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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 Mg and baryonic mass Mb, and the relations between the maximum NS mass supported through uniform rotation (Mmax) and that of nonrotating NSs (MTOV). 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 R1.4 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 (\(({M_b} = {M_g}\; + \,{A_1}\; \times \;M_g^2\; + \,{A_2}\; \times \;M_g^3)\)). We also find a very tight and general correlation between the normalized mass gain due to spin Δm = (MmaxMTOV)/MTOV and the spin period normalized to the Keplerian period \(\mathcal{P}\), i.e., \({\log _{10}}{\rm{\Delta}}m = (- 2.74 \pm 0.05){\log _{10}}{\mathcal P} + {\log _{10}}(0.20 \pm 0.01)\), 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.

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This work was supported by the National Natural Science Foundation of China under Grant Nos. 11722324, 11603003, 11633001, 11690024, and 11873040, the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB23040100 and the Fundamental Research Funds for the Central Universities. A. B. acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement No. 759253 and by the Sonderforschungsbereich SFB 881 “The Milky WaySystem” (Subproject A10) of the German Research Foundation (DFG).

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Correspondence to He Gao.

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arXiv: 1905.03784.

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Gao, H., Ai, SK., Cao, ZJ. et al. Relation between gravitational mass and baryonic mass for non-rotating and rapidly rotating neutron stars. Front. Phys. 15, 24603 (2020).

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  • gravitational waves