Magneto-seismology of solar atmospheric loops by means of longitudinal oscillations

There is increasingly strong observational evidence that slow magnetoacoustic modes arise in the solar atmosphere. Solar magneto-seismology is a novel tool to derive otherwise directly un-measurable properties of the solar atmosphere when magnetohydrodynamic (MHD) wave theory is compared to wave observations. Here, MHD wave theory is further developed illustrating how information about the magnetic and density structure along coronal loops can be determined by measuring the frequencies of the slow MHD oscillations. The application to observations of slow magnetoacoustic waves in coronal loops is discused.Comment: 4 pages, 2 figures, to appear in Proceedings of IAU Symp 286, Comparative Magnetic Minima, C. H. Mandrini, ed

MHD wave modes resolved in fine-scale chromospheric magnetic structures

Within the last decade, due to significant improvements in the spatial and temporal resolution of chromospheric data, magnetohydrodynamic (MHD) wave studies in this fascinating region of the Sun's atmosphere have risen to the forefront of solar physics research. In this review we begin by reviewing the challenges and debates that have manifested in relation to MHD wave mode identification in fine-scale chromospheric magnetic structures, including spicules, fibrils and mottles. Next we go on to discuss how the process of accurately identifying MHD wave modes also has a crucial role to play in estimating their wave energy flux. This is of cardinal importance for estimating what the possible contribution of MHD waves is to solar atmospheric heating. Finally, we detail how such advances in chromospheric MHD wave studies have also allowed us, for the first time, to implement cutting-edge magnetoseismological techniques that provide new insight into the sub-resolution plasma structuring of the lower solar atmosphere.Comment: 16 pages, 6 figures, to appear as a chapter in the upcoming AGU/Wiley book "Low-frequency Waves in Space Plasmas

Magneto-seismology: effect of inhomogeneous magnetic field on transversal coronal loop oscillations

The extreme-ultraviolet (EUV) imagers onboard the planned Solar Dynamics Observatory (SDO) and Solar Orbiter (SO) will offer us the best chance yet of using observations of post-flare loop oscillations to probe the fine structure of the corona. Recently developed magnetohydrodynamic (MHD) wave theory has shown that the properties of loop oscillations depend on their plasma fine structure. Up to this point, many studies have concentrated solely on the effect of plasma density stratification on coronal loop oscillations. In this paper we develop MHD wave theory which models the effect of an inhomogeneous magnetic field on coronal loop oscillations. The results have the potential to be used in testing the efficacy of photospheric magnetic field extrapolations and have important implications regarding magneto-seismology of the corona

Longitudinal oscillations in density stratified and expanding solar waveguides

Waves and oscillations can provide vital information about the internal structure of waveguides they propagate in. Here, we analytically investigate the effects of density and magnetic stratification on linear longitudinal magnetohydrodynamic (MHD) waves. The focus of this paper is to study the eigenmodes of these oscillations. It is our specific aim is to understand what happens to these MHD waves generated in flux tubes with non-constant (e.g., expanding or magnetic bottle) cross-sectional area and density variations. The governing equation of the longitudinal mode is derived and solved analytically and numerically. In particular, the limit of the thin flux tube approximation is examined. The general solution describing the slow longitudinal MHD waves in an expanding magnetic flux tube with constant density is found. Longitudinal MHD waves in density stratified loops with constant magnetic field are also analyzed. From analytical solutions, the frequency ratio of the first overtone and fundamental mode is investigated in stratified waveguides. For small expansion, a linear dependence between the frequency ratio and the expansion factor is found. From numerical calculations it was found that the frequency ratio strongly depends on the density profile chosen and, in general, the numerical results are in agreement with the analytical results. The relevance of these results for solar magneto-seismology is discussed.Comment: 10 pages, 5 figures, published in ApJ, uses emulateap

Resonantly Damped Propagating Kink Waves in Longitudinally Stratified Solar Waveguides

It has been shown that resonant absorption is a robust physical mechanism to explain the observed damping of magnetohydrodynamic (MHD) kink waves in the solar atmosphere due to naturally occurring plasma inhomogeneity in the direction transverse to the direction of the magnetic field. Theoretical studies of this damping mechanism were greatly inspired by the first observations of post-flare standing kink modes in coronal loops using the Transition Region And Coronal Explorer (TRACE). More recently, these studies have been extended to explain the attenuation of propagating coronal kink waves observed by the Coronal Multi-Channel Polarimeter (CoMP). In the present study, for the first time we investigate the properties of propagating kink waves in solar waveguides including the effects of both longitudinal and transverse plasma inhomogeneity. Importantly, it is found that the wavelength is only dependent on the longitudinal stratification and the amplitude is simply a product of the two effects. In light of these results the advancement of solar atmospheric magnetoseismology by exploiting high spatial/temporal resolution observations of propagating kink waves in magnetic waveguides to determine the length scales of the plasma inhomogeneity along and transverse to the direction of the magnetic field is discussed.Comment: Accepted for publication in Ap

