Magneto-acoustic waves in sunspots: first results from a new 3D nonlinear magnetohydrodynamic code

TL;DR

This paper introduces a new 3D nonlinear magnetohydrodynamic code to model wave propagation and mode transformation in sunspots, providing insights into observed wave behaviors and energy transfer mechanisms.

Contribution

The paper presents the first implementation of a 3D nonlinear MHD code specifically designed for simulating wave dynamics in sunspots, including mode transformation processes.

Findings

Acoustic to Alfvén mode conversion is limited and occurs only off the sunspot axis.

Evanescent waves with 5-minute periods remain mostly below the beta=1 level due to cut-off effects.

Higher frequency waves propagate along magnetic field lines, dominating chromospheric power.

Abstract

Waves observed in the photosphere and chromosphere of sunspots show complex dynamics and spatial patterns. The interpretation of high-resolution sunspot wave observations requires modeling of three-dimensional non-linear wave propagation and mode transformation in the sunspot upper layers in realistic spot model atmospheres. Here we present the first results of such modeling. We have developed a 3D non-linear numerical code specially designed to calculate the response of magnetic structures in equilibrium to an arbitrary perturbation. The code solves the 3D nonlinear MHD equations for perturbations; it is stabilized by hyper-diffusivity terms and is fully parallelized. The robustness of the code is demonstrated by a number of standard tests. We analyze several simulations of a sunspot perturbed by pulses of different periods at subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of three and five minutes. We present a detailed description of the three-dimensional mode transformation in a non-trivial sunspot-like magnetic field configuration, including the conversion between fast and slow magneto-acoustic waves and the Alfv\'en wave, by calculation of the wave energy fluxes. Our main findings are the following: (1) the conversion from acoustic to the Alfv\'en mode is only observed if the the driving pulse is located out of the sunspot axis, but this conversion is energetically inefficient; (2) as a consequence of the cut-off effects and refraction of the fast magneto-acoustic mode, the energy of the evanescent waves with periods around 5 minutes remains almost completely below the level beta=1; (3) waves with frequencies above the cut-off propagate field-aligned to the chromosphere and their power becomes dominating over that of evanescent 5-minute oscillations, in agreement with observations.