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LISA will detect $\sim \! 10^4$ Galactic binaries, the majority being doublewhite dwarfs. However, approximately $\sim \! 1 \textrm{--} 5 \%$ of thesesystems will contain neutron stars which, if they can be correctly identified,will provide new opportunities for studying binary evolution pathways involvingmass reversal and supernovae as well as being promising targets formulti-messenger observations. Eccentricity, expected from neutron star natalkicks, will be a key identifying signature for binaries containing a neutronstar. Eccentric binaries radiate at widely-spaced frequency harmonics that mustfirst be identified as originating from a single source and then analysedcoherently. A multi-harmonic heterodyning approach for this type of dataanalysis is used to perform Bayesian parameter estimation on a range ofsimulated eccentric LISA signals. This is used to: (i) investigate LISA'sability to measure orbital eccentricity and to quantify the minimum detectableeccentricity; (ii) demonstrate how eccentricity and periastron precession helpto break the mass degeneracy allowing the individual component masses to beinferred, potentially confirming the presence of a neutron star; (iii)investigate the possibility of source misidentification when the individualharmonics of an eccentric binary masquerade as separate circular binaries; and(iv) investigate the possibility of source reclassification, where parameterestimation results of multiple circular analyses are combined in postprocessingto quickly infer the parameters of an eccentric source. The broaderimplications of this for the ongoing design of the LISA global fit are alsodiscussed.

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