A simple linear model to aid in analyses of the β Pictoris moving group

Abstract

We build a 4D linear model of object membership in the $\beta$ Pictoris moving group (BPMG), using two nested applications of Principal Component Analysis (PCA) for ~1.5 million objects with high-quality data. These data consist of 3D-Galactic space velocities and Gaia G magnitudes. Through PCA, they ultimately result in a 4D straight line, referred to as PC 1', about which both the bona fide members used to obtain the straight line and the candidate members used to test the model congregate at generally small distances. As a proof of concept, we select bona fide members from a recent, Gaia DR2-based compilation and candidate members mostly from a (pre-Gaia DR2) compilation from 2017. Using a standard procedure to flag groups of outliers in data sets, we find possible outliers flagged on account of their large distances to PC 1', and find evidence that discrepant radial velocity measurements may indeed bring into question their validity as BPMG members. We propose that PC 1' be added to the tool set for BPMG analyses and potentially extended to other young stellar moving groups.