Using equation of state constraints to classify low-mass compact binary mergers

Compact objects observed via gravitational waves are classified as black holes or neutron stars primarily based on their inferred mass with respect to stellar evolution expectations. However, astrophysical expectations for the lowest mass range, $\ensuremath{\lesssim}1.2{M}_{\ensuremath{\bigodot}}$, are uncertain. If such low-mass compact objects exist, ground-based gravitational wave detectors may observe them in binary mergers. Lacking astrophysical expectations for classifying such observations, we go beyond the mass and explore the role of tidal effects. We evaluate how combined mass and tidal inference can inform whether each binary component is a black hole or a neutron star based on consistency with the supranuclear-density equation of state. Low-mass neutron stars experience a large tidal deformation; its observational identification (or lack thereof) can therefore aid in determining the nature of the binary components. Using simulated data, we find that the presence of a sub-solar mass neutron star (black hole) can be established with odds $\ensuremath{\sim}100\ensuremath{\mathbin:}1$ when two neutron stars (black holes) merge and emit gravitational waves at signal-to-noise ratio $\ensuremath{\sim}20$. For the same systems, the absence of a black hole (neutron star) can be established with odds $\ensuremath{\sim}10\ensuremath{\mathbin:}1$. For mixed neutron star-black hole binaries, we can establish that the system contains a neutron star with odds $\ensuremath{\gtrsim}5\ensuremath{\mathbin:}1$. Establishing the presence of a black hole in mixed neutron star-black hole binaries is more challenging, except for the case of a $\ensuremath{\lesssim}1{M}_{\ensuremath{\bigodot}}$ black hole with a $\ensuremath{\gtrsim}1{M}_{\ensuremath{\bigodot}}$ neutron star companion. On the other hand, classifying each individual binary component suffers from an inherent labeling ambiguity.