Multi-modal MHD oscillations in the solar corona, and their use in coronal seismology

The solar atmosphere is a dynamic, inhomogeneous environment which acts as a natural plasma laboratory for a keen community of observers and researchers at the forefront of modern physics. Colossal plasma non-uniformities on the Sun are seen to host a wide variety of magnetoacoustic oscillatory motions, which may be used as probes into the local plasma conditions using the theory of long wavelength, large scale magnetohydrodynamics (MHD): this process is known as coronal seismology. The focus of this thesis is to contribute to the detailed observation of these waves and their use in coronal seismology, particularly the usefulness of observing multiple harmonics and understanding of dispersion. Fast kink-mode oscillations of coronal loops, observed as rapidly decaying transverse displacements, are a well-understood wave mode used for seismology. The simultaneous detection of multiple harmonics can provide more information, allowing one to match the observed dispersion with that predicted by theory. Extreme ultraviolet observations of a coronal loop hosting a standing kink oscillation are analysed using image processing and time series techniques. The presence of two simultaneous harmonics is revealed, a fundamental mode at a period of ∼ 8 minutes and its third harmonic at ∼ 2.6 minutes. The ratio of periods P1/3P3 was found to be ∼ 0.87, whose departure from unity indicates a non-uniform distribution of kink speed through the loop. For all locations, the ratio of damping time to period for the two harmonics were found to agree within error, validating the widely assumed 1d resonant absorption theory used to explain a kink oscillation’s rapid damping. This is the first time a measurement of the signal quality for a higher harmonic of a kink oscillation has been reported with spatially resolved data. One exciting development in coronal seismology is the recent detection of decay-less oscillations, which are a different regime of fast-kink oscillations omnipresent in coronal loops. The first detection of a coronal loop exhibiting multi-modal decay-less oscillations is presented, in which both the loop’s fundamental mode (P1 = 10.3 +1.5 −1.7 minutes) and its second harmonic (P2 = 7.4 +1.1 −1.3 minutes) are detected. To make this detection possible, the observational data was passed through a novel motion magnification algorithm to accentuate transverse oscillations. An illustration of seismology using the ratio P1/2P2 ∼ 0.7 to estimate the density scale height is presented. The existence of multiple harmonics has implications for understanding the driving and damping mechanisms for decay-less oscillations, and adds credence to their interpretation as standing kink mode oscillations. There is a myriad of MHD oscillation modes, and whilst fast-kink modes are observed as transverse displacements of the plasma non-uniformity, slow modes may be observed as intensity enhancements. Analysis of such propagating slow modes observed in a fan of coronal loops above a sunspot is performed. The instantaneous velocities and periods of these intensity enhancements are measured and compared in different temperature passbands and azimuthal angles. The waves seen in the 171˚A channel (∼ 0.6 MK) appeared slower than when observed co-spatially in the 193˚A (∼ 1.58 MK). This contradicts the expectation that the phase speed is approximately the local sound speed, which varies as the square root of the temperature. This discrepancy is resolved by attributing the difference in apparent velocity to different inclination angles, which are estimated to be 9° ± 3° from the vertical for the waves seen in 193 A, and 19° ± 4° when seen in 171 A. This provides some evidence supporting the theory that coronal loops are formed of several distinct, unresolved strands of different temperature. From the theoretical point of view, the dispersion relation governing slow MHD modes in the presence of a wave-induced misbalance between the plasma heating and cooling mechanisms is developed. The thin flux tube approximation is used to account for finite-β effects, and thermal conduction is also included. The dispersion relation in the limits of weak non-adiabaticity and strong non-adiabaticity with finite-β is identified. It is found that the characteristic timescales of this imbalance (e.g. damping time) may be expressed in terms of the partial derivatives of the combined heating/cooling function with respect to constant gas pressure and constant magnetic pressure. Moreover, these characteristic timescales for the thermal misbalance coincide with typical MHD wave periods for a large range of densities and temperatures typical of the corona. Thus in the general case the dispersion on slow waves by the wave-induced thermal misbalance should not be neglected, and its inclusion may resolve some contradictions that have arisen when attributing the rapid damping of slow modes to thermal conduction or compressive viscosity alone. Instability criteria for the slow mode and entropy (thermal) mode are expressed in terms of a parameterisation of the unknown coronal heating function, under this thin flux tube approximation. Finally, noting that observations of slow modes in the corona do not show over-stability, and that the thermal mode does not appear to be unstable in general (with the exception of coronal rain), a new way of constraining the coronal heating function is presented

Seismological constraints on the solar coronal heating function

Aims. The hot solar corona exists because of the balance between radiative and conductive cooling and some counteracting heating mechanism that remains one of the major puzzles in solar physics. Methods. The coronal thermal equilibrium is perturbed by magnetoacoustic waves, which are abundantly present in the corona, causing a misbalance between the heating and cooling rates. As a consequence of this misbalance, the wave experiences a back-reaction, either losing or gaining energy from the energy supply that heats the plasma, at timescales comparable to the wave period. Results. In particular, the plasma can be subject to wave-induced instability or over-stability, depending on the specific choice of the coronal heating function. In the unstable case, the coronal thermal equilibrium would be violently destroyed, which does not allow for the existence of long-lived plasma structures typical for the corona. Based on this, we constrained the coronal heating function using observations of slow magnetoacoustic waves in various coronal plasma structures