Selective spatial damping of propagating kink wavesto resonant absorption

There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. In this paper we show that resonant absorption provides a simple explanation to the spatial damping of these waves. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated. The damping length of propagating kink waves due resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies the damping length is exactly inversely proportional to frequency and we denote this as the TGV relation. When moving to high frequencies the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low frequency waves and can efficiently remove high frequency waves from a broad band spectrum of kink waves. It is selective as the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Hence kink wave trains travelling along, e.g., coronal loops, will have a greater proportion of the high frequency components dissipated lower down in the atmosphere. This could have important consequences with respect to the spatial distribution of wave heating in the solar atmospher

Identication of linear slow sausage waves in magnetic pores

The analysis of an 11-hour series of high resolution white light observations of a large pore in the sunspot group NOAA 7519, observed on 5 June 1993 with the Swedish Vacuum Solar Telescope at La Palma on Canary Islands, has been recently described by Dorotovič et al. (2002). Special attention was paid to the evolution of a filamentary region attached to the pore, to horizontal motions around the pore, and to small-scale morphological changes. One of the results, relevant to out work here, was the determination of temporal area evolution of the studied pore where the area itself showed a linear trend of decrease with time at an average rate of −0.23 Mm2h−1 during the entire observing period. Analysing the time series of the are of the pore, there is strong evidence that coupling between the solar interior and magnetic atmosphere can occur at various scales and that the referred decrease of the area may be connected with a decrease of the magnetic field strength according to the magnetic field-to-size relation. Periods of global acoustic, e.g. p-mode, driven waves are usually in the range of 5–10 minutes, and are favourite candidates for the coupling of interior oscillations with atmospheric dynamics. However, by assuming that magneto-acoustic gravity waves may be there too, and may act as drivers, the observed periodicities (frequencies) are expected to be much longer (smaller), falling well within the mMHz domain. In this work we determine typical periods of such range in the area evolution of the pore using wavelet analysis. The resulted periods are in the range of 20–70 minutes, suggesting that periodic elements of the temporal evolution of the area of this studied pore could be linked to, and considered as, observational evidence of linear low-frequency slow sausage (magneto-acoustic gravity) waves in magnetic pores. This would give us further evidence on the coupling of global solar oscillations to the overlaying magnetic atmosphere

Spatial magneto-seismology : effect of density stratification on the first harmonic amplitude profile of transversal coronal loop oscillations

Context. The new generation of extreme-ultraviolet (EUV) imagers onboard missions such as the Solar Dynamics Observatory (SDO)and Solar Orbiter (SO) will provide the most accurate spatial measurements of post-flare coronal loop oscillations yet. The amplitude profiles of these loop oscillations contain important information about plasma fine structure in the corona. Aims. We show that the position of the anti-nodes of the amplitude profile of the first harmonic of the standing fast kink wave of a coronal loop relate to the plasma density stratification of that loop. Methods. The MHD kink transversal waves of coronal loops are modelled both numerically and analytically. The numerical model implements the implicit finite element code pollux. Dispersion relations are derived and solved analytically. The results of the two methods are compared and verified. Results. Density stratification causes the anti-nodes of the first harmonic to shift towards the loop footpoints. The greater the density stratification, the larger the shift. The anti-node shift of the first harmonic of a semi-circular coronal loop with a density scale height H = 50 Mm and loop half length L = 100 Mm is approximately 5.6Mm. Shifts in the Mm range are measureable quantities providing valuable information about the subresolution structure of coronal loops. Conclusions. The measurement of the anti-node shift of the first harmonic of the standing fast kink wave of coronal loops is potentially a new tool in the field of solar magneto-seismology, providing a novel complementary method of probing plasma fine structure in the corona

The generation and damping of propagating MHD kink waves in the solar atmosphere

The source of the non-thermal energy required for the heating of the upper solar atmosphere to temperatures in excess of a million degrees and the acceleration of the solar wind to hundreds of kilometers per second is still unclear. One such mechanism for providing the required energy flux is incompressible torsional Alfven and kink magnetohydrodynamic (MHD) waves, which are magnetically dominated waves supported by the Sun's pervasive and complex magnetic field. In particular, propagating MHD kink waves have recently been observed to be ubiquitous throughout the solar atmosphere, but, until now, critical details of the transport of the kink wave energy throughout the Sun's atmosphere were lacking. Here, the ubiquity of the waves is exploited for statistical studies in the highly dynamic solar chromosphere. This large-scale investigation allows for the determination of the chromospheric kink wave velocity power spectra, a missing link necessary for determining the energy transport between the photosphere and corona. Crucially, the power spectra contain evidence for horizontal photospheric motions being an important mechanism for kink wave generation in the quiescent Sun. In addition, a comparison with measured coronal power spectra is provided for the first time, revealing frequency-dependent transmission profiles, suggesting that there is enhanced damping of kink waves in the lower corona