Large scale coherent magnetohydrodynamic oscillations in a sunspot

Abstract

Although theoretically predicted, the simultaneous excitation of several resonant modes in sunspots has not been observed. Like any harmonic oscillator, a solar magnetic flux tube can support a variety of resonances, which constitute the natural response of the system to external forcing. Apart from a few single low order eigenmodes in small scale magnetic structures, several simultaneous resonant modes were not found in extremely large sunspots. Here we report the detection of the largest-scale coherent oscillations observed in a sunspot, with a spectrum significantly different from the Sun’s global acoustic oscillations, incorporating a superposition of many resonant wave modes. Magnetohydrodynamic numerical modeling agrees with the observations. Our findings not only demonstrate the possible excitation of coherent oscillations over spatial scales as large as 30–40 Mm in extreme magnetic flux regions in the solar atmosphere, but also paves the way for their diagnostic applications in other astrophysical contexts.

Comparison of Exact and Approximate MHD Slow Body Mode Solutions in Photospheric Waveguides

“…Instead, reliable solutions can be obtained by solving a Helmholtz-like differential equation with Dirichlet boundary conditions. This approximation also allows us to more easily determine the eigenvalues of various modes in magnetic waveguides with cross sections of arbitrary shape and further validates the sunspot umbra modeling of Albidah et al (2022) and Stangalini et al (2022), who made the vertical velocity or density/pressure perturbations zero at the umbra/ penumbra boundary to be consistent with observational data (it was observed that the oscillations decayed very rapidly at the boundary region). This also had the added advantage of making the computations of the eigenmodes using the observed irregular cross-sectional shapes more straightforward, since matching the transverse velocity and pressure perturbations for a magnetic waveguide with a complex cross-sectional shape is a nontrivial problem.…”

“…However, these conditions also constitute an obstacle in modeling the MHD modes with realistic cross-sectional shapes, since, mathematically, we do not have arbitrary coordinates to help us in the modeling process. Recent studies by Albidah et al (2022) and Stangalini et al (2022) demonstrated the importance of taking into account the actual cross-sectional shape of sunspot umbrae in giving a correct interpretation of the observed modes by taking the vertical (i.e., longitudinal) velocity or density/ pressure perturbations to be zero at the umbra-penumbra boundary, to be consistent with the observation data.…”

“…Motivated by the findings of Albidah et al (2022) and Stangalini et al (2022) in this paper, we demonstrate that the eigenvalues, and hence eigenfunctions, of slow body modes can be found without solving the full dispersion relation. The paper is structured as follows.…”

The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores

“…Natural variance in I-V is expected at chromospheric heights due to aspects of radiative damping (Severino et al 2013), but not to the extent observed in Figure 12 indicative of a nonunified structuring of wave activity. In larger flux tubes, such as sunspots, certain wave modes have been observed to oscillate in a monolithic fashion radially across the tube, akin to a drum skin (Jess et al 2012a;Stangalini et al 2021Stangalini et al , 2022. However, recent work has revealed that on small scales, sunspots show a "corrugated" magnetic structure, with a range of fibrils permeating across the flux tube (Rouppe van der Voort & de la Cruz Rodríguez 2013; Yurchyshyn et al 2014;Nelson et al 2017).…”

The Temporal and Spatial Evolution of Magnetohydrodynamic Wave Modes in Sunspots

“…Waves observed with high accuracy in various wavelengths make it possible to diagnose plasma parameters, e.g., density, temperature, chemical composition, and heating/cooling functions, and analyze the magnetic field structure and magnitude. Sunspots support a large variety of MHD waves propagating along and across the magnetic field, making them an ideal location for studying MHD waves given their stability, a relatively simple magnetic configuration that can be observed, and long lifetime (Jess et al 2015;Khomenko & Collados 2015;Albidah et al 2021Albidah et al , 2022Stangalini et al 2021Stangalini et al , 2022, to name but a few).…”