WaLSA Team | Image of the Month

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Research Illustrations

Every month, an image (or video) related to the WaLSA Team’s activities is showcased on this page. For greater details, please visit the original source given at the bottom of each image's caption.

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 Sun’s photosphere. When compared to sunspots, they are much smaller in diameter and hence can be impacted 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 synonymous with higher-order MHD wave signatures due to seeing effects produced in the Earth’s atmosphere. Hence, we have 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 have been 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 (POD) techniques on the boundary oscillations, provide 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 towards the transfer of energy into the upper solar atmosphere. We find that the four pores examined have approximately 56%, 72%, 52%, and 34% of their total wave energy associated with the identified sausage modes, and around 23%, 17%, 39%, and 49% to their kink modes, respectively, while the first pore also has around an 11% contribution linked to the fluting mode. This study marks the first-time identification of concurrent sausage, kink, and fluting MHD wave modes in solar magnetic pores.

Figure: Four small pores of interest marked on a Stokes I continuum image (left) and a CP map (right; with a range of [-2.9,5.7]% in the units of Stokes I continuum), corresponding to the middle of the time series. The concurrent presence of MHD wave modes in the small magnetic pores captured by SO/PHI-HRT, identified using the Proper Orthogonal Decomposition (POD) technique, are illustrated.

Copyright: Jafarzadeh, S.; Schiavo, L. A. C.; Fedun, V.; Solanki, S. K.; Stangalini, M.; Calchetti, D.; Verth, G.; Jess, D. B.; Grant, S. D. T.; Ballai, I.; Gafeira, R.; Keys, P. H.; Fleck, B.; Morton, R. J.; Browning, P. K.; Silva, S. A.; Appourchaux, T.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; Kahil, F.; Orozco Suárez, D.; Schou, J.; Strecker, H.; Iniesta, del Toro Iniesta, J. C.; Valori, G.; Volkmer, R.; Woch, J. 2024, Astronomy & Astrophysics, in press (doi: 10.1051/0004-6361/202449685) | ADS

Alfvén Waves in the Lower Solar Atmosphere

The flow of energy through the solar atmosphere and the heating of the Sun’s outer regions are still not understood. Here, we report the detection of oscillatory phenomena associated with a large bright-point group that is 430,000 square kilometers in area and located near the solar disk center. Wavelet analysis reveals full-width half-maximum oscillations with periodicities ranging from 126 to 700 seconds originating above the bright point and significance levels exceeding 99%. These oscillations, 2.6 kilometers per second in amplitude, are coupled with chromospheric line-of-sight Doppler velocities with an average blue shift of 23 kilometers per second. A lack of cospatial intensity oscillations and transversal displacements rules out the presence of magneto-acoustic wave modes. The oscillations are a signature of Alfvén waves produced by a torsional twist of T22 degrees. A phase shift of 180 degrees across the diameter of the bright point suggests that these torsional Alfvén oscillations are induced globally throughout the entire brightening. The energy flux associated with this wave mode is sufficient to heat the solar corona.

Figure: Expanding magnetic flux tube sandwiched between photospheric and chromospheric intensity images obtained with the SST, undergoing a torsional Alfvénic perturbation and generating a wave that propagates longitudinally in the vertical direction. At a given position along the flux tube, the Alfvénic displacements are torsional oscillations that remain perpendicular to the direction of propagation and magnetic field outlining constant magnetic surfaces. The largest FWHM will be produced when the torsional velocity is at its maximum (at zero displacement from the equilibrium position). The figure is not to scale.

Copyright: David B. Jess, Mihalis Mathioudakis, Robert Erdélyi, Philip J. Crockett, Francis P. Keenan, Damian J. Christian 2009, Science, 323, 1582 (doi: 10.1126/science.1168680) | ADS

Magnetohydrodynamic Poynting Flux Vortices in the Solar Atmosphere and Their Role in Concentrating Energy

The nature of energy generation, transport, and effective dissipation responsible for maintaining a hot solar upper atmosphere is still elusive. The Poynting flux is a vital parameter for describing the direction and magnitude of the energy flow, which is mainly used in solar physics for estimating the upward energy generated by photospheric plasma motion. This study presents a pioneering 3D mapping of the magnetic energy transport within a numerically simulated solar atmosphere. By calculating the Finite Time Lyapunov Exponent of the energy velocity, defined as the ratio of the Poynting flux to the magnetic energy density, we precisely identify the sources and destinations of the magnetic energy flow throughout the solar atmosphere. This energy mapping reveals the presence of transport barriers in the lower atmosphere, restricting the amount of magnetic energy from the photosphere reaching the chromosphere and corona. Interacting kinematic and magnetic vortices create energy channels, breaking through these barriers and allowing three times more energy input from photospheric motions to reach the upper atmosphere than before the vortices formed. The vortex system also substantially alters the energy mapping, acting as a source and deposition of energy, leading to localized energy concentration. Furthermore, our results show that the energy is transported following a vortical motion: the Poynting flux vortex. In regions where these vortices coexist, they favor conditions for energy dissipation through ohmic and viscous heating, since they naturally create large gradients in the magnetic and velocity fields over small spatial scales. Hence, the vortex system promotes local plasma heating, leading to temperatures around a million Kelvins.

Note: Flow or kinetic vortices (K-vortex), which are defined as vertical rotating columns of plasma flow (Silva et al. 2020) can excite and act as a waveguide to Alfvén waves, as found in MHD simulations and observations. By interacting with magnetic flux tubes, the vortical motions create enough energy to be transported upward and even more effectively produce Poynting flux than other horizontal motions (Yadav et al. 2021).

Figure: Simulation domain of the Bifrost identity number ch024031_by200bz005 at t = 4200 s. Left (a): The simulated solar surface of the Bifrost numerical domain covers 768x768 pixels or 24x24 Mm². The xy-plane is colored by the vertical component of the velocity field and the green square shows the selected 300x300 pixels region (≈9.4x9.4 Mm²) used in our analysis. Middle (b): Close view of the selected region. The simulated surface is showing the z-component of the magnetic field in grayscale and the plane placed at 7 Mm above the surface is colored by the vertical velocity. The blue lines show the velocity field lines inside the K-vortex. Right (c): Poynting flux, in volume rendering, within the purple cuboid shown in the middle panel at t = 4200 s, when vortices are established throughout the atmosphere. An animation of this figure is available here. It starts at t = 3850 s and ends at 4450 s, with 50 s intervals. The real-time duration of the animation is 6.5 s.

Copyright: Suzana S. A. Silva, Gary Verth, Erico L. Rempel, Istvan Ballai, Shahin Jafarzadeh, and Viktor Fedun 2024, The Astrophysical Journal, 963, 10 (doi: 10.3847/1538-4357/ad1403) | ADS

Alfvén wave dissipation in the solar chromosphere

Magneto-hydrodynamic (MHD) Alfvén waves have been a focus of laboratory plasma physics and astrophysics for over half a century. Their unique nature makes them ideal energy transporters, and while the solar atmosphere provides preferential conditions for their existence, direct detection has proved difficult as a result of their evolving and dynamic observational signatures. The viability of Alfvén waves as a heating mechanism relies upon the efficient dissipation and thermalization of the wave energy, with direct evidence remaining elusive until now. Here we provide the first observational evidence of Alfvén waves heating chromospheric plasma in a sunspot umbra through the formation of shock fronts. The magnetic field configuration of the shock environment, alongside the tangential velocity signatures, distinguish them from conventional umbral flashes. Observed local temperature enhancements of 5% are consistent with the dissipation of mode-converted Alfvén waves driven by upwardly propagating magneto-acoustic oscillations, providing an unprecedented insight into the behaviour of Alfvén waves in the solar atmosphere and beyond.

