Inferring flare loop parameters with measurements of standing sausage modes

TL;DR

This paper develops a method to infer physical parameters of solar flare loops from measurements of standing sausage modes, emphasizing the importance of spatially resolved multi-mode observations for accurate parameter estimation.

Contribution

The study derives a generic dispersion relation for sausage modes and demonstrates how multi-mode, spatially resolved measurements enable more precise inference of flare loop parameters.

Findings

Inversion is under-determined with single-mode data.

Spatial resolution improves parameter constraints.

Multi-mode measurements allow for better estimation of loop properties.

Abstract

Standing fast sausage modes in flare loops were suggested to account for a considerable number of quasi-periodic pulsations (QPPs) in the light curves of solar flares. This study continues our investigation into the possibility to invert the measured periods $P$ and damping times $\tau$ of sausage modes to deduce the transverse Alfv\'en time $R/v_{\rm Ai}$, density contrast $\rho_{\rm i}/\rho_{\rm e}$, and the steepness of the density distribution transverse to flare loops. A generic dispersion relation (DR) governing linear sausage modes is derived for pressureless cylinders where density inhomogeneity of arbitrary form takes place within the cylinder. We show that in general the inversion problem is under-determined for QPP events where only a single sausage mode exists, be the measurements spatially resolved or unresolved. While $R/v_{\rm Ai}$ can be inferred to some extent, the range of possible steepness parameters may be too broad to be useful. However, for spatially resolved measurements where an additional mode is present, it is possible to deduce self-consistently $\rho_{\rm i}/\rho_{\rm e}$, the profile steepness, and the internal Alfv\'en speed $v_{\rm Ai}$. We show that at least for a recent QPP event that involves a fundamental kink mode in addition to a sausage one, flare loop parameters are well constrained, even if the specific form of the transverse density distribution remains unknown. We conclude that spatially resolved, multi-mode QPP measurements need to be pursued for inferring flare loop parameters.