Accuracy and Applicability of the Hartle-Thorne and Komatsu-Eriguchi-Hachisu Methods for Modeling Rotating Neutron Stars

TL;DR

This paper addresses how rotation and nuclear matter properties influence neutron-star structure by comparing the Hartle-Thorne perturbative approach with the fully relativistic KEH method using RMF-based EoSs where the slope of the symmetry energy $L$ is varied. The study demonstrates that rotation increases stellar radii and that the extent of this increase is highly sensitive to $L$, with HT and KEH diverging notably at modest to high spin. It shows that HT remains reasonably accurate only at very low rotation, while at higher spins ($\Omega$ up to $800\,$Hz) the deformation and radius predictions differ by substantial margins, underscoring the necessity of fully GR computations. The results emphasize the pivotal role of $L$ in radial expansion and rotational deformation and suggest that fully GR treatments are indispensable for reliable analyses of rotating neutron-star interiors and stability, with future work extending to additional nuclear matter properties and more complex rotation profiles.

Abstract

Neutron stars, which are composed of extremely dense nuclear matter, serve as natural laboratories to study nuclear interactions beyond the terrestrial experiments. Recent researches have actively explored how the equation of state (EoS) can be constrained by observed neutron star masses and radii, and how nuclear interactions affect their macroscopic properties. Most of these studies, however, rely on the Tolman-Oppenheimer-Volkoff (TOV) equations, which assumed static, spherically symmetric neutron stars. Since neutron stars are rotating objects and thus axisymmetrically deformed, the TOV calculation may be insufficient to capture their realistic structure. In this work, we investigate the influence of nuclear matter properties on the physical quantities of rotating neutron stars using two approaches: the perturbative Hartle-Thorne (HT) method and fully general relativistic Komatsu-Eriguchi-Hachisu (KEH) method. For nuclear EoS parameter sets, we emamine the OMEG series, in which the slope of the symmetry energy $L$ is systematically varied. We find that rotational effects lead to a noticeable increase in the stellar radius, which depends sensitively on values of $L$. Additionally, focusing on the rotational deformation, we show that the results obtained by these two methods deviate each other even for the slowly rotating case such as $Ω=200$ Hz. These results reveal that, for detailed discussions on the internal structure and stability of rotating neutron stars, the fully general relativistic method such as KEH is indispensable.

Figures (4)

• Figure 1: Equations of state calculated under the $\beta$-equilibrium and charge neutrality conditions using OMEG parameter sets. Pressure $P$ is shown as a function of baryon number density $n$. Results are shown for three OMEG parameter sets: OMEG1 (red), OMEG2 (blue), OMEG3 (black)
• Figure 2: Mass-radius relations for neutron stars obtained from the TOV equation using the OMEG+MYN13 EoSs. The red, blue, and black curves correspond to OMEG1, OMEG2, and OMEG3, respectively.
• Figure 3: Mass–radius relations for neutron stars calculated using the HT (dashed lines) and KEH (solid lines) methods at various rotational frequencies (200, 400, 600, and 800 Hz) for three different EoSs: OMEG1 (a), OMEG2 (b), and OMEG3 (c). The black solid line represents the TOV result. Both methods show that the neutron star mass and radius increase with rotational frequency, and the difference between the HT and KEH results becomes significant above 400 Hz, especially for a canonical $1.4 \ M_\odot$ neutron star.
• Figure 4: Angular frequency $(\Omega)$ is shown as a function of the deformation ratio, $R_\text{ratio}\!=\!R_{\text{pol}}/R_{\text{eq}}$, for neutron stars with $M=1.4M_\odot$. Panels (a), (b), and (c) correspond to the OMEG1, OMEG2, and OMEG3 EOSs, respectively. The red and blue curves represent results from the KEH and HT methods, respectively. The inset panel shows an enlarged view of the nearly spherical regime $(R_\text{ratio} \geq0.99 )$, where the two methods yield nearly identical results below 200 Hz.