Figure: A cartoon representation of a sunspot umbral atmosphere demonstrating a variety of shock phenomena. A side- on perspective of a typical sunspot atmosphere, showing magnetic field lines (orange cylinders) anchored into the photospheric umbra (bottom of image) and expanding laterally as a function of atmospheric height. The light blue annuli highlight the lower and upper extents of the mode conversion region for the atmospheric heights of interest. The mode conversion region on the left-hand side portraits a schematic of non-linear Alfvén waves resonantly amplifying magneto-acoustic waves, increasing the shock formation efficiency in this location. The mode conversion region on the righthand side demonstrates the coupling of upwardly propagating magneto-acoustic oscillations (the sinusoidal motions) into Alfvén waves (the elliptical structures), which subsequently develop tangential blue- and red-shifted plasma during the creation of Alfvén shocks. The central portion represents the traditional creation of UFs that result from the steepening of magneto-acoustic waves as they traverse multiple density scale heights in the lower solar atmosphere. Image not to scale.

Copyright: Samuel D. T. Grant, David B. Jess, Teimuraz V. Zaqarashvili, Christian Beck, Hector Socas-Navarro, Markus J. Aschwanden, Peter H. Keys, Damian J. Christian, Scott J. Houston, and Rebecca L. Hewitt 2018, Nature Physics, 14, 480 (doi: 10.1038/s41567-018-0058-3) | ADS

Are There Alfvén Waves in the Solar Atmosphere?

The Sun’s outer coronal layer exists at a temperature of millions of kelvins, much hotter than the solar surface we observe. How this high temperature is maintained and what energy sources are involved continue to puzzle and fascinate solar researchers. Recently, the Hinode spacecraft was launched to observe and measure the plasma properties of the Sun’s outer layers. The data collected by Hinode reveal much about the role of magnetic field interactions and how plasma waves might transport energy to the corona. These results open a new era in high-resolution observation of the Sun.

Figure: (A) Magnetic flux tube showing two snapshots (at positions Z 1and Z2) of Alfvén wave perturbations propagating in the longitudinal z direction along field lines. At a given position, the Alfvénic perturbations are torsional oscillations (i.e., oscillations are in the ϕ direction, perpendicular to the background field). (B) Alfvén waves propagating along a magnetic discontinuity. The Alfvénic perturbations are within the magnetic surface (yz plane) at the discontinuity, perpendicular to the background field (y direction), whereas the waves themselves propagate along the field lines (z direction). Density enhancements are visualized here as a yellow-red thin blob that follows the field lines. Vertical arrows indicate the magnetic field gradient increasing from left to right.

Copyright: R. Erdélyi and V. Fedun 2007, Science, 318, 1572 (doi: 10.1126/science.1153006) | ADS

The Fibre Resolved OpticAl and Near-Ultraviolet Czerny–Turner Imaging Spectropolarimeter (FRANCIS)

The solar physics community is entering a golden era that is ripe with next-generation ground- and space-based facilities, advanced spectral inversion techniques, and realistic simulations that are becoming more computationally streamlined and efficient. With ever-increasing resolving power stemming from the newest observational telescopes, it becomes more challenging to obtain (near-)simultaneous measurements at high spatial, temporal and spectral resolutions, while operating at the diffraction limit of these new facilities. Hence, in recent years there has been increased interest in the capabilities integral field units (IFUs) offer towards obtaining the trifecta of high spatial, temporal and spectral resolutions contemporaneously. To date, IFUs developed for solar physics research have focused on mid-optical and infrared measurements. Here, we present an IFU prototype that has been designed for operation within the near-ultraviolet to mid-optical wavelength range, which enables key spectral lines (e.g., Ca II H/K, Hβ, Sr II, Na I D1/D2, etc.) to be studied, hence providing additional spectral coverage to the instrument suites developed to date. The IFU was constructed as a low-budget proof-of-concept for the upcoming class Indian National Large Solar Telescope and employs circular cross-section fibres to guide light into a Czerny–Turner configuration spectrograph, with the resulting spectra captured using a high quantum efficiency scientific CMOS camera. Mapping of each input fibre allows for the reconstruction of two-dimensional spectral images, with frame rates exceeding 20 s^-1 possible while operating in a non-polarimetric configuration. Initial commissioning of the instrument was performed at the Dunn Solar Telescope, USA, during August 2022. The science verification data presented here highlights the suitability of fibre-fed IFUs operating at near-ultraviolet wavelengths for solar physics research. Importantly, the successful demonstration of this type of instrument paves the way for further technological developments to make a future variant suitable for upcoming ground-based and space-borne telescope facilities.

Some important highlights: The extensive wavelength range provides many isolated spectral lines, formed over a wide range of heights in the solar atmosphere, which enables a multitude of wave propagation studies to be undertaken through the analyses of oscillatory phase lags bridging different spectral features. Furthermore, the rapid cadences associated with FRANCIS data products will enable the development of highly dynamic shock phenomena within the chromosphere to be examined with unprecedented resolution.

Figure: Three-dimensional visualisations of FRANCIS data, alongside complementary high-cadence images obtained by the DST/ROSA instrument. Here, ROSA G-band and Ca II K line-core images are shown using black/white and blue colour tables, respectively. In the left panel, the spatially-resolved FRANCIS spectra, extracted from a window centred on the Ca II K spectral line at 393.366 nm, is displayed with the wavelength axis orientated along the vertical direction, where the Ca II K line core is placed in the same plane as the corresponding Ca II K ROSA image. The right panel depicts spatially-resolved intensities extracted from the FRANCIS spectra at photospheric (Ca II K continuum) and chromospheric (Ca II K line core) heights, which are placed on top of the ROSA G-band and Ca II K line-core images, respectively. Hovering above the ROSA Ca II K image is a sample spectral cube (x,y,z) acquired instantaneously by the FRANCIS instrument, where the spectral morphology of the underlying sunspot is clearly visible through the examination of spatially-resolved absorption lines that are seen along the vertical (wavelength) domain of the depicted sample cube. These types of novel visualisation tools will greatly assist with the identification, extraction, and analyses of dynamic solar features manifesting in FRANCIS data products.

Copyright: Jess, D. B.; Grant, S. D. T.; Bate, W.; Liu, J.; Jafarzadeh, S.; Keys, P. H.; Vieira, L. E. A.; Dal Lago, A.; Guarnieri, F. L.; Christian, D. J.; Gilliam, D.; Banerjee, D. 2023, Solar Physics, 298, 146 (doi: 10.1007/s11207-023-02237-z) | ADS

Sixth meeting of the WaLSA Team
Rosseland Centre for Solar Physics, University of Oslo, Norway, 8-12 January 2024

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.

