Modulational Instability of Fast Sausage Mode as One of the Possible Mechanisms for Quasiperiodic Pulsations during Solar Flares

Abstract

Abstract Quasiperiodic pulsations (QPPs) are frequently observed in the entire range of the electromagnetic spectrum during solar flares, and there can be many possible mechanisms leading to this phenomenon. In the present work, we demonstrate the possibility of the generation of QPPs by a nonlinear fast sausage mode in a coronal loop. The coronal loop itself is represented by an infinitely long homogenous magnetic flux tube, which in many cases is a good approximation, and the nonlinearity of the fast sausage mode is modeled by the nonlinear Schrödinger equation (NSE) with a cubic nonlinearity. We have shown that the frequency-renormalized plane wave solution, which happens to be an exact solution of the NSE, transforms into a series of quasiperiodic oscillations (QPOs) due to the so-called modulational instability or the Benjamin–Feir instability. Our numerical solutions show that such QPOs evolve at almost every point above a certain height along the magnetic flux tube, which represents the coronal loop. As the fast sausage mode perturbs the plasma density strongly, the density perturbations caused by the QPOs of the nonlinear fast sausage mode correspondingly modulate the radiation throughout the electromagnetic spectrum, resulting in the emergence of the corresponding QPPs. This mechanism should therefore be able to describe some of the observed QPPs.