EUV observations of a multi-thermal coronal loop, taken by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO), which exhibits decay-less kink oscillations are presented. The datacube of the quiet Sun coronal loop was passed through a motion magnification algorithm to accentuate transverse oscillations. Timedistance 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 show the presence of two periods within the loop; P 1 = 10.3 +1.5 −1.7 minutes and P 2 = 7.4 +1.1 −1.3 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 behaviour 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.

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.

Context. Slow magnetoacoustic waves are routinely observed in astrophysical plasma systems such as the solar corona, and are usually seen to damp rapidly. As a slow wave propagates through a plasma, it modifies the equilibrium quantities of density, temperature, and magnetic field. In the corona and other plasma systems, the thermal equilibrium is comprised of a balance between continuous heating and cooling processes, the magnitudes of which vary with density, temperature and magnetic field. Thus the wave may induce a misbalance between these competing processes. Its back reaction on the wave has been shown to lead to dispersion, and amplification or damping, of the wave. Aims. This effect of heating/cooling misbalance has previously been studied in the infinite magnetic field approximation, in a plasma whose thermal equilibrium comprises of optically thin radiative losses and field-aligned thermal conduction, balanced by an (unspecified) heating process. In this work we extend this analysis by considering a non-zero β plasma. The importance of the effect of magnetic field in the rapid damping of slow waves in the solar corona is evaluated, and compared to the effects of thermal conduction. Methods. A linear perturbation under the thin flux tube approximation is considered, and a dispersion relation describing the slow magnetoacoustic modes is found. The dispersion relation's limits of strong non-adiabaticity and weak non-adiabaticity are studied. The characteristic timescales are calculated for plasma systems with a range of typical coronal densities, temperatures and magnetic field strengths. Results. The number of timescales characterising the effect of misbalance is found to remain at two, as with the infinite magnetic field case. In the non-zero β case, these two timescales correspond to the partial derivatives of the combined heating/cooling function with respect to constant gas pressure and with respect to constant magnetic pressure. The predicted damping times of slow waves from thermal misbalance in the solar corona are found to be of the order of 10-100 minutes, coinciding with the wave periods and damping times observed. Moreover the slow wave damping by thermal misbalance is found to be comparable to the damping by field-aligned thermal conduction. The change in damping with plasma-β is complex and depends on the coronal heating function's dependence upon the magnetic field in particular. Nonetheless we show that in the infinite field limit, the wave dynamics is insensitive to the dependence of the heating function on the magnetic field, and this approximation is found to be valid in the corona so long as the magnetic field strength is greater than approximately 10 G for quiescent loops and plumes, and 100 G for hot and dense loops. Conclusions. Thermal misbalance may damp slow magnetoacoustic waves rapidly in much of the corona, and its inclusion in our understanding of slow mode damping may resolve discrepancies between observations and theory relying on compressive viscosity and thermal conduction...

Aims. An observation of a coronal loop standing kink mode is analysed to search for higher harmonics, aiming to reveal the relation between different harmonics’ quality factors. Methods. Observations of a coronal loop were taken by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The loop’s axis was tracked at many spatial positions along the loop to generate time series data. Results. The distribution of spectral power of the oscillatory transverse displacements throughout the loop reveals the presence of two harmonics, a fundamental at a period of ∼8 min and its third harmonic at ∼2.6 min. The node of the third harmonic is seen at approximately a third of the way along the length of the loop, and cross correlations between the oscillatory motion on opposing sides of the node show a change in phase behaviour. The ratio of periods P1/3P3 was found to be ∼0.87, indicating a non-uniform distribution of kink speed through the loop. The quality factor for the fundamental mode of oscillation was measured to be ∼3.4. The quality factor of the third harmonic was measured for each spatial location and, where data was reliable, yielded a value of ∼3.6. For all locations, the quality factors for the two harmonics were found to agree within error as expected from 1d resonant absorption theory. 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.

Context. Transverse oscillations are ubiquitously observed in the solar corona, both in coronal loops and in open magnetic flux tubes. Numerical simulations suggest that their dissipation could heat coronal loops, thus 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 cutoff 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 cutoff of kink waves affects their propagation into the corona and to characterize the variation of the cutoff 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, which starts in the chromosphere and extends into the corona. We drove kink waves at four different frequencies and determined whether they experienced a cutoff. 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 cutoff 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.