Figure: Left: First 10 POD modes of the circular sunspot. Every column shows a POD mode, and the rows show how the modes change at each time interval, T_ci, of the data time series. Every time interval contains 50 images and has a duration of 37.5 minutes. Every time interval is shifted by 20 images, i.e., the initial time of T_ci+1 is after the initial time of T_ci by 20 images, which corresponds to 15 minutes.
Right: Theoretical eigenfunctions that correspond to the changing shapes of the observed circular sunspot (see left panel). Every row shows the spatial structure of the models at different times and the changing shape. The columns represent different types of slow-body modes, and they are labeled by M_i, where i = 1,...,10. In particular, M₁ is for fundamental sausage (n = 0), M₂ and M₃ are for fundamental kink (n = 1), M₄ and M₅ are for fluting (n = 2), M₆ is for sausage overtone (n = 0), M₇ and M₈ are for fluting (n = 3), and the last two columns (M₉ and M₁₀) are for kink overtone (n = 1).

Table: The first column represents the theoretical modes, which are labeled according to the right panel of the Figure. The second column shows the time interval of the subdata in which the mode was observed. In the third column, the POD mode numbers are presented as in the left panel of the Figure. The fourth column contains the frequencies (in mHz) that correspond to the peaks in the power spectrum density (PSD) of the time coefficient of the POD mode. The fifth column shows the frequency (in mHz) that corresponds to the DMD mode. Finally, the last column displays the MHD wave mode for which the POD mode and DMD mode agree well. FSBS denotes the fundamental slow-body sausage (n = 0) mode, FSK denotes the fast-surface kink (n = 1) mode, and SBF denotes the slow-body fluting (n = 2) mode. Here, (I) and (II) refer to two different (perpendicular) directions of the wave polarization, and n refers to the number of nodes along the azimuthal direction.

Copyright: Albidah, A. B., Fedun, V., Aldhafeeri, A. A., Ballai, I., Jess, D. B., Brevis, W., Higham, J., Stangalini, M., Silva, S. S. A., MacBride, C. D., Verth, G. 2023, The Astrophysical Journal, 954, 30 (doi: 10.3847/1538-4357/acd7eb) | ADS

Numerical Simulations of Conversion to Alfvén Waves in Sunspots

We study the conversion of fast magnetoacoustic waves to Alfvén waves by means of 2.5D numerical simulations in a sunspot-like magnetic configuration. A fast, essentially acoustic, wave of a given frequency and wave number is generated below the surface and propagates upward through the Alfvén/acoustic equipartition layer where it splits into upgoing slow (acoustic) and fast (magnetic) waves. The fast wave quickly reflects off the steep Alfvén speed gradient, but around and above this reflection height it partially converts to Alfvén waves, depending on the local relative inclinations of the background magnetic field and the wavevector. To measure the efficiency of this conversion to Alfvén waves we calculate acoustic and magnetic energy fluxes. The particular amplitude and phase relations between the magnetic field and velocity oscillations help us to demonstrate that the waves produced are indeed Alfvén waves. We find that the conversion to Alfvén waves is particularly important for strongly inclined fields like those existing in sunspot penumbrae. Equally important is the magnetic field orientation with respect to the vertical plane of wave propagation, which we refer to as "field azimuth". For a field azimuth less than 90° the generated Alfvén waves continue upward, but above 90° downgoing Alfvén waves are preferentially produced. This yields negative Alfvén energy flux for azimuths between 90° and 180°. Alfvén energy fluxes may be comparable to or exceed acoustic fluxes, depending upon geometry, though computational exigencies limit their magnitude in our simulations.

Figure: Schematic diagram illustrating the various mode conversions and reflections as a seismic ray (labeled "Fast Wave (acoustic)") enters the solar atmosphere in a region of strong inclined magnetic field. Field lines (pale blue) are oriented out of the plane and are shown here in projection. Their orientation is given by the inclination angle θ from vertical (0° ≤ θ ＜ 90°) and azimuth angle φ measured clockwise from the wave propagation plane. By symmetry we need only consider 0° ≤ φ ≤ 180°, with φ ＜ 90° in the left panel and φ > 90° in the right panel. First, at the Alfvén-acoustic equipartition level v_A = c_S the ray splits into an essentially acoustic field-guided slow wave (depicted in red) and a fast magnetically dominated wave (black). The slow wave may or may not reflect depending on whether ω ＜ ω_ccos θ. The fast wave goes on to reflect higher in the atmosphere due to the rapidly increasing Alfvén speed with height. On its way downward it again mode converts at the equipartition level. In the scenario depicted on the left (φ ＜ 90°), the upward slow wave is much stronger than the downward one because the fast ray is more closely aligned with the magnetic field (small attack angle) on the upstroke than on the downstroke. This situation is reversed if the magnetic field were inclined in the opposite direction (equivalent to φ > 90°, right panel). In a nebulous region around and above the fast wave reflection point (which may extend far higher than the fuzzy blob used to represent it here), fast-to-Alfvén conversion occurs, in the case on the left predominantly to an upgoing Alfvén wave. For the φ > 90° (right), the downgoing Alfvén wave is favored. The fast-to-Alfvén conversion may only occur where the wave vector and the magnetic field lines are not in the same vertical plane. This diagram extends the description in Cally (2007) by including fast-to-Alfvén conversion.

Copyright: Khomenko, E. and Cally, P. S. 2012, The Astrophysical Journal, 746, 68 (doi: 10.1088/0004-637X/746/1/68) | ADS

On the propagation of gravity waves in the lower solar atmosphere in different magnetic configurations

Gravity waves are generated by turbulent subsurface convection overshooting or penetrating locally into a stably stratified medium. While propagating energy upwards, their characteristic negative phase shift over height is a well-recognized observational signature. Since their first detailed observational detection and estimates of energy content, a number of studies have explored their propagation characteristics and interaction with magnetic fields and other waves modes in the solar atmosphere. Here, we present a study of the atmospheric gravity wave dispersion diagrams utilizing intensity observations that cover photospheric to chromospheric heights over different magnetic configurations of quiet-Sun (magnetic network regions), a plage, and a sunspot as well as velocity observations within the photospheric layer over a quiet and a sunspot region. In order to investigate the propagation characteristics, we construct two-height intensity-intensity and velocity-velocity cross-spectra and study phase and coherence signals in the wavenumber-frequency dispersion diagrams and their association with background magnetic fields. We find signatures of association between magnetic fields and much reduced coherence and phase shifts over height from intensity-intensity and velocity-velocity phase and coherence diagrams, both indicating suppression/scattering of gravity waves by the magnetic fields. Our results are consistent with the earlier numerical simulations, which indicate that gravity waves are suppressed or scattered and reflected back into the lower solar atmosphere in the presence of magnetic fields.

