Nonlinear saturation of gravito-inertial modes excited by tidal resonances in binary neutron stars

¹ Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany
² School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
³ Departament de Física Aplicada, Universitat d’Alacant, Ap. Correus 99, E-03080 Alacant, Spain
⁴ Theoretical Astrophysics, IAAT, University of Tübingen, Tübingen D-72076, Germany

^★ Corresponding author: alexis.reboul-salze@aei.mpg.de

Received: 31 March 2025
Accepted: 27 August 2025

Abstract

Context. During the last seconds of a binary neutron-star merger, the tidal force can excite stellar oscillation modes to large amplitudes. From the perspective of premerger electromagnetic emissions and next-generation gravitational wave (GW) detectors, gravity (g-) modes constitute a propitious class. However, existing estimates for their impact employ linear schemes, which may be inaccurate for large amplitudes, as achieved by tidal resonances. With rotation, inertial modes can be excited as well, and while their nonlinear saturation has been studied, an extension to fully consistent gravito-inertial modes, especially in the neutron-star context, is an open problem.

Aims. We study linear gravito-inertial modes and the nonlinear saturation of these modes and investigate the astrophysical consequences for binary neutron-star mergers, including the possibility of tidally excited dynamo activity.

Methods. A new (non)linear formulation based on the separation of equilibrium and dynamical tides is developed. Implementing this into the 3D pseudo-spectral code MagIC, a suite of nonlinear simulations of tidally excited flows with an entropy and/or composition gradient in a stably stratified Boussinesq spherical-shell are carried out.

Results. The new formulation accurately reproduces results of linear calculations for gravito-inertial modes with a free surface for low frequencies. For a constant-density cavity, we show that the axisymmetric differential rotation induced by nonlinear ₂g and ₁g modes may theoretically be large enough to amplify an ambient magnetic field to ≳10¹⁴ G. In addition, rich nonlinear dynamics are observed in the form of parametric instabilities of the ₁g mode. The stars are also spun-up, which extends the resonance window for any given mode.

Conclusions. This study provides nonlinear numerical support for a recently proposed scenario where, to accommodate the nonthermal precursor flares seen in some short gamma-ray bursts, the magnetic field of a premerger star is amplified by resonant g-modes. It further suggests that g-mode resonances may have a stronger impact on GW signals than previously estimated.