Magnetohydrodynamic Wave Modes Research Articles

Sausage, kink, and fluting magnetohydrodynamic wave modes identified in solar magnetic pores by Solar Orbiter/PHI

Solar pores are intense concentrations of magnetic flux that emerge through the solar photosphere. When compared to sunspots, they are much smaller in diameter and can therefore be affected and buffeted by neighbouring granular activity to generate significant magnetohydrodynamic (MHD) wave energy flux within their confines. However, observations of solar pores from ground-based telescope facilities may struggle to capture subtle motions that are synonymous with higher-order MHD wave signatures because of the seeing effects that are produced in the Earth’s atmosphere. Hence, we exploited timely seeing-free and high-quality observations of four small magnetic pores from the High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (PHI) on board the Solar Orbiter spacecraft during its first close perihelion passage in March 2022 (at a distance of 0.5 au from the Sun). Through acquisition of data under stable observing conditions, we were able to measure the area fluctuations and horizontal displacements of the solar pores. Cross correlations between perturbations in intensity, area, line-of-sight velocity, and magnetic fields, coupled with the first-time application of novel proper orthogonal decomposition techniques on the boundary oscillations, provided a comprehensive diagnosis of the embedded MHD waves as sausage and kink modes. Additionally, the previously elusive m = 2 fluting mode is identified in the most magnetically isolated of the four pores. An important consideration lies in how the identified wave modes contribute to the transfer of energy into the upper solar atmosphere. Approximately 56%, 72%, 52%, and 34% of the total wave energy of the four pores we examined is associated with the identified sausage modes and about 23%, 17%, 39%, and 49% with their kink modes, while the first pore also receives a contribution of about 11% linked to the fluting mode. This study reports the first-time identification of concurrent sausage, kink, and fluting MHD wave modes in solar magnetic pores.

Direct imaging of magnetohydrodynamic wave mode conversion near a 3D null point on the sun

Mutual conversion of various kinds of magnetohydrodynamic (MHD) waves can have profound impacts on wave propagation, energy transfer, and heating of the solar chromosphere and corona. Mode conversion occurs when an MHD wave travels through a region where the Alfvén and sound speeds are equal (e.g., a 3D magnetic null point). Here we report the direct extreme ultraviolet (EUV) imaging of mode conversion from a fast-mode to a slow-mode MHD wave near a 3D null point using Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA) observations. An incident fast EUV wavefront associated with an adjacent eruptive flare propagates laterally through a neighboring pseudostreamer. Shortly after the passage of the fast EUV wave through the null point, a slow-mode wave appears near the null that propagates upward along the open structures and simultaneously downward along the separatrix encompassing the fan loops of the pseudostreamer base. These observations suggest the existence of mode conversion near 3D nulls in the solar corona, as predicted by theory and MHD simulations. Moreover, we observe decaying transverse oscillations in both the open and closed structures of the pseudostreamer, along with quasiperiodic type III radio bursts indicative of repetitive episodes of electron acceleration.

Identifying Alfvén wave modes in the solar corona

Context. Oscillations are observed to be pervasive throughout the solar corona, but it remains challenging to positively identify different wave modes. Improving this identification would provide a powerful tool for investigating coronal wave heating and improving seismological inversions. Aims. We aim to establish whether theoretical methods used to identify magnetohydrodynamical wave modes in numerical simulations can be employed on observational datasets. Methods. We applied wave identifiers based on fundamental wave characteristics such as compressibility and direction of propagation to a fully 3D numerical simulation of a transversely oscillating coronal loop. The same wave identifiers were applied to the line-of-sight integrated synthetic emission derived from the numerical simulation data to investigate whether this method could feasibly be useful for observational studies. Results. We established that for particular line(s) of sight and assumptions about the magnetic field, we can correctly identify the properties of the Alfvén mode in synthetic observations of a transversely oscillating loop. Under suitable conditions, there is a strong agreement between the simulation and synthetic emission results. Conclusions. For the first time, we have provided a proof of concept that this theoretically derived classification of magnetohydrodynamic wave modes can be applied to observational data.