Figure: Top: Plots on the right show the average coherence versus the average (unsigned) longitudinal component of the magnetic fields over kh = 1.0 – 3.0, 2.75 – 4.1 Mm−1, and ν = 1 – 2 mHz, estimated from Ic − Iuv1, and Ic − Iuv2 intensity pairs, over M1, M2, P and S regions, respectively, as indicated on the left panel. Bottom: Plots on the right show the average coherence versus the average (unsigned) longitudinal component of the magnetic fields over ν=1–2 mHz, and kh =1.0–3.0, 2.75–4.1, and 4.1–5.5 Mm−1, estimated from Ic−Iuv1 and Ic−Iuv2 intensity pairs, over Q, R1 and R2 regions, respectively, as indicated on the left panel.

Copyright: Kumar, H., Kumar, B., and Rajaguru, S. P. 2023, Advances in Space Research, 72, 5, 1898 (doi: 10.1016/j.asr.2023.04.054) | ADS

Waves in the lower solar atmosphere: the dawn of next-generation solar telescopes

Waves and oscillations have been observed in the Sun’s atmosphere for over half a century. While such phenomena have readily been observed across the entire electromagnetic spectrum, spanning radio to gamma-ray sources, the underlying role of waves in the supply of energy to the outermost extremities of the Sun's corona has yet to be uncovered. Of particular interest is the lower solar atmosphere, including the photosphere and chromosphere, since these regions harbor the footpoints of powerful magnetic flux bundles that are able to guide oscillatory motion upwards from the solar surface. As a result, many of the current- and next-generation ground-based and space-borne observing facilities are focusing their attention on these tenuous layers of the lower solar atmosphere in an attempt to study, at the highest spatial and temporal scales possible, the mechanisms responsible for the generation, propagation, and ultimate dissipation of energetic wave phenomena. Here, we present a two-fold review that is designed to overview both the wave analyses techniques the solar physics community currently have at their disposal, as well as highlight scientific advancements made over the last decade. Importantly, while many ground-breaking studies will address and answer key problems in solar physics, the cutting-edge nature of their investigations will naturally pose yet more outstanding observational and/or theoretical questions that require subsequent follow-up work. This is not only to be expected, but should be embraced as a reminder of the era of rapid discovery we currently find ourselves in. We will highlight these open questions and suggest ways in which the solar physics community can address these in the years and decades to come.

Figure: Top: Various wave speeds in a flux tube in the lower solar atmosphere, from the hot `NC5' flux tube model put forward by Bruls and Solanki (1993), in combination with the surrounding cool VAL-A atmosphere (Vernazza et al. 1981). Bottom: A dispersion diagram is shown for a representative photospheric magnetic cylinder. It can be seen that there are two distinct horizontal bands with slower and faster phase speeds. The fast band is bounded between [c₀,c_e] and the slow band between [c_T,c₀]. The adjectives "slow" and "fast" here have a quite distinct meaning from the terms slow and fast when referring to the magnetoacoustic wave modes of a homogeneous and unbounded plasma. Adapted from Edwin and Roberts (1983).

Copyright: Jess, D. B., Jafarzadeh, S., Keys, P. H., Stangalini, M., Verth, G., and Grant, S. D. T. 2023, Living Reviews in Solar Physics, 20, 1 (doi: 10.1007/s41116-022-00035-6) | ADS

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

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. The aim of the analysis is the detection of magnetohydrodynamic (MHD) wave modes in an active region by exploiting the capabilities of spectropolarimetric measurements. 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-ω and phase-difference analyses are applied on line-of-sight velocity and circular polarization maps and other averaged quantities. 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. 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.

Figure: Results of the Fourier analysis of one of the pores studied here. Top panel: continuum intensity of the region of interesty. The green contour shows the tracked region at this specific time step. Bottom panel: power spectral densities (PSDs) obtained by averaging the signal in the pore. Black line: Circular Polarization (CP). Red line: Line-of-sight (LoS) velocity field. Yellow line: Continuum intensity. Blue line: Cross section. The PSDs have been normalized to their total power (i.e. frequency integrated).

Copyright: Calchetti, D., Stangalini, M., Jafarzadeh, S. et al. 2023, Astronomy & Astrophysics, 674, A109 (doi: 10.1051/0004-6361/202245826) | ADS

High-frequency Oscillations in Small Magnetic Elements Observed with Sunrise/SuFI

We characterize waves in small magnetic elements and investigate their propagation in the lower solar atmosphere from observations at high spatial and temporal resolution. We use the wavelet transform to analyze oscillations of both horizontal displacement and intensity in magnetic bright points found in the 300 nm and the Ca II H 396.8 nm passbands of the filter imager on board the Sunrise balloon-borne solar observatory. Phase differences between the oscillations at the two atmospheric layers corresponding to the two passbands reveal upward propagating waves at high frequencies (up to 30 mHz). Weak signatures of standing as well as downward propagating waves are also obtained. Both compressible and incompressible (kink) waves are found in the small- scale magnetic features. The two types of waves have different, though overlapping, period distributions. Two independent estimates give a height difference of approximately 450±100 km between the two atmospheric layers sampled by the employed spectral bands. This value, together with the determined short travel times of the transverse and longitudinal waves provide us with phase speeds of 2±2 km/s and 31±2 km/s, respectively. We speculate that these phase speeds may not reflect the true propagation speeds of the waves. Thus, effects such as the refraction of fast longitudinal waves may contribute to an overestimate of the phase speed.

Figure: Top left: Examples of the Sunrise/SuFI images recorded at the 300 nm (left) and the Ca II H (right panel) passbands. The yellow boxes include a sample magnetic bright point studied in the present work.

Top right: Contribution functions for the Sunrise/SuFI 300 nm and Ca II H passbands from the RH radiative transfer code, for two atmospheric models. The vertical dashed lines indicate the corresponding average formation heights.

Bottom: Phase diagram (2D histogram of phase-lag vs. period) of the horizontal-displacement oscillations (a) and the intensity perturbations (b) in small magnetic bright points observed in the passbands of 300 nm and Ca II H. Positive phase-lags represent upward propagation in the solar atmosphere. The dashed curve, surrounded by the shaded area, represents the dispersion relation of acoustic waves for a height difference of 450±100 km between the formation heights of the two passbands. The solid-line contours separate the statistically reliable regions from extreme outliers. The green line identifies zero phase difference.

Copyright: Jafarzadeh, S., Solanki, S. K., Stangalini, M., Steiner, O., Cameron, R. H., Danilovic, S. 2017, The Astrophysical Journal Supplement Series, 229,10 739 (doi: 10.3847/1538-4365/229/1/10) | ADS

Numerical Modeling of Magnetohydrodynamic Wave Propagation and Refraction in Sunspots

We present numerical simulations of magnetoacoustic wave propagation from the photosphere to the low chromosphere in a magnetic sunspot-like structure. A thick flux tube, with dimensions typical of a small sunspot, is perturbed by a vertical or horizontal velocity pulse at the photospheric level. The type of mode generated by the pulse depends on the ratio between the sound speed c_S and the Alfvén speed v_A, on the magnetic field inclination at the location of the driver, and on the shape of the pulse in the horizontal direction. Mode conversion is observed to occur in the region in which both characteristic speeds have similar values. The fast (magnetic) mode in the region c_S < v_A does not reach the chromosphere and reflects back to the photosphere at a somewhat higher layer than the c_S = v_A line. This behavior is due to wave refraction, caused primarily by the vertical and horizontal gradients of the Alfvén speed. The slow (acoustic) mode continues up to the chromosphere along the magnetic field lines with increasing amplitude. We show that this behavior is characteristic for waves in a wide range of periods generated at different distances from the sunspot axis. Since an important part of the energy of the pulse is returned back to the photosphere by the fast mode, the mechanism of energy transport from the photosphere to the chromosphere by waves in sunspots is rather ineffective.

