Detection of periodicity based on independence tests - IV. Phase distance correlation periodogram for two-dimensional astrometry

I present an extension of the phase distance correlation periodogram to two-dimensional astrometric data. I show that this technique is more suitable than previously proposed approaches to detect eccentric Keplerian orbits, and that it overcomes the inherent bias of the joint periodogram to circular orbits. This new technique might prove to be essential in the context of future astrometric space missions such as Theia.