The Temporal and Spatial Evolution of Magnetohydrodynamic Wave Modes in Sunspots

Through their lifetime, sunspots undergo a change in their area and shape and, as they decay, they fragment into smaller structures. Here, for the first time we analyze the spatial structure of the magnetohydrodynamic (MHD) slow-body and fast-surface modes in the observed umbrae as their cross-sectional shape changes. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques were used to analyze 3 and 6 hr Solar Dynamics Observatory/Helioseismic and Magnetic Imager time series of Doppler velocities at the photospheric level of approximately circular and elliptically shaped sunspots. Each time series was divided into equal time intervals to evidence the change in the shape of the sunspots. To identify the physical wave modes, the POD/DMD modes were cross-correlated with a slow-body mode model using the exact shape of the umbra, whereas the shape obtained by applying a threshold level of the mean intensity for every time interval. Our results show that the spatial structure of MHD modes are affected, even by apparently small changes in the umbral shape, especially in the case of the higher-order modes. For the data sets used in our study, the optimal time intervals to consider the influence of the change in the shape on the observed MHD modes is 37–60 minutes. The choice of these intervals is crucial to properly quantify the energy contribution of each wave mode to the power spectrum.

Spectropolarimetric investigation of magnetohydrodynamic wave modes in the photosphere: First results from PHI on board Solar Orbiter

Context.In November 2021, Solar Orbiter started its nominal mission phase. The remote-sensing instruments on board the spacecraft acquired scientific data during three observing windows surrounding the perihelion of the first orbit of this phase.Aims.The aim of the analysis is the detection of magnetohydrodynamic (MHD) wave modes in an active region by exploiting the capabilities of spectropolarimetric measurements.Mthods.The High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (SO/PHI) on board the Solar Orbiter acquired a high-cadence data set of an active region. This is studied in the paper. B-ωand phase-difference analyses are applied on line-of-sight velocity and circular polarization maps and other averaged quantities.Results.We find that several MHD modes at different frequencies are excited in all analysed structures. The leading sunspot shows a linear dependence of the phase lag on the angle between the magnetic field and the line of sight of the observer in its penumbra. The magnetic pore exhibits global resonances at several frequencies, which are also excited by different wave modes.Conclusions.The SO/PHI measurements clearly confirm the presence of magnetic and velocity oscillations that are compatible with one or more MHD wave modes in pores and a sunspot. Improvements in modelling are still necessary to interpret the relation between the fluctuations of different diagnostics.

Five-minute oscillations of photospheric and chromospheric swirls

Context. Swirls are ubiquitous in the solar atmosphere. They are thought to be related to the excitation of different modes of magnetohydrodynamic waves and pulses, as well as spicules. However, statistical studies of their collective behaviour are rare. Aims. We aim to study the collective as well as the individual behaviour of photospheric and chromospheric swirls detected by the automated swirl detection algorithm (ASDA) from observations obtained by the Swedish 1-m Solar Telescope and the Hinode satellite. Methods. We performed a detailed analysis of six different parameters of photospheric and chromospheric swirls with the wavelet analysis. Two clusters with periods with significant wavelet power, one from 3 − 8 min and the other from 10 − 14 min, were found. The former coincides with the dominant period of the global p-mode spectrum. The wavelet and fast Fourier transform analysis of example swirls also revealed similar periods. Results. These results suggest that global p-modes might be important in triggering photospheric and thus chromospheric swirls. A novel scenario of global p-modes providing energy and mass fluxes to the upper solar atmosphere via generating swirls, Alfvén pulses, and spicules is then proposed.