Figure: Top Panels: Variations of the transversal component of the magnetic field (upper-left), pressure (upper-right), and transverse velocity (lower-left) longitudinal velocity (lower-right) at an elapsed time, t=100 s, after the beginning of the simulations for a vertical longitudinal driver with a 10 s (100 mHz) periodicity. In each panel, the horizontal axis represents the radial distance from the sunspot axis. The black inclined lines indicate magnetic field lines. The two red lines indicate contours of constant c_S²/v_A², with the thicker line corresponding to c_S=v_A and the thinner line to c_S² /v_A²=0.1. The black thick line inclined to the left indicates the direction of ∇v_A, starting at the location of the pulse. The ∇v_A line represents the boundary that separates waves refracting to the right from those refracting to the left, which is perpendicular to the contours of constant v_A at every geometric height.

Bottom Panels: Same as Top Panels, but for a horizontal transverse driver with a 10 s (100 mHz) periodicity.

Copyright: E. Khomenko and M. Collados 2006, The Astrophysical Journal, 653, 739 (doi: 10.1086/507760) | ADS

The Influence of the Magnetic Field on Running Penumbral Waves in the Solar Chromosphere

We use images of high spatial and temporal resolution, obtained using both ground- and space-based instrumentation, to investigate the role magnetic field inclination angles play in the propagation characteristics of running penumbral waves in the solar chromosphere. Analysis of a near-circular sunspot, close to the center of the solar disk, reveals a smooth rise in oscillatory period as a function of distance from the umbral barycenter. However, in one directional quadrant, corresponding to the north direction, a pronounced kink in the period–distance diagram is found. Utilizing a combination of the inversion of magnetic Stokes vectors and force-free field extrapolations, we attribute this behavior to the cut-off frequency imposed by the magnetic field geometry in this location. A rapid, localized inclination of the magnetic field lines in the north direction results in a faster increase in the dominant periodicity due to an accelerated reduction in the cut-off frequency. For the first time, we reveal how the spatial distribution of dominant wave periods, obtained with one of the highest resolution solar instruments currently available, directly reflects the magnetic geometry of the underlying sunspot, thus opening up a wealth of possibilities in future magnetohydrodynamic seismology studies. In addition, the intrinsic relationships we find between the underlying magnetic field geometries connecting the photosphere to the chromosphere, and the characteristics of running penumbral waves observed in the upper chromosphere, directly supports the interpretation that running penumbral wave phenomena are the chromospheric signature of upwardly propagating magneto-acoustic waves generated in the photosphere.

Figure: Left Images: Simultaneous images of the blue continuum (photosphere; upper left) and Hɑ core (chromosphere; upper right) acquired at 16:44 UT on 2011 December 10. A white cross marks the barycenter of the sunspot umbra, while a white dashed line in the continuum image displays the extent of the photospheric β = 1 isocontour. The white concentric circles overlaid on the chromospheric image depict a sample annulus used to extract wave characteristics as a function of distance from the umbral barycenter. The dashed white lines isolate the active region into four distinct regions, corresponding to the N, W, S, and E quadrants. The scale is in heliocentric coordinates where 1 arcsec ≈ 725 km. The remaining panels display a series of chromospheric power maps extracted through Fourier analysis of the Hɑ time series, indicating the locations of high oscillatory power (white) with periodicities equal to 180, 300, 420, and 540 s. As the period of the wave becomes longer, it is clear that the location of peak power expands radially away from the umbral barycenter.
Right Panels: Top: azimuthally averaged absolute Fourier power displayed as a function of radial distance from the umbral barycenter. Middle: power spectra from the top panel normalized by the average power for that periodicity within the entire field of view. Thus, the vertical axis represents a factor of how much each period displays power above its spatially and temporally averaged background. Bottom: power spectra normalized to their own respective maxima. The vertical dashed lines represent the radial extent of the umbral and penumbral boundaries, while the graduated color spectrum, displayed at the very top, assigns display colors to a series of increasing periodicities between 45 and 1200 s.

Copyright: D. B. Jess, V. E. Reznikova, T. Van Doorsselaere, P. H. Keys, and D. H. Mackay 2013, The Astrophysical Journal, 779, 168 (doi: 10.1088/0004-637X/779/2/168) | ADS

Theory of solar oscillations in the inertial frequency range:
Amplitudes of equatorial modes from a nonlinear rotating convection simulation

Several types of inertial modes have been detected on the Sun. Properties of these inertial modes have been studied in the linear regime, but have not been studied in nonlinear simulations of solar rotating convection. Comparing the nonlinear simulations, the linear theory, and the solar observations is important to better understand the differences between the models and the real Sun.
Our aim is to detect and characterize the modes present in a nonlinear numerical simulation of solar convection, in particular to understand the amplitudes and lifetimes of the modes. We developed a code with a Yin-Yang grid to carry out fully nonlinear numerical simulations of rotating convection in a spherical shell. The stratification is solar-like up to the top of the computational domain at 0.96 R_☉. The simulations cover a duration of about 15 solar years, which is more than the observational length of the Solar Dynamics Observatory (SDO). Various large-scale modes at low frequencies (comparable to the solar rotation frequency) are extracted from the simulation. Their characteristics are compared to those from the linear model and to the observations.
Among other modes, both the equatorial Rossby modes and the columnar convective modes are seen in the simulation. The columnar convective modes, with north-south symmetric longitudinal velocity v_ϕ, contain most of the large-scale velocity power outside the tangential cylinder and substantially contribute to the heat and angular momentum transport near the equator. Equatorial Rossby modes with no radial nodes (n = 0) are also found; they have the same spatial structures as the linear eigenfunctions. They are stochastically excited by convection and have the amplitudes of a few m/s and mode linewidths of about 20−30 nHz, which are comparable to those observed on the Sun. We also confirm the existence of the “mixed” Rossby modes between the equatorial Rossby modes with one radial node (n = 1) and the columnar convective modes with north-south antisymmetric v_ϕ in our nonlinear simulation, as predicted by the linear eigenmode analysis. We also see the high-latitude mode with m = 1 in our nonlinear simulation, but its amplitude is much weaker than that observed on the Sun.

Figure: Top: Three-dimensional visualization of the columnar convective modes. Left: snapshot of pressure perturbation (nonaxisymmetric component) from the nonlinear simulation shown as a 3D volume rendering. The red-yellow and blue-cyan parts correspond to the regions with positive and negative pressure perturbations, respectively. Right: eigenfunctions of pressure perturbation of the columnar convective modes extracted from the simulation data using singular-value decomposition (SVD). The cases with m = 2 and m = 12 are shown.
Bottom: Reynolds stresses associated with the extracted modes in our simulations summed over m = 1 − 39. Panels a–c: z-velocity ζ_z-symmetric columnar convective modes, the n = 0 equatorial Rossby modes, and the mixed Rossby modes, respectively. Panel d: the total Reynolds stresses (including other modes and small-scale convection) is shown. Upper and lower panel: respectively corresponds to ρ₀⟨v_rv_ϕ⟩ and ρ₀⟨v_ϕv_θ⟩.

