Nonlinear coupling between magnetar QPOs

TL;DR

This paper investigates the nonlinear interactions of magnetar QPOs, revealing that their intermittent appearance and frequency drifts can be explained by mode coupling, which offers insights into the star's internal magnetic structure.

Contribution

It introduces an analytical model of nonlinear mode coupling in magnetar QPOs, explaining their intermittence and frequency drifts, and linking these features to the star's magnetic field geometry.

Findings

Mode coupling explains QPO intermittence and frequency drifts.

Analytical solutions describe the collective evolution of oscillation triplets.

Insights into internal magnetic field geometry are gained from QPO behavior.

Abstract

The quasi-periodic oscillations (QPOs) observed in the tails of magnetar giant $\gamma$-ray flares have long been interpreted as normal oscillation modes of these stars. However, most studies modelling QPOs have neglected some key features in the analyses of the signals, namely that QPOs appear to be detectable only intermittently and exhibit drifts in their frequencies. These are typical characteristics of nonlinear mode coupling, where, at leading order, the modes couple and evolve collectively as triplets. Using a representative triplet of modes, we solve the system's nonlinear equations of motion analytically and argue that the coupling is likely axial-axial-polar in nature, with the observed intermittence and frequency drifts providing a way to infer details of the magnetar's internal magnetic field geometry.