Identifying galactic binary systems of neutron stars and black holes with LISA

The Laser Interferometer Space Antenna (LISA) will detect ~ 100 galactic binary systems comprised of black holes (BHs) and neutron stars (NSs). Identifying the nature of the constituents of these binaries as BHs or NSs, and distinguishing them from $\sim 10^4$ detected double white dwarfs will be challenging. In the absence of any other information, the inferred values of the component masses can be used to classify the nature of these objects. However, short-period galactic binaries $\sim 10^7 - 10^3$ yr from coalescence produce a quasi-monochromatic signal which carries little information about their masses. We generate synthetic LISA data sets containing gravitational waves (GWs) from galactic binary BHs, binary NSs and BHNSs drawn from an astrophysically realistic population produced through the isolated binary evolution channel. We process the data with an end-to-end Bayesian inference pipeline to explore the accuracy with which the individual component masses can be measured. We find that for $\approx 10\% - 50\%$ of the detected systems LISA will be able to measure the individual component masses by measuring the orbital eccentricity, periapse precession frequency, and GW induced frequency derivative. Typical fractional mass errors are $\approx 1\% - 100\%$ (depending on the specific value of the source parameters), which will enable in many circumstances the classification of the objects as BHs or NSs. For these binaries, LISA will also be able to determine their 3-dimensional position in the Milky Way. The LISA-detected sample of these double compact objects will provide new information about the galactic population of BHs and NSs, the star formation history of the Milky Way and the astrophysical processes leading to the formation of these systems. However, for a significant fraction of the LISA-detected binaries the nature of their constituent objects may remain unclear.