Universal relations between the quasinormal modes of neutron stars and magnetic tidal deformability

TL;DR

This work investigates how the magnetic tidal deformability $\\Sigma_2$ encodes neutron-star interior information through gravitational-wave asteroseismology. The authors solve axial gravitomagnetic perturbations on static neutron-star backgrounds to compute $\\Sigma_2$ across several EOS and establish near-universal relations between $\\Sigma_2$ and the quasinormal-mode spectrum. They derive five fits linking the $f$-mode, $p_1$-mode, and $w_1$-mode frequencies and damping rates to $-\\Sigma_2$ by expressing the mode properties as functions of $x=\\log_{10}(-\\Sigma_2)$, with typical canonical-star accuracy of a few percent. The results complement the well-known $\\Lambda_2$ universality and have practical implications for GW waveform modeling and gravitational-wave asteroseismology, enabling interior constraints even when the EOS is uncertain. The paper also discusses observational prospects and the relevance to GW phase corrections in inspiral due to magnetic tides.

Abstract

Tidal deformabilities are one of the observable quantities characterizing neutron stars, which are strongly associated with the stellar compactness, the ratio of the stellar mass to the radius. In addition to the tidal deformability, the quasinormal modes excited in a neutron star are also an important property for extracting information about the neutron star interior, adopting gravitational wave asteroseismology. In this study, we especially focus on the magnetic tidal deformability, which acts on the gravitational waveform from a neutron star binary merger as a higher-order effect than the electric tidal deformability, and derive the universal relations expressing the quasinormal modes, such as the fundamental ($f$-), 1st pressure ($p_1$-), and 1st spacetime ($w_1$-) modes, as a function of the magnetic tidal deformability. The universal relations derived in this study exhibit accuracy more or less comparable to those of the electric tidal deformability.

Figures (7)

• Figure 1: Mass-radius relations for the neutron star models constructed with the EOS adopted in this study. For reference, we also plot the constraints obtained from the astronomical observations, i.e, PSR J0030+0451; PSR J0740+6620; GW170817; and GRB200415A, and the expected region assuming the fiducial values of nuclear saturation parameters such as $L=60\pm 20$ MeV and $K_0=240\pm 20$ MeV in the right-bottom region (see text for details).
• Figure 2: $-\Sigma_2$ is shown as a function of the stellar compactness, $M/R$, for various EOS, where the thick solid line denotes the fitting formula given by Eq. (\ref{['eq:Sigma_MR']}). The bottom panel shows the absolute values of the relative deviation of $-\Sigma_2$ from the fitting formula.
• Figure 3: $-\Sigma_2$ is shown as a function of $\Lambda_2$ for various EOS, where the thick solid line denotes the fitting formula given by Eq. (\ref{['eq:Sigma_Lambda']}). In the bottom panel, the relative deviation from the fitting formula is also shown.
• Figure 4: The mass-scaled $f$-mode frequencies (top-left panel) and mass-scaled damping rate (top-right panel) are shown as a function of $-\Sigma_2$. In both panels, the solid lines denote the fitting formulae given by Eqs. (\ref{['eq:ffM-Sigma']}) and (\ref{['eq:ftauM-Sigma']}). The bottom panels show the relative deviation from the fitting formulae, i.e., $\Delta=|A^{\rm N}-A^{\rm F}|/A^{\rm N}$ with the values determined numerically, $A^{\rm N}$, and those estimated from the fitting formulae, $A^{\rm F}$.
• Figure 5: Same as in Fig. \ref{['fig:ffM-ftauM']}, but for the $p_1$-mode frequencies with the fitting formula given by Eq. (\ref{['eq:fp1M-Sigma']}).