CO enhancement by magnetohydrodynamic waves

Context. The formation of molecular gas in interstellar clouds is a slow process, but can be enhanced by gas compression. Magneto-hydrodynamic (MHD) waves can create compressed quasi-periodic linear structures, referred to as striations. Striations are observed at the column densities at which the transition from atomic to molecular gas takes place. Aims. We explore the role of MHD waves in the CO chemistry in regions with striations within molecular clouds. Methods. We targeted a region with striations in the Polaris Flare cloud. We conducted a CO J = 2−1 survey in order to probe the molecular gas properties. We used archival starlight polarization data and dust emission maps in order to probe the magnetic field properties and compare against the CO morphological and kinematic properties. We assessed the interaction of compressible MHD wave modes with CO chemistry by comparing their characteristic timescales. Results. The estimated magnetic field is 38–76 µG. In the CO integrated intensity map, we observe a dominant quasiperiodic intensity structure that tends to be parallel to the magnetic field orientation and has a wavelength of approximately one parsec. The periodicity axis is ~17° off from the mean magnetic field orientation and is also observed in the dust intensity map. The contrast in the CO integrated intensity map is ~2.4 times higher than the contrast of the column density map, indicating that CO formation is enhanced locally. We suggest that a dominant slow magnetosonic mode with an estimated period of 2.1–3.4 Myr and a propagation speed of 0.30–0.45 km s−1 is likely to have enhanced the formation of CO, hence created the observed periodic pattern. We also suggest that within uncertainties, a fast magnetosonic mode with a period of 0.48 Myr and a velocity of 2.0 km s−1 could have played some role in increasing the CO abundance. Conclusions. Quasiperiodic CO structures observed in striation regions may be the imprint of MHD wave modes. The Alfvénic speed sets the dynamical timescales of the compressible MHD modes and determines which wave modes are involved in the CO chemistry.

3D MHD wave propagation near a coronal null point: New wave mode decomposition approach

Context. Ubiquitous vortex flows at the solar surface excite magnetohydrodynamic (MHD) waves that propagate to higher layers of the solar atmosphere. In the solar corona, these waves frequently encounter magnetic null points. The interaction of MHD waves with a coronal magnetic null in realistic 3D setups requires an appropriate wave identification method. Aims. We present a new MHD wave decomposition method that overcomes the limitations of existing wave identification methods. Our method allows for an investigation of the energy fluxes in different MHD modes at different locations of the solar atmosphere as waves generated by vortex flows travel through the solar atmosphere and pass near the magnetic null. Methods. We used the open-source MPI-AMRVAC code to simulate wave dynamics through a coronal null configuration. We applied a rotational wave driver at our bottom photospheric boundary to mimic vortex flows at the solar surface. To identify the wave energy fluxes associated with different MHD wave modes, we employed a wave decomposition method that is able to uniquely distinguish different MHD modes. Our proposed method utilizes the geometry of an individual magnetic field-line in the 3D space to separate the velocity perturbations associated with the three fundamental MHD waves. We compared our method with an existing wave decomposition method that uses magnetic flux surfaces instead. Over the selected flux surfaces, we calculated and analyzed the temporally averaged wave energy fluxes, as well as the acoustic and magnetic energy fluxes. Our wave decomposition method allowed us to estimate the relative strengths of individual MHD wave energy fluxes. Results. Our method for wave identification is consistent with previous flux-surface-based methods and provides the expected results in terms of the wave energy fluxes at various locations of the null configuration. We show that ubiquitous vortex flows excite MHD waves that contribute significantly to the Poynting flux in the solar corona. Alfvén wave energy flux accumulates on the fan surface and fast wave energy flux accumulates near the null point. There is a strong current density buildup at the spine and fan surface. Conclusions. The proposed method has advantages over previously utilized wave decomposition methods, since it may be employed in realistic simulations or magnetic extrapolations, as well as in real solar observations whenever the 3D fieldline shape is known. The essential characteristics of MHD wave propagation near a null – such as wave energy flux accumulation and current buildup at specific locations – translate to the more realistic setup presented here. The enhancement in energy flux associated with magneto-acoustic waves near nulls may have important implications in the formation of jets and impulsive plasma flows.