Copyright: Yuto Bekki, Robert H. Cameron, and Laurent Gizon 2022, Astronomy & Astrophysics, 666, A135 (doi: 10.1051/0004-6361/202244150) | ADS

The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores

Solar pores are efficient magnetic conduits for propagating magnetohydrodynamic wave energy into the outer regions of the solar atmosphere. Pore observations often contain isolated and/or unconnected structures, preventing the statistical examination of wave activity as a function of the atmospheric height. Here, using high-resolution observations acquired by the Dunn Solar Telescope, we examine photospheric and chromospheric wave signatures from a unique collection of magnetic pores originating from the same decaying sunspot. Wavelet analysis of high-cadence photospheric imaging reveals the ubiquitous presence of slow sausage-mode oscillations, coherent across all photospheric pores through comparisons of intensity and area fluctuations, producing statistically significant in-phase relationships. The universal nature of these waves allowed an investigation of whether the wave activity remained coherent as they propagate. Utilizing bisector Doppler velocity analysis of the Ca II 8542 Å line, alongside comparisons of the modeled spectral response function, we find fine-scale 5 mHz power amplification as the waves propagate into the chromosphere. Phase angles approaching zero degrees between co-spatial line depths spanning different line depths indicate standing sausage modes following reflection against the transition region boundary. Fourier analysis of chromospheric velocities between neighboring pores reveals the annihilation of the wave coherency observed in the photosphere, with examination of the intensity and velocity signals from individual pores indicating they behave as fractured waveguides, rather than monolithic structures. Importantly, this work highlights that wave morphology with atmospheric height is highly complex, with vast differences observed at chromospheric layers, despite equivalent wave modes being introduced into similar pores in the photosphere.

Figure: Left: Temporally and spatially averaged Ca II 8542 Å profile for the full field of view (including pores, small-scale magnetic elements, and quiet-Sun locations). The blue line illustrates the calculated line core for these observations (8542.03 Å), with the red dashed lines highlighting the percentage line depths used to calculate the corresponding bisector velocities.
Right: Energy spectral density of the spatially averaged bisector velocities from one of the pores (pore P3), plotted in a color scheme represented in the legend above, where the unit corresponds to the percentage line depth of the Ca II 8542 Å line. It is clear that the ∼3 mHz photospheric contribution is not present in any of the bisector velocities, indicating that the cutoff height is below that sampled by the 40% line depth. In contrast, the ∼5 mHz chromospheric oscillation is prominent across all 40%–90% line depths, with a shift in the dominant frequency found throughout the line depths, from ≈4.5 mHz (221 s) at 40%, to a peak at ≈5.6 mHz (179 s) for 90%. As such, the derived bisector velocity time series provides observational evidence of the gradual enhancement of three-minute wave power as the waves propagate through to higher chromospheric heights. The ≈5 mHz spectral energy density increases incrementally by a factor of 2 across the range of 40%–90% of the Ca II 8542 Å line depth, and in the case of ≈7 mHz by a factor of 10.

Copyright: S. D. T. Grant, D. B. Jess, M. Stangalini, S. Jafarzadeh, V. Fedun, G. Verth, P. H. Keys, S. P. Rajaguru, H. Uitenbroek, C. D. MacBride, W. Bate, and C. A. Gilchrist-Millar 2022, The Astrophysical Journal, 938, 143 (doi: 10.3847/1538-4357/ac91ca) | ADS

Propagating Spectropolarimetric Disturbances in a Large Sunspot

We present results derived from the analysis of spectropolarimetric measurements of active region AR12546, which represents one of the largest sunspots to have emerged onto the solar surface over the last 20 years. The region was observed with full-Stokes scans of the Fe i 617.3 nm and Ca ii 854.2 nm lines with the Interferometric BIdimensional Spectrometer instrument at the Dunn Solar Telescope over an uncommon, extremely long time interval exceeding three hours. Clear circular polarization (CP) oscillations localized at the umbra–penumbra boundary of the observed region were detected. Furthermore, the multi-height data allowed us to detect the downward propagation of both CP and intensity disturbances at 2.5–3 mHz, which was identified by a phase delay between these two quantities. These results are interpreted as a propagating magnetohydrodynamic surface mode in the observed sunspot.

Figure: Left: Phase lag diagram between the CP signals in the photosphere and chromosphere computed in the annular region highlighted by the dashed lines on the right-most panel.
Middle: Phase lag map of CP fluctuations at 3 mHz (with a bandwidth of 0.7 mHz) between the photosphere and chromosphere.
Right: Coherence map at 3 mHz (with a bandwidth of 0.7 mHz) for the same CP disturbances.

Copyright: M. Stangalini, S. Jafarzadeh, I. Ermolli, R. Erdélyi, D. B. Jess, P. H. Keys, F. Giorgi, M. Murabito, F. Berrilli, and D. Del Moro 2018, The Astrophysical Journal, 869 110 (doi: 10.3847/1538-4357/aaec7b) | ADS

The effect of linear background rotational flows on magnetoacoustic modes of a photospheric magnetic flux tube

Magnetoacoustic waves in solar magnetic flux tubes may be affected by the presence of background rotational flows. Here, we investigate the behaviour of m = 0 and m = ±1 modes of a magnetic flux tube in the presence of linear background rotational flows embedded in a photospheric environment. We show that the inclusion of a background rotational flow is found to have little effect on the obtained eigensolutions for the axisymmetric m = 0 sausage mode. However, solutions for the kink mode are dependent on the location of the flow resonance modified by the slow frequency. A background rotational flow causes the modified flow resonances to possess faster phase speeds in the thin-tube (TT) limit for the case m = 1. This results in solutions for the slow body and slow surface kink modes to follow this trajectory, changing their dispersive behaviour. For a photospheric flux tube in the TT limit, we show that it becomes difficult to distinguish between the slow surface and fast surface kink (m = 1) modes upon comparison of their eigenfunctions. 2D velocity field plots demonstrate how these waves, in the presence of background rotational flows, may appear in observational data. For slow body kink modes, a swirling pattern can be seen in the total pressure perturbation. Furthermore, the tube boundary undergoes a helical motion from the breaking of azimuthal symmetry, where the m = 1 and m = −1 modes become out of phase, suggesting the resulting kink wave is circularly polarized. These results may have implications for the seismology of magnetohydrodynamic waves in solar magnetic vortices.

Figure: The three-dimensional structure of the slow body kink mode for a magnetic flux tube in the presence of a background rotational flow, by visualizing the normalized total pressure perturbation P̂_T. On the left-hand panel, the magnetic flux tube is immersed in the volume rendering of P̂_T. The three cross-sectional cuts (shown as coloured rings at three different heights, z = 0.0, 2.5, and 5.0) correspond to the corresponding right subplots. These three subplots show the LIC (Line Integral Contour) visualization at the same heights. The white rings represent the boundary of the flux tube.

