Probe and Prejudice: Classification of compact objects and model comparison using EOS knowledge

Nuclear theory and experiments, alongside astrophysical observations, constrain the equation of state (EOS) of supranuclear-dense matter. Conversely, knowledge of the EOS allows an improved interpretation of nuclear or astrophysical data. In this article, we use several established constraints on the EOS and the new NICER measurement of PSR J0437-4715 to comment on the nature of the primary companion in GW230529 and the companion of PSR J0514-4002E. We find that, with a probability of $\gtrsim 84\%$ and $\gtrsim 68\%$, respectively, both objects are black holes. These likelihoods increase to above $95\%$ when one uses GW170817's remnant as an upper limit on the TOV mass. We also demonstrate that the current knowledge of the EOS substantially disfavors high masses and radii for PSR J0030+0451, inferred recently when combining NICER with XMM-Newton background data and using particular hot-spot models. Finally, we also use our obtained EOS knowledge to comment on measurements of the nuclear symmetry energy, finding that the large value predicted by the PREX-II measurement displays some mild tension with other constraints on the EOS.