Magnetohydrodynamic Wave Mode Identification in Circular and Elliptical Sunspot Umbrae: Evidence for High-order Modes

Abstract In this paper, we provide clear direct evidence of multiple concurrent higher-order magnetohydrodynamic (MHD) modes in circular and elliptical sunspots by applying both proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) techniques on solar observational data. These techniques are well documented and validated in the areas of fluid mechanics, hydraulics, and granular flows but are relatively new to the field of solar physics. While POD identifies modes based on orthogonality in space and provides a clear ranking of modes in terms of their contribution to the variance of the signal, DMD resolves modes that are orthogonal in time. The clear presence of the fundamental slow sausage and kink body modes, as well as higher-order slow sausage and kink body modes, have been identified using POD and DMD analysis of the chromospheric Hα line at 6562.808 Å for both the circular and elliptical sunspots. Additionally, for the various slow body modes, evidence for the presence of the fast surface kink mode was found in the circular sunspot. All of the MHD mode patterns were cross-correlated with their theoretically predicted counterparts, and we demonstrated that ellipticity cannot be neglected when interpreting MHD wave modes. The higher-order MHD wave modes are even more sensitive to irregularities in umbral cross-sectional shapes; hence, this must be taken into account for more accurate modeling of the modes in sunspots and pores.

The need for new techniques to identify the high-frequency MHD waves of an oscillating coronal loop

Context. Magnetic arcades in the solar atmosphere, or coronal loops, are common structures known to host magnetohydrodynamic (MHD) waves and oscillations. Of particular interest are the observed properties of transverse loop oscillations, such as their frequency and mode of oscillation, which have received significant attention in recent years because of their seismological capability. Previous studies have relied on standard data analysis techniques, such as a fast Fourier transform (FFT) and wavelet transform (WT), to correctly extract periodicities and identify the MHD modes. However, the ways in which these methods can lead to artefacts requires careful investigation. Aims. We aim to assess whether these two common spectral analysis techniques in coronal seismology can successfully identify high-frequency waves from an oscillating coronal loop. Methods. We examine extreme ultraviolet images of a coronal loop observed by the Atmospheric Imaging Assembly in the 171 Å waveband on board the Solar Dynamics Observatory. We perform a spectral analysis of the loop waveform and compare our observation with a basic simulation. Results. The spectral FFT and WT power of the observed loop waveform is found to reveal a significant signal with frequency ∼2.67 mHz superposed onto the dominant mode of oscillation of the loop (∼1.33 mHz), that is, the second harmonic of the loop. The simulated data show that the second harmonic is completely artificial even though both of these methods identify this mode as a real signal. This artificial harmonic, and several higher modes, are shown to arise owing to the periodic but non-uniform brightness of the loop. We further illustrate that the reconstruction of the ∼2.67 mHz component, particularly in the presence of noise, yields a false perception of oscillatory behaviour that does not otherwise exist. We suggest that additional techniques, such as a forward model of a 3D coronal arcade, are necessary to verify such high-frequency waves. Conclusions. Our findings have significant implications for coronal seismology, as we highlight the dangers of attempting to identify high-frequency MHD wave modes using these standard data analysis techniques.

Symmetric wave modes in coronal flux tubes with magnetically twisted layer

ABSTRACT The properties of axisymmetric magnetohydrodynamic wave modes are studied for the model of coronal magnetic tube, consisting of a central cord with homogeneous axial magnetic field, surrounded by an annulus with twisted magnetic field. This model mimics the coronal loops with radially localized magnetic twist. The derived dispersion relation is solved numerically. A number of limiting cases are examined analytically. The two families of axisymmetric modes are found to exist in the model. The first one includes an infinite number of fast-sausage modes (FSMs), modified by the twist and the second one is a set of modes with frequencies, lying in a narrow band, closed to Alfvén frequency of a twisted layer ωA0. The fundamental FSM (the mode of the lowest radial order) exists as a trapped mode for the entire range of axial wavenumbers. Its phase speed is always below the Alfvén speed of a magnetically twisted layer. This mode has a weak dispersion in the range of long and intermediate wavelengths. The higher radial order FSMs were found to be less sensitive to the presence of the magnetic twist. Both the fundamental FSM in the case of a weak magnetic twist and a set of symmetric modes for arbitrary twist have very similar frequencies, which are nearly equal to ωA0. This property implies that aforementioned wave modes behave like Alfvén torsional modes in the twisted annulus and like the radial modes in the untwisted core and environment, moreover they are strongly coupled. The main results of the study are discussed in the framework of their applications to coronal seismology.

