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BANYAN_Sigma calculates the membership probability that a given astrophysical object belongs to one of the currently known 27 young associations within 150 pc of the Sun, using Bayesian inference. This tool uses the sky position and proper motion measurements of an object, with optional radial velocity (RV) and distance (D) measurements, to derive a Bayesian membership probability. By default, the priors are adjusted such that a probability threshold of 90% will recover 50%, 68%, 82% or 90% of true association members depending on what observables are input (only sky position and proper motion, with RV, with D, with both RV and D, respectively). The algorithm is implemented in a Python package, in IDL, and is also implemented as an interactive web page.
CoMover determines the probability that two stars are co-moving and thus gravitationally bound. It uses the sky position, proper motion, parallax and optionally the heliocentric radial velocity of a host star (with their respective measurement errors), and compares it to the observables of a potential companion (with their respective measurement errors). The sky position and proper motion of the potential companion star are required, and its heliocentric radial velocity and parallax are facultative inputs to refine its co-moving probability.
If all kinematic observables of the host star are provided, a single spatial-kinematic model is built, consisting of a single 6-dimensional multivariate Gaussian in Galactic coordinates (XYZ) and space velocities (UVW). The observables of the potential companion are then compared to this model and a given field-stars model with Bayes' theorem by marginalizing over any missing kinematic observables of the companion star with analytical integral solutions. The field stars are modeled using a 10-component multivariate Gaussian, accurate for stars within a few hundred parsecs of the Sun. In the case where a heliocentric radial velocity is missing for the host star, the single host-star multivariate Gaussian model is replaced with a series of host star models and numerically marginalized over by taking the numerical sum of the host-star model probabilities.