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

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_g and baryonic mass M_b, and the relations between the maximum NS mass supported through uniform rotation (M_max) and that of nonrotating NSs (M_TOV). We find that for an EOS-independent quadratic, universal transformation formula (M_b =M_g +A ×M_g²), 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_⊙ for non-spin or maximum-spin, but is as large as ∼ 0.2M_⊙ for all spins. For different EOSs, we find that the parameter A for non-rotating NSs is proportional to R_1.4^-1 (where R_1.4 is NS radius for 1.4M_⊙ 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_⊙ for the quadratic form and less than 0.01M_⊙ for the cubic form ((M_b =M_g +A₁ ×M_g²+A₂ ×M_g³)). We also find a very tight and general correlation between the normalized mass gain due to spin Δm = (M_max - M_TOV)/M_TOV and the spin period normalized to the Keplerian period P , i.e., log₁₀ Δ m =(-2.74 ±0.05 )log₁₀ P +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.