A novel approach to identify resonant MHD wave modes in solar pores and sunspot umbrae: B − ω analysis

The umbral regions of sunspots and pores in the solar photosphere are generally dominated by 3 mHz oscillations, which are due to p-modes penetrating the magnetic region. In these locations, wave power is also significantly reduced with respect to the quiet Sun. However, here we study a pore where not only is the power of the oscillations in the umbra comparable to, or even larger than, that of the quiet Sun, but the main dominant frequency is not 3 mHz as expected, but instead 5 mHz. By combining Doppler velocities and spectropolarimetry and analysing the relationship between magnetic field strength and frequency, the resultant B − ω diagram reveals distinct ridges that are remarkably clear signatures of resonant magneto-hydrodynamic (MHD) oscillations confined within the pore umbra. We demonstrate that these modes, in addition to velocity oscillations, are also accompanied by magnetic oscillations, as predicted from MHD theory. The novel technique of B − ω analysis proposed in this article opens up an exciting new avenue for identifying MHD wave modes in the umbral regions of both pores and sunspots.

Magnetohydrodynamic Wave Modes of Solar Magnetic Flux Tubes with an Elliptical Cross Section

Abstract The purpose of this paper is to study the behavior of magnetohydrodynamic (MHD) wave modes that propagate in compressible magnetic flux tubes with an elliptical cross section embedded in a magnetic environment. The dispersion relation that describes the behavior of MHD wave modes permitted in an elliptical magnetic flux tube is solved numerically. Distortion of the spatial structure of the purely real eigenmodes from the well-known circular flux tube model has been considered. It has been studied under both photospheric and coronal conditions. It has been shown that (i) solutions in the form of even Mathieu functions are more sensitive to the value of eccentricity than solutions with the form of odd Mathieu functions; (ii) if the ellipticity of the cross section of the magnetic flux tube increases, a sausage mode (m = 0) cannot be easily identified; (iii) even solutions that correspond to the fluting mode (m = 3) can be misinterpreted as a kink mode (m = 1) due to their similarities. In contrast to the fluting modes that are polarized along the major axis and strongly depend on the ellipticity of the magnetic flux tube, the kink and sausage surface modes are practically unaffected by ellipticity. Several examples of the spatial structure of the eigenmodes permitted in the pores and sunspots have been visualized. The solutions obtained in the approximation of cylindrical symmetry are in agreement with previous studies.

Proper orthogonal and dynamic mode decomposition of sunspot data.

High-resolution solar observations show the complex structure of the magnetohydrodynamic (MHD) wave motion. We apply the techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) to identify the dominant MHD wave modes in a sunspot using the intensity time series. The POD technique was used to find modes that are spatially orthogonal, whereas the DMD technique identifies temporal orthogonality. Here, we show that the combined POD and DMD approaches can successfully identify both sausage and kink modes in a sunspot umbra with an approximately circular cross-sectional shape. This article is part of the Theo Murphy meeting issue 'High-resolution wave dynamics in the lower solar atmosphere'.