Copyright: S. J. Skirvin, V. Fedun, S. S. A. Silva, T. Van Doorsselaere, N. Claes, M. Goossens, and G. Verth 2023, Monthly Notices of the Royal Astronomical Society, 518, 6355 (doi: 10.1093/mnras/stac3550) | ADS

Phase Shifts Measured in Evanescent Acoustic Waves above the Solar Photosphere and Their Possible Impacts on Local Helioseismology

A set of 464 minutes of high-resolution high-cadence observations were acquired for a region near the Sun’s disk center using the Interferometric BI-dimensional Spectrometer (IBIS) installed at the Dunn Solar Telescope (DST). Ten sets of Dopplergrams are derived from the bisector of the spectral line corresponding approximately to different atmospheric heights, and two sets of Dopplergrams are derived using an MDI-like algorithm and center-of-gravity method. These data are then filtered to keep only acoustic modes, and phase shifts are calculated between Doppler velocities of different atmospheric heights as a function of acoustic frequency. The analysis of the frequency- and height-dependent phase shifts shows that, for evanescent acoustic waves, oscillations in the higher atmosphere lead those in the lower atmosphere by an order of 1 s when their frequencies are below about 3.0 mHz, and lags behind by about 1 s when their frequencies are above 3.0 mHz. Nonnegligible phase shifts are also found in areas with systematic upward or downward flows. All these frequency-dependent phase shifts cannot be explained by vertical flows or convective blueshifts, but are likely due to complicated hydrodynamics and radiative transfer in the nonadiabatic atmosphere in and above the photosphere. These phase shifts in the evanescent waves pose great challenges to the interpretation of some local helioseismic measurements that involve data acquired at different atmospheric heights or in regions with systematic vertical flows. More quantitative characterization of these phase shifts is needed so that they can either be removed during measuring processes or be accounted for in helioseismic inversions.

Figure: Top: (a) A continuum image showing the field of view of the observation with a sunspot at the center of the field. (b) A sample image of Doppler velocities V₄₀, with blue representing blueshift and red representing redshift. The area between the two dashed circles in both panels is used as quiet-Sun region in this study.
Bottom: (a) Power diagram for the cross spectrum between the SDO/HMI-observed line-core intensity and continuum intensity. (b) Phase diagram for the same cross spectrum, with the logarithm of the power overplotted as contours to show relative locations of the power ridges. (c) Phase diagram for the cross spectrum between the IBIS-observed line-core intensity and continuum intensity. The low-ℓarea is left blank in the plot. The color bar on the right shows color scales of relative phases in both panels (b) and (c). The magenta dashed lines in panels (b) and (c) indicate the middle line separating f and p₁ ridges, below which signals are filtered out in the phase-shift analyses.

Copyright: Junwei Zhao, S. P. Rajaguru, and Ruizhu Chen 2022, The Astrophysical Journal, 933, 109 (doi: 10.3847/1538-4357/ac722d) | ADS

Propagation of transverse waves in the solar chromosphere probed at different heights with ALMA sub-bands

The Atacama Large Millimeter/sub-millimeter Array (ALMA) has provided us with an excellent diagnostic tool for studies of the dynamics of the Solar chromosphere, albeit through a single receiver band at one time presently. Each ALMA band consists of four sub-bands that are comprised of several spectral channels. To date, however, the spectral domain has been neglected in favour of ensuring optimal imaging, so that time-series observations have been mostly limited to full-band data products, thereby limiting studies to a single chromospheric layer. Here, we report the first observations of a dynamical event (i.e., wave propagation) for which the ALMA Band 3 data (centred at 3 mm; 100 GHz) is split into a lower and an upper sideband. In principle, this approach is aimed at mapping slightly different layers in the Solar atmosphere. The side-band data were reduced together with the Solar ALMA Pipeline (SoAP), resulting in time series of brightness-temperature maps for each side-band. Through a phase analysis of a magnetically quiet region, where purely acoustic waves are expected to dominate, the average height difference between the two side-bands is estimated as 73±16 km. Furthermore, we examined the propagation of transverse waves in small-scale bright structures by means of wavelet phase analysis between oscillations at the two atmospheric heights. We find 6% of the waves to be standing, while 54% and 46% of the remaining waves are propagating upwards and downwards, respectively, with absolute propagating speeds on the order of ≈96 km/s, resulting in a mean energy flux of 3800 W/m².

Figure: Top: Same time frame for ALMA lower sideband LSB (left) and upper sideband USB (middle), as well as the absolute difference between the two sidebands (right). The white box depicts a relatively quiet region of the field of view and the blue crosses mark the location of five bright features analysed in this study.
Bottom Left: Phase diagram as a 2D histogram of phase angle vs. period of the horizontal velocity oscillations in the five small bright features observed simultaneously in the LSB and the USB. Positive and negative phase angles represent upward and downward propagation in the solar chromosphere, respectively.
Bottom Right: Histogram of phase velocities for the transverse waves present in the five analysed features, with a bin width of 10 km/s.

Copyright: J. C. Guevara Gómez, S. Jafarzadeh, S. Wedemeyer, and M. Szydlarski 2022, Astronomy & Astrophysics, 665, L2 (doi: 10.1051/0004-6361/202244387) | ADS

Polarized Kink Waves in Magnetic Elements: Evidence for Chromospheric Helical Waves

In recent years, new high spatial resolution observations of the Sun's atmosphere have revealed the presence of a plethora of small-scale magnetic elements (SSME) down to the resolution limit of the current cohort of solar telescopes (∼100–120 km on the solar photosphere). These small magnetic field concentrations, due to the granular buffeting, can support and guide several magnetohydrodynamic wave modes that would eventually contribute to the energy budget of the upper layers of the atmosphere. In this work, exploiting the high spatial and temporal resolution chromospheric data acquired with the Swedish 1-m Solar Telescope, and applying the empirical mode decomposition technique to the tracking of the solar magnetic features, we analyze the perturbations of the horizontal velocity vector of a set of chromospheric magnetic elements. We find observational evidence that suggests a phase relation between the two components of the velocity vector itself, resulting in its helical motion.

Figure: Left: Cartoon of the typical displacement of a SSME as measured in the solar chromosphere. A low-frequency helical displacement is superimposed on a high-frequency kink-like oscillation (red line).
Top Right: Periodogram of the two components of horizontal velocity (v_x: red line, v_y: dashed blue line). In the same plot, we also show with the coherence spectrum between these two components, smoothed with an averaging window 3 points wide (red circles).
Bottom Right: Velocity vector (orientation and magnitude) as a function of time.

Copyright: M. Stangalini, F. Giannattasio, R. Erdélyi, S. Jafarzadeh, G. Consolini, S. Criscuoli, I. Ermolli, S. L. Guglielmino, and F. Zuccarello 2017, The Astrophysical Journal, 840, 19 (doi: 10.3847/1538-4357/aa6c5e) | ADS

Photospheric Observations of Surface and Body Modes in Solar Magnetic Pores

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.

