Relation between gravitational mass and baryonic mass for non-rotating and rapidly rotating neutron stars

Abstract

With a selected sample of neutron star (NS) equations of state (EOSs) that are consistent with the current observations and have a range of maximum masses, we investigate the relations between NS gravitational mass M<inf>g</inf> and baryonic mass M<inf>b</inf>, and the relations between the maximum NS mass supported through uniform rotation (M<inf>max</inf>) and that of nonrotating NSs (M<inf>TOV</inf>). We find that for an EOS-independent quadratic, universal transformation formula (Mb=Mg+A×Mg2), the best-fit A value is 0.080 for non-rotating NSs, 0.064 for maximally rotating NSs, and 0.073 when NSs with arbitrary rotation are considered. The residual error of the transformation is ∼ 0.1M<inf>⊙</inf> for non-spin or maximum-spin, but is as large as ∼ 0.2M<inf>⊙</inf> for all spins. For different EOSs, we find that the parameter A for non-rotating NSs is proportional to R1.4−1 (where R<inf>1.4</inf> is NS radius for 1.4M<inf>⊙</inf> in units of km). For a particular EOS, if one adopts the best-fit parameters for different spin periods, the residual error of the transformation is smaller, which is of the order of 0.01M<inf>⊙</inf> for the quadratic form and less than 0.01M<inf>⊙</inf> for the cubic form ((Mb=Mg+A1×Mg2+A2×Mg3)). We also find a very tight and general correlation between the normalized mass gain due to spin Δm = (M<inf>max</inf> − M<inf>TOV</inf>)/M<inf>TOV</inf> and the spin period normalized to the Keplerian period P, i.e., log10Δm=(−2.74±0.05)log10P+log10(0.20±0.01), which is independent of EOS models. These empirical relations are helpful to study NS-NS mergers with a long-lived NS merger product using multi-messenger data. The application of our results to GW170817 is discussed.