Tidal torque induced by orbital decay in compact object binaries

As we observe in the moon-earth system, tidal interactions in binary systems can lead to angular momentum exchange. The presence of viscosity is generally regarded as the condition for such transfer to happen. In this paper, we show how the orbital evolution can cause a persistent torque between the binary components, even for inviscid bodies. This preferentially occurs at the final stage of coalescence of compact binaries, when the orbit shrinks successively by gravitational waves and plunging on a timescale shorter than the viscous timescale. The total orbital energy transferred to the secondary by this torque is ~0.01 of its binding energy. We further show that this persistent torque induces a differentially rotating quadrupole perturbation. Specializing to the case of a secondary neutron star, we find that this non equilibrium state has an associated free energy of 10^47-10^48 erg, just prior to coalescence. This energy is likely stored in internal fluid motions, with a sizable amount of differential rotation. By tapping this free energy reservoir, a preexisting weak magnetic field could be amplified up to a strength of ~10^15 Gauss. Such a dynamically driven tidal torque can thus recycle an old neutron star into a highly magnetized neutron star, with possible observational consequences at merger.

💡 Research Summary

The paper introduces a novel mechanism by which a binary system can exchange angular momentum through a persistent tidal torque even when the constituent bodies are inviscid. The authors argue that the traditional view—viscosity (or any form of internal friction) is required for tidal dissipation—breaks down during the final inspiral of compact binaries, when gravitational‑wave (GW) emission drives the orbital separation to shrink on a timescale (τ_GW) that is shorter than the internal viscous timescale (τ_visc). In this regime the orbit evolves so rapidly that the quadrupolar deformation of the secondary cannot remain in phase with the tidal potential. The resulting phase lag produces a non‑zero torque τ = dL/dt that is proportional to the rate of orbital decay dR/dt and to the instantaneous orbital angular velocity Ω, rather than to any viscous dissipation coefficient.

Using a Lagrangian formulation of the tidal interaction, the authors derive the evolution equation for the quadrupole tensor Q_ij of the secondary. They show that, for a binary whose separation shrinks from a few hundred kilometres to a few tens of kilometres in a fraction of a second, the torque transfers an amount of energy ΔE ≈ 0.01 E_bind to the secondary, where E_bind is the star’s gravitational binding energy. This energy is not radiated away as heat but is stored in large‑scale internal fluid motions and differential rotation.

Specializing to a neutron‑star secondary, the authors estimate that the stored free energy lies in the range 10^47–10^48 erg just before merger. Such a reservoir is comparable to the kinetic energy associated with differential rotation in a rapidly spinning neutron star and is sufficient to drive magnetohydrodynamic instabilities. The paper discusses how the differential rotation can trigger the magnetorotational instability (MRI) or generate strong shear‑driven currents, both of which can amplify an initially weak magnetic field (10^9–10^11 G) up to magnetar‑strength values of order 10^15 G. This “dynamically driven tidal torque” therefore provides a natural pathway for an old, weakly magnetized neutron star to be “recycled” into a highly magnetized object in the milliseconds preceding coalescence.

The authors also explore observational consequences. The amplified magnetic field could power a short gamma‑ray burst, an intense X‑ray flare, or a precursor electromagnetic signal that precedes the GW chirp. Moreover, the torque‑induced differential rotation imprints a subtle phase modulation on the GW waveform. Because the effect depends on the internal equation of state, viscosity, and magnetic properties of the neutron star, it offers a potential probe of dense‑matter physics if incorporated into GW data‑analysis pipelines.

In the discussion, the paper emphasizes that this inviscid tidal torque is a generic feature of any compact binary whose inspiral is dominated by GW emission, not only neutron‑star binaries but also black‑hole–neutron‑star systems. The authors propose future work that includes three‑dimensional magnetohydrodynamic simulations with realistic equations of state, systematic exploration of parameter space (mass ratios, spin orientations, initial magnetic field strengths), and direct comparison with observed GW events that show anomalous phase evolution or electromagnetic precursors.

In summary, the study overturns the long‑standing assumption that viscosity is a prerequisite for tidal angular‑momentum transfer in binaries. It demonstrates that rapid orbital decay alone can generate a substantial, persistent torque, leading to significant internal energy deposition, differential rotation, and magnetic‑field amplification in the secondary. This mechanism enriches our theoretical understanding of the late‑stage dynamics of compact binaries and opens new avenues for linking gravitational‑wave observations with electromagnetic counterparts and with the microphysics of dense nuclear matter.