rife with uncertainty. Here, we use hierarchical Bayesian modeling to model the galaxy group velocity dispersion function (GVDF) for the ECO (Environmental COntext) catalog, a complete mass- and volume-limited sample, thereby allowing the full data set to constrain dispersions for low-N groups. Before applying our model to ECO, we calibrate on mock catalogs matched to ECO – we use the mocks to assess the performance of our model for both “true” and friends-of-friends (FoF) groups in the, then apply our model to the real ECO catalog. We find the use of hierarchical Bayesian modeling shows some potential for improvement over GVDFs constructed from traditional techniques and single-level Bayesian modeling. Further, we show that the shrinkage properties of hierarchical Bayesian modeling affords us with better estimates of dispersion on an individual group level. In a broader context, we hope that our statistical framework may serve as proof of concept for the application of hierarchical Bayesian modeling to complete and volume-limited samples in astronomy.