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

Abstract

With a selected sample of neutron star (NS) equation-of-states (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 ($M_{\mathrm{TOV}}$). We find that if one intends to apply an EOS-independent quadratic, universal transformation formula ($M_b=M_g+A\times M_g^2$) to all EOSs, the best fit $A$ value is 0.080 for non-rotating NSs only and 0.073 when different spin periods are considered. The residual error of the transformation is as large as $\sim 0.1M_{\odot }$. 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$M_{\odot }$ in unit 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$M_{\odot }$ for the quadratic form and less than 0.01$M_{\odot }$ 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 $\Delta m\equiv (M_{\max }-M_{\mathrm{TOV}})/M_{\mathrm{TOV}}$ and the spin period normalized to the Keplerian period $\mathcal{P}$, i.e. $\mathrm{lo}{\mathrm{g}}_{10}\Delta m=(-2.74\pm 0.05)\mathrm{lo}{\mathrm{g}}_{10}\mathcal{P}+\mathrm{lo}{\mathrm{g}}_{10}(0.20\pm 0.01)$, which is independent of EOS models. Applications of our results to GW170817 is discussed.

7 pages, 3 figures

References in corpus (1)

• Welcome to the Multi-Messenger Era! Lessons from a Neutron Star Merger and the Landscape Ahead

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