The anisotropy and magnetic field structure of neutron stars through gravitational wave

TL;DR

This paper addresses how pressure anisotropy and internal magnetic-field structure inside neutron stars affect their gravitational-wave signatures. It develops a RO/TO framework by extending the TOV equations with a magnetic term $\frac{B^2}{8\pi}$ in $\frac{dm}{dr}$ and a phenomenological anisotropy $\Delta$ controlled by $\kappa$, then computes tidal deformabilities via the perturbation equation to yield $\Lambda=\frac{2}{3}k_2\frac{R_{ m NS}^5}{M_{ m NS}^5}$. The study finds that anisotropy and magnetic fields raise the maximum mass and alter $\Lambda$, with RO configurations producing larger shifts and more compact stars than TO configurations; TO effects are weaker. Using four binary mass configurations and the O4 noise curve, the authors estimate SNR thresholds for interior-structure distinguishability, e.g., $\mathrm{SNR}\approx 26$ for RO versus $\mathrm{SNR}\approx 48$ for TO in a $1.2M_\odot$+ $1.2M_\odot$ system, suggesting current detectors could marginally constrain interiors and future detectors will enable robust inferences.

Abstract

We investigate how gravitational wave (GW) observations can probe the internal physics of neutron stars by extending the Tolman-Oppenheimer-Volkoff framework to include pressure anisotropy and internal magnetic fields. Two representative magnetic field configurations, radial orientation dominated (RO) and transverse orientation dominated (TO), are implemented with strength and decay prescriptions. We found that both anisotropy and magnetic fields increase the maximum supported mass and modify the tidal deformability $Λ$, thereby imprinting measurable signatures on GW signals. For the equal mass binary ($1.2M_\odot$-$1.2M_\odot$), anisotropy neutron star with RO magnetic field yield more compact stars and a larger shift in $Λ$, allowing discrimination at signal-to-noise ratios (SNRs) as low as $\sim18$ using the O4 power spectra density. TO fields produce weaker effects and require substantially higher SNRs for detection. In conclusion, we conclude that gravitational waves are capable of probing the internal structure of neutron stars.

Figures (2)

• Figure 1: $M_{\rm NS}-R_{\rm NS}$ curves for different parameter combinations. The solid line represents the solution of TOV eqaution. The dash line and dash dotted line represent the RO magnetic field and TO magnetic field, respectively.
• Figure 2: $M_{\rm NS}-\Lambda$ curves for different parameter combinations. The solid line represents the solution of TOV eqaution. The dash line and dash dotted line represent the RO magnetic field and TO magnetic field, respectively.