Excitation of elliptical and toroidal Alfvén eigenmodes by 3He-ions of the MeV-energy range in hydrogen-rich JET plasmas

Elliptical (EAE) and toroidal Alfvén eigenmode (TAE) instabilities have been observed in hydrogen-rich JET discharges of the D-(3He)-H ion cyclotron resonance heating (ICRH) scenario, which is characterized by strong absorption of radio frequency waves at very low concentrations of the resonant 3He-ions. In the experiments, core localized TAEs with a frequency fTAE ≈ 280 kHz with mode numbers n= 3, 4, 5 and 6 were detected. Following the phase with TAE excitation, EAE modes at higher frequencies fEAE ≈ 550–580 kHz with mode numbers n = 1, 3, 5 were seen. These high frequency modes indicate that a MeV range population of trapped energetic ions was present in the plasma. The experimental evidence of existence of the MeV-energy 3He-ions able to excite the AEs is provided by neutron and gamma-ray diagnostics as well as fast ion loss measurements. The ICRH modelling code calculations confirm the acceleration of 3He-ions to MeV energies. The magnetohydrodynamic (MHD) analysis results are consistent with the experimental data showing that the MeV 3He ions satisfy to resonant conditions interacting with TAE and EAE modes. This experiment demonstrates the efficient plasma heating mimicking the conditions representative for the ITER plasmas and contribute to the understanding of fast-ion interaction with MHD wave modes.

Thermal instabilities: Fragmentation and field misalignment of filament fine structure

Context. Prominences show a surprising amount of fine structure and it is widely believed that their threads, as seen in Hα observations, provide indirect information concerning magnetic field topology. Both prominence and coronal rain condensations most likely originate from thermal instabilities in the solar corona. It is still not understood how non-linear instability evolution shapes the observed fine structure of prominences. Investigating this requires multidimensional, high-resolution simulations to resolve all emerging substructure in great detail. Aims. We investigate the spontaneous emergence and evolution of fine structure in high-density condensations formed through the process of thermal instability under typical solar coronal conditions. Our study reveals intricate multidimensional processes that occur through in situ condensations in a representative coronal volume in a low plasma beta regime. Methods. We quantified slow wave eigenfunctions used as perturbations and discuss under which conditions the thermal mode is unstable when anisotropic thermal conduction effects are included. We performed 2D and 3D numerical simulations of interacting slow magnetohydrodynamic (MHD) wave modes when all relevant non-adiabatic effects are included. Multiple levels of adaptive mesh refinement achieve a high resolution near regions with high density, thereby resolving any emerging fine structure automatically. Our study employs a local periodic coronal region traversed by damped slow waves inspired by the presence of such waves observed in actual coronal magnetic structures. Results. We show that the interaction of multiple slow MHD wave modes in a regime unstable to the thermal mode leads to thermal instability. This initially forms pancake-like structures almost orthogonal to the local magnetic field, while low-pressure induced inflows of matter generate rebound shocks. This is succeeded by the rapid disruption of these pancake sheets through thin-shell instabilities evolving naturally from minute ram pressure imbalances. This eventually creates high-density blobs accompanied by thread-like features from shear flow effects. The further evolution of the blobs follows the magnetic field lines, such that a dynamical realignment with the background magnetic field appears. However, the emerging thread-like features are not at all field-aligned, implying only a very weak link between fine structure orientation and magnetic field topology. Conclusions. As seen in our synthetic Hα views, threads formed by non-linear thermal instability evolution do not strictly outline magnetic field structure and this finding has far-reaching implications for field topology interpretations based on Hα observations.

Persistent Quasi-periodic Pulsations during a Large X-class Solar Flare

Abstract Solar flares often display pulsating and oscillatory signatures in the emission, known as quasi-periodic pulsations (QPP). QPP are typically identified during the impulsive phase of flares, yet in some cases, their presence is detected late into the decay phase. Here, we report extensive fine structure QPP that are detected throughout the large X8.2 flare from 2017 September 10. Following the analysis of the thermal pulsations observed in the Geostationary Operational Environmental Satellite/X-ray sensor and the 131 Å channel of Solar Dynamics Observatory/Atmospheric Imaging Assembly, we find a pulsation period of ∼65 s during the impulsive phase followed by lower amplitude QPP with a period of ∼150 s in the decay phase, up to three hours after the peak of the flare. We find that during the time of the impulsive QPP, the soft X-ray source observed with the Reuven Ramaty High Energy Solar Spectroscopic Imager rapidly rises at a velocity of approximately 17 km s−1 following the plasmoid/coronal mass ejection eruption. We interpret these QPP in terms of a manifestation of the reconnection dynamics in the eruptive event. During the long-duration decay phase lasting several hours, extended downward contractions of collapsing loops/plasmoids that reach the top of the flare arcade are observed in EUV. We note that the existence of persistent QPP into the decay phase of this flare are most likely related to these features. The QPP during this phase are discussed in terms of magnetohydrodynamic wave modes triggered in the post-flaring loops.

