Tracing the Hercules stream around the Galaxy

It has been proposed that the Hercules stream, a group of co-moving stars in the Solar neighborhood offset from the bulk of the velocity distribution, is the result of resonant interactions between stars in the outer disk and the Galactic bar. So far it has only been seen in the immediate Solar neighborhood, but the resonance model makes a prediction over a large fraction of the Galactic disk. I predict the distribution of stellar velocities and the changing Hercules feature in this distribution as a function of location in the Galactic disk in a simple model for the Galaxy and the bar that produces the observed Hercules stream. The Hercules feature is expected to be strong enough to be unambiguously detected in the distribution of line-of-sight velocities in selected directions. I identify quantitatively the most promising lines of sight for detection in line-of-sight velocities using the Kullback-Leibler divergence between the predictions of the resonance model and an axisymmetric model; these directions are at 250 deg <~ l <~ 290 deg. The predictions presented here are only weakly affected by distance uncertainties, assumptions about the distribution function in the stellar disk, and the details of the Galactic potential including the effect of spiral structure. Gaia and future spectroscopic surveys of the Galactic disk such as APOGEE and HERMES will be able to robustly test the origin of the Hercules stream and constrain the properties of the Galactic bar

Inferring the eccentricity distribution

Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple histogram of estimated eccentricities is not a good estimate of the true eccentricity distribution. Here we develop and test a hierarchical probabilistic method for performing the relevant meta-analysis, that is, inferring the true eccentricity distribution, taking as input the likelihood functions for the individual-star eccentricities, or samplings of the posterior probability distributions for the eccentricities (under a given, uninformative prior). The method is a simple implementation of a hierarchical Bayesian model; it can also be seen as a kind of heteroscedastic deconvolution. It can be applied to any quantity measured with finite precision--other orbital parameters, or indeed any astronomical measurements of any kind, including magnitudes, parallaxes, or photometric redshifts--so long as the measurements have been communicated as a likelihood function or a posterior sampling.Comment: Ap