Discovering neutron stars with LISA via measurements of orbital eccentricity in Galactic binaries

LISA will detect 10⁴ Galactic binaries, the majority being double white dwarfs. However, approximately 1-5% of these systems will contain neutron stars (NSs) which, if they can be correctly identified, will provide new opportunities for studying binary evolution pathways as well as being promising targets for multi-messenger observations. Eccentricity, expected from NS natal kicks, will be a key identifying signature for binaries containing a NS. Eccentric binaries radiate at widely-spaced frequency harmonics that must first be identified as originating from a single source and then analysed coherently. In this work we use a multi-harmonic heterodyning approach to perform Bayesian parameter estimation on a range of simulated eccentric LISA signals. This is used to investigate LISA's ability to measure orbital eccentricity, to demonstrate how eccentricity and periastron precession help to break the mass degeneracy (allowing the individual component masses to be inferred), and to investigate the possibility of source misidentification when the individual harmonics of an eccentric binary masquerade as separate circular binaries. The broader implications of this for the ongoing design of the LISA global fit are also discussed.