Background: Constraining the nuclear matter equation of state (EoS) from neutron star observations is one of the main subjects in nuclear physics today. Most studies are based on the Tolman-Oppenheimer-Volkoff equation, which describes a star in spherical hydrostatic equilibrium in general relativity. In general, however, neutron stars rotate rapidly and the structure of neutron stars can be affected by rotation, especially in millisecond pulsars. To better constrain the nuclear EoS, it is important to describe neutron star structure taking into account the effects of rotation in a fully relativistic manner.

Purpose: In this study, we investigate the internal structure of neutron stars under the influence of rotation. We explore correlations between rotational effects and EoS parameters, based on fully general relativistic calculations of rapidly rotating neutron stars.

Methods: We consider the standard class of neutron stars with cores composed of neutrons, protons, electrons, and muons ($npe\mu$ matter), surrounded by the crust. For the EoS, we employ Skyrme-type energy density functionals for $npe\mu$ matter and the conventional Baym-Pethick-Sutherland (BPS) EoS for the inner and outer crusts. To account for the rotational effects, we employ a method proposed by Komatsu, Eriguchi, and Hachisu (the KEH method), which provides stable solutions for axially symmetric rotating equilibrium configurations.

Results: Using five different Skyrme-type EoS parameter sets, we find that the maximum angular frequency achievable by rotating neutron stars, as calculated via the KEH method, varies depending on the stiffness of the equation of state. We confirm that an increase in the rotating frequency leads to an overall increase in both the mass and radius along the $M\text{−}R$ curve, consistent with earlier studies. By performing calculations for three frequently referenced neutron stars, we further examine how the changes in mass and radius correlate with the nuclear matter properties at saturation density. Our results suggest that the often-quoted 716 Hz rotational constraint may require a more conservative interpretation when accounting for realistic stellar deformation effects.

Conclusions: To place stringent constraints on the nuclear EoS based on observational data, it is sometimes essential to account for the effects of rotation in neutron star models. In particular, the influence of rotation becomes increasingly significant at higher spin frequencies and cannot be neglected in rapidly rotating systems with $\nu \gtrsim 400\mathrm{Hz}$.

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• Equations of state of nuclear matter
• General relativity
• Nuclear astrophysics
• Nuclear density functional theory
• Nuclear matter in neutron stars
• Symmetry energy