High mode magnetohydrodynamic waves propagation in a twisted rotating jet emerging from a filament eruption

We study the conditions under which high mode magnetohydrodynamic (MHD) waves propagating on a rotating jet emerging from the filament eruption on 2013 April 10--11 can became unstable against the Kelvin--Helmholtz instability (KHI). The evolution of jet indicates the blob like structure at its boundary which could be one of the observable features of the KHI development. We model the jet as a twisted rotating axially moving magnetic flux tube and explore the propagation characteristics of the running MHD modes on the basis of dispersion relations derived in the framework of the ideal magnetohydrodynamics. It is established that unstable MHD waves with wavelengths in the range of $12$--$15$~Mm and instability developing times from $1.5$ to $2.6$~min can be detected at the excitation of high mode MHD waves. The magnitude of the azimuthal mode number $m$ crucially depends upon the twist of the internal magnetic field. It is found that at slightly twisted magnetic flux tube the appropriate azimuthal mode number is $m = 16$ while in the case of a moderately twisted flux tube it is equal to $18$.

Photospheric Observations of Surface and Body Modes in Solar Magnetic Pores

Abstract Over the past number of years, great strides have been made in identifying the various low-order magnetohydrodynamic wave modes observable in a number of magnetic structures found within the solar atmosphere. However, one aspect of these modes that has remained elusive, until now, is their designation as either surface or body modes. This property has significant implications for how these modes transfer energy from the waveguide to the surrounding plasma. Here, for the first time to our knowledge, we present conclusive, direct evidence of these wave characteristics in numerous pores that were observed to support sausage modes. As well as outlining methods to detect these modes in observations, we make estimates of the energies associated with each mode. We find surface modes more frequently in the data, as well as that surface modes appear to carry more energy than those displaying signatures of body modes. We find frequencies in the range of ∼2–12 mHz, with body modes as high as 11 mHz, but we do not find surface modes above 10 mHz. It is expected that the techniques we have applied will help researchers search for surface and body signatures in other modes and in differing structures from those presented here.

Incompressible magnetohydrodynamic modes in the thin magnetically twisted flux tube

Context. Observations have shown that twisted magnetic fields naturally occur, and indeed are omnipresent in the Sun's atmosphere. It is therefore of great theoretical interest in solar atmospheric waves research to investigate the types of magnetohydrodynamic (MHD) wave modes that can propagate along twisted magnetic flux tubes. Aims. Within the framework of ideal MHD, the main aim of this work is to investigate small amplitude incompressible wave modes of twisted magnetic flux tubes with m more or equal 1. The axial magnetic field strength inside and outside the tube will be allowed to vary, to ensure the results will not be restricted to only cold plasma equilibria conditions. Methods. The dispersion equation for these incompressible linear MHD wave modes was derived analytically by implementing the long wavelength approximation. Results. It is shown, in the long wavelength limit, that both the frequency and radial velocity profile of the m = 1 kink mode are completely unaffected by the choice of internal background magnetic twist. However, fluting modes with m more or equal 2 are sensitive to the particular radial profile of magnetic twist chosen. Furthermore, due to background twist, a low frequency cut-off is introduced for fluting modes that is not present for kink modes. From an observational point of view, although magnetic twist does not affect the propagation of long wavelength kink modes, for fluting modes it will either work for or against the propagation, depending on the direction of wave travel relative to the sign of the background twist.