Nonradial oscillations of stratified neutron stars with solid crusts: Mode characterization and tidal resonances in coalescing binaries

TL;DR

This work addresses how dynamical tides in neutron-star binaries excite nonradial oscillations in stars with a solid crust and compositional stratification, using fully relativistic linear perturbation theory to obtain the quasinormal-mode spectrum and tidal overlaps. By modeling the tidal response as driven harmonic oscillators, it quantifies energy transfer, gravitational-wave phase shifts, and crustal stresses, highlighting that the fundamental f-mode dominates energy deposition while g- and i-modes contribute modestly under typical conditions. A key finding is that stratification eliminates the i-mode and reshapes low-frequency g-modes into mixed gravity–interfacial modes, with the crust effectively permeable to several modes depending on the buoyancy and shear properties; crust breaking can occur even before the strongest resonances, potentially powering electromagnetic precursors. The results have important implications for multimessenger observations, offering a more realistic framework for dynamical tides in NS binaries and guiding future explorations of EOS sensitivity, crustal physics, and nonlinear magnetospheric coupling.

Abstract

Dynamical tides of neutron stars in the late stages of binary inspirals provide a viable probe into dense matter through gravitational waves, and potentially trigger electromagnetic precursors. We model the tidal response as a set of driven harmonic oscillators, where the natural frequencies are given by the quasinormal modes of a nonrotating neutron star. These modes are calculated in general relativity by applying linear perturbation theory to stellar models that include a solid crust and compositional stratification. For the mode spectrum, we find that the canonical interface mode associated with the crust-core boundary vanishes in stratified neutron stars and is replaced by compositional gravity modes with mixed gravity-interfacial character, driven primarily by strong buoyancy in the outer core. We also find that fluid modes such as the core gravity mode and the fundamental mode can penetrate the crust, and we establish a criterion for such penetration. Regarding the tidal interaction, we find that transfer of binding energy to oscillations is dominated by the fundamental mode despite its frequency being too high to resonate with the tidal forcing. In general, we find that lower-frequency modes induce gravitational-wave phase shifts smaller than $\sim 10^{-3},\rm rad$ for the equation of state we consider. We discover that nonresonant fundamental and crustal shear modes can trigger crust breaking already near the first gravity-mode resonance, while gravity-mode resonance concentrates strain at the base of the crust and may marginally crack it. These results suggest that both resonant and nonresonant excitations can overstress the crust and may channel energy into the magnetosphere prior to merger, potentially powering electromagnetic precursors. Our work represents an important step toward realistic modeling of dynamical tides of neutron stars in multimessenger observations.

Figures (21)

• Figure 1: The adiabatic indices $\Gamma_0$ and $\Gamma_1$ as functions of rest-mass density for the TW99 EOS.The vertical dashed lines indicate the neutron drip density $\rho_{\rm nd}$ and the crust-core interface density $\rho_{\rm cc}$, respectively.
• Figure 2: The shear speed $v_{\rm s}$ in the solid crust (normalized by the sound speed $c$) as a function of rest-mass density $\rho$. The vertical dashed lines indicate the neutron drip density $\rho_{\rm nd}$ and the crust-core interface density $\rho_{\rm cc}$, respectively.
• Figure 3: Real parts of the oscillation spectra, computed with and without compositional stratification, for the canonical star ($M = 1.35\,M_\odot$, top panel) and the higher-mass star ($M = 1.8\,M_\odot$, bottom panel). See the text for details and \ref{['tab:model']} for the background parameters.
• Figure 4: Top: Relation between the frequency of the $f$-mode and the mass. Bottom: Normalized radial and tangential eigenfunctions of the $f$-mode for the canonical model with $M=1.35\,M_{\odot}$. The eigenfunctions for the $M = 1.8\,M_{\odot}$ model are also shown as dashed lines. The two vertical dashed lines (from left to right) indicate the crust-core boundaries of the $1.8\,M_{\odot}$ and $1.35\,M_{\odot}$ models, respectively.
• Figure 5: Shear modes $s_1$ and $s_2$ for the canonical model. The format of the figure follows that of \ref{['fig:f_mode']}, except that only the results for the canonical model are shown. The tangential eigenfunctions have been divided by a factor of 10 for better visibility.