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_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\times 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 ~0.1M_⊙ 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 0.01 M_⊙ for the quadratic form and less than 0.01M⊙ for the cubic form (M_b=M_g+A_1\times M_g^2+A_2\times M_g^3). We also find a very tight and general correlation between the normalized mass gain due to spin \mathrm{\Delta }m\equiv (M_{\max }-M_{\mathrm{T}\mathrm{O}\mathrm{V}})/M_{\mathrm{T}\mathrm{O}\mathrm{V}} and the spin period normalized to the Keplerian period \mathcal{P}, i.e., {\log }_{10}\mathrm{\Delta }m=(-2.74\pm 0.05){\log }_{10}\mathcal{P}+{\log }_{10}(0.20\pm 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.

Keywords

gravitational waves

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