Membership lists for 431 open clusters in Gaia DR2 using extreme deconvolution gaussian mixture models

Open clusters are groups of stars that form at the same time, making them an ideal laboratory to test theories of star formation, stellar evolution, and dynamics in the Milky Way disk. However, the utility of an open cluster can be limited by the accuracy and completeness of its known members. Here, we employ a "top-down" technique, {\it extreme deconvolution gaussian mixture models} (XDGMM), to extract and evaluate known open clusters from Gaia DR2 by fitting the distribution of stellar parallax and proper motion along a line-of-sight. Extreme deconvolution techniques can recover the intrinsic distribution of astrometric quantities, accounting for the full covariance matrix of the errors; this allows open cluster members to be identified even when presented with relatively uncertain measurement data. To date, open cluster studies have only applied extreme deconvolution to specialized searches for individual systems. We use XDGMM to characterize the open clusters reported by Ahumada et al. 2007 and are able to recover 420 of the 426 open clusters therein (98.1\%). Our membership list contains the overwhelming majority ($>95\%$) of previously known cluster members. We also identify a new, significant, and relatively faint cluster member population and validate their membership status using Gaia eDR3. We report the fortuitous discovery of 11 new open cluster candidates within the lines of sight we analyzed. We present our technique, its advantages and challenges, as well as publish our membership lists and updated cluster parameters.