Cut-off of transverse waves through the solar transition region

Context. Transverse oscillations are ubiquitously observed in the solar corona, both in coronal loops and open magnetic flux tubes. Numerical simulations suggest that their dissipation could heat coronal loops, counterbalancing radiative losses. These models rely on a continuous driver at the footpoint of the loops. However, analytical works predict that transverse waves are subject to a cut-off in the transition region. It is thus unclear whether they can reach the corona, and indeed heat coronal loops. Aims. Our aims are to determine how the cut-off of kink waves affects their propagation into the corona, and to characterize the variation of the cut-off frequency with altitude. Methods. Using 3D magnetohydrodynamic simulations, we modelled the propagation of kink waves in a magnetic flux tube, embedded in a realistic atmosphere with thermal conduction, that starts in the chromosphere and extends into the corona. We drove kink waves at four different frequencies, and determined whether they experienced a cut-off. We then calculated the altitude at which the waves were cut-off, and compared it to the prediction of several analytical models. Results. We show that kink waves indeed experience a cut-off in the transition region, and we identified the analytical model that gives the best predictions. In addition, we show that waves with periods shorter than approximately 500 s can still reach the corona by tunnelling through the transition region, with little to no attenuation of their amplitude. This means that such waves can still propagate from the footpoints of loop, and result in heating in the corona.Comment: Accepted for publication in A&A. 8 pages, 7 figure

Detection of the second harmonic of decay-less kink oscillations in the solar corona

EUV observations of a multi-thermal coronal loop, taken by the Atmospheric Imaging Assembly of the Solar Dynamics Observatory, which exhibits decay-less kink oscillations are presented. The data cube of the quiet-Sun coronal loop was passed through a motion magnification algorithm to accentuate transverse oscillations. Time–distance maps are made from multiple slits evenly spaced along the loop axis and oriented orthogonal to the loop axis. Displacements of the intensity peak are tracked to generate time series of the loop displacement. Fourier analysis on the time series shows the presence of two periods within the loop: ${P}_{1}={10.3}_{-1.7}^{+1.5}$ minutes and ${P}_{2}={7.4}_{-1.3}^{+1.1}$ minutes. The longer period component is greatest in amplitude at the apex and remains in phase throughout the loop length. The shorter period component is strongest further down from the apex on both legs and displays an anti-phase behavior between the two loop legs. We interpret these results as the coexistence of the fundamental and second harmonics of the standing kink mode within the loop in the decay-less oscillation regime. An illustration of seismological application using the ratio P 1/2P 2 ~ 0.7 to estimate the density scale height is presented. The existence of multiple harmonics has implications for understanding the driving and damping mechanisms for decay-less oscillations and adds credence to their interpretation as standing kink mode oscillations

Influence of the Lower Atmosphere on Wave Heating and Evaporation in Solar Coronal Loops

We model a coronal loop as a three-dimensional magnetic cylinder in a realistic solar atmosphere that extends from the chromosphere to the corona. Kink oscillations, believed ubiquitous in the solar corona, are launched in the loop. Heating is expected due to the dissipation of wave energy at small structures that develop from the Kelvin-Helmholtz instability induced by kink oscillations. Increases in temperature and internal energy can be observed in the coronal counterpart of the driven loop. With the presence of thermal conduction, chromospheric evaporation can also be seen. Although the volume averaged temperature and density changes seem slight ($\sim4\%$ relative to a non-driven loop), the enthalpy flow from the lower atmosphere redistributes the density and temperature in the vertical direction, thus enhancing the dissipation of wave energy in the corona. The efficient heating in the coronal counterpart of the loop can complement the thermal conductive losses shown in the current model and thus maintain the internal energy in the corona.Comment: Accepted for publication in ApJ

Influence of the Lower Atmosphere on Wave Heating and Evaporation in Solar Coronal Loops

We model a coronal loop as a 3D magnetic cylinder in a realistic solar atmosphere that extends from the chromosphere to the corona. Kink oscillations, believed to be ubiquitous in the solar corona, are launched in the loop. Heating is expected owing to the dissipation of wave energy at small structures that develop from the Kelvin–Helmholtz instability induced by kink oscillations. Increases in temperature and internal energy can be observed in the coronal counterpart of the driven loop. With the presence of thermal conduction, chromospheric evaporation can also be seen. Although the volume-averaged temperature and density changes seem slight (∼4% relative to a nondriven loop), the enthalpy flow from the lower atmosphere redistributes the density and temperature in the vertical direction, thus enhancing the dissipation of wave energy in the corona. The efficient heating in the coronal counterpart of the loop can complement the thermal conductive losses shown in the current model and thus maintain the internal energy in the corona