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 g 2 ), 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 ~0.1 M ⊙ for non-spin or maximum-spin, but is as large as ~0.2 M ⊙ 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 1.4 M ⊙ 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 0.01 M ⊙ for the quadratic form and less than 0.01M⊙ for the cubic form ( M b = M g + A 1 × M g 2 + A 2 × M g 3 ). We also find a very tight and general correlation between the normalized mass gain due to spin Δ m ≡ ( M max ⁡ − M T O V ) / M T O V and the spin period normalized to the Keplerian period P , i.e., log ⁡ 10 Δ m = ( − 2.74 ± 0.05 ) log ⁡ 10 P + log ⁡ 10 ( 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.