Figure: Panel a: Simplified representation of magnetic flux tubes, with the arrows at the top indicating the magnetic field, B. Plasma parameters (e.g., magnetic field, density) of the internal and external plasma differ. Magnetic flux tubes that support the MHD sausage mode are subject to a periodic variation in pressure and area (with these oscillations depicted by the arrows at the bottom). The surface plots (upper images) demonstrate the spatial structure of the pressure perturbation amplitude, which can have two distinct distributions. The amplitude of the body mode (left) is maximal at the central, inner part of the flux tube, with the power decaying close to the boundary. On the other hand, surface modes (right) are maximal at the tube boundary defined by the sharp changes in equilibrium quantities modeled as a discontinuity. The two-dimensional projection of the power is also demonstrated by the colored disks and can be compared to the observed distributions.
Panel b: An example of a body mode in an elliptical pore. Upper left image: two-dimensional power map for the pore filtered at a central frequency of 11.1 mHz. Lower left image: a G-band intensity image of the pore. Right plot: one-dimensional power plot across the pore, along the blue line shown on the right.
Panel c: A similar example for a surface mode. Left: a G-band intensity image of the pore. Right plot: one-dimensional power plot (along the blue line shown on the right), filtered at a central frequency of 2.2 mHz.
Red dashed lines in the one-dimensional power plots indicate the pore boundary in both instances. The body mode is characterized by a central peak decaying to the pore boundary, while the surface mode is characterized by peaks in power at the pore boundary decaying to zero in the center of the pore.

Copyright: Peter H. Keys, Richard J. Morton, David B. Jess, Gary Verth, Samuel D. T. Grant, Mihalis Mathioudakis, Duncan H. Mackay, John G. Doyle, Damian J. Christian, Francis P. Keenan, and Robertus Erdélyi 2018, The Astrophysical Journal, 857, 28 (doi: 10.3847/1538-4357/aab432) | ADS

Alfvénic Perturbations in a Sunspot Chromosphere Linked to Fractionated Plasma in the Corona

In this study, we investigate the spatial distribution of highly varying plasma composition around one of the largest sunspots of solar cycle 24. Observations of the photosphere, chromosphere, and corona are brought together with magnetic field modeling of the sunspot in order to probe the conditions that regulate the degree of plasma fractionation within loop populations of differing connectivities. We find that, in the coronal magnetic field above the sunspot umbra, the plasma has photospheric composition. Coronal loops rooted in the penumbra contain fractionated plasma, with the highest levels observed in the loops that connect within the active region. Tracing field lines from regions of fractionated plasma in the corona to locations of Alfvénic fluctuations detected in the chromosphere shows that they are magnetically linked. These results indicate a connection between sunspot chromospheric activity and observable changes in coronal plasma composition.

Figure: Upper panel: SDO/AIA 193 Å (a) and 171 Å (b) images at the time of the EIS observation at 07:24 UT on 2016 May 20. The images are overlaid with boxes showing the larger Hinode/EIS and smaller IBIS FOVs.
Lower panel: (a) Hinode/EIS Si X/S X FIP bias map at 07:24 UT on 2016 May 20. Contours: (i) SDO/HMI continuum umbra and penumbra boundaries (thin black lines), (ii) SDO/HMI LoS magnetogram ±500 G (thick green/black lines = positive/negative polarity), (iii) location of Alfvénic waves from IBIS Ca II observation (blue dots), and (iv) IBIS FOV (white dashed box). (b) Selected high FIP bias field lines connecting high FIP bias in the corona to the umbra–penumbra boundary (orange), starting from values of FIP bias >2.7. Height of the FIP bias map is z=3.6 CEA-deg and the value of the linear force-free parameter α=−0.2 CEA-deg⁻¹ (Conversion factor is 1 CEA-deg ≃ 12.17 Mm). Green contour represents the 500 G isocontour of the vertical magnetic field in the SHARP data.

Copyright: Deborah Baker, Marco Stangalini, Gherardo Valori, David H. Brooks, Andy S. H. To, Lidia van Driel-Gesztelyi, Pascal Démoulin, David Stansby, David B. Jess, and Shahin Jafarzadeh 2021, The Astrophysical Journal, 907, 16 (doi: 10.3847/1538-4357/abcafd) | ADS

Wave Damping Observed in Upwardly Propagating Sausage-mode Oscillations Contained within a Magnetic Pore

We present observational evidence of compressible MHD wave modes propagating from the solar photosphere through to the base of the transition region in a solar magnetic pore. High cadence images were obtained simultaneously across four wavelength bands using the Dunn Solar Telescope. Employing Fourier and wavelet techniques, sausage-mode oscillations displaying significant power were detected in both intensity and area fluctuations. The intensity and area fluctuations exhibit a range of periods from 181 to 412 s, with an average period ∼290 s, consistent with the global p-mode spectrum. Intensity and area oscillations present in adjacent bandpasses were found to be out of phase with one another, displaying phase angles of 6.12, 5.82, and 15.97 degrees between the 417 nm continuum–G-band, G-band–Na I D1, and Na I D1–Ca II K heights, respectively, reiterating the presence of upwardly propagating sausage-mode waves. A phase relationship of ∼0 degrees between same-bandpass emission and area perturbations of the pore best categorizes the waves as belonging to the "slow" regime of a dispersion diagram. Theoretical calculations reveal that the waves are surface modes, with initial photospheric energies in excess of 35,000 Wm^-2. The wave energetics indicate a substantial decrease in energy with atmospheric height, confirming that magnetic pores are able to transport waves that exhibit appreciable energy damping, which may release considerable energy into the local chromospheric plasma.

Figure: Images: The left column consists of co-spatial images of the full ROSA/CSUNcam field of view, stacked from the photosphere through to the chromosphere. From bottom to top, the images represent the vertical magnetic field strength, Bz, determined from HMI vector magnetograms with the scale saturated at ±1000 G to aid clarity, magnetic field inclination angles, where 0 and 180 degrees represent fields outwardly and inwardly normal to the solar surface, ROSA 417 nm continuum, G-band, Na I D1 and Ca II K images. A white dashed line interconnects the pore between bandpasses, while the solid boxes define the sub-fields displayed in the right-hand column. Here, the pore is shown in detail for each imaging bandpass, with the binary map pixels shown at each height using a red contour.
Plot: The calculated energy flux of 210 s (red) and 290 s (blue) sausage mode oscillations, both in Wm^-2. The heights from the solar surface are approximate values, with the energy flux values plotted on a logarithmic scale to better highlight the rapid decrease in observed energies with increasing atmospheric height.

Copyright: Grant, S. D. T., Jess, D. B., Moreels, M. G., Morton, R. J., Christian, D. J., Giagkiozis, I., Verth, G., Fedun, V., Keys, P. H., Van Doorsselaere, T., Erdélyi, R. 2015, The Astrophysical Journal, 806, 132 (doi: 10.1088/0004-637X/806/1/132) | ADS

High-frequency Waves in Chromospheric Spicules

Using high-cadence observations from the Hydrogen-alpha Rapid Dynamics camera imaging system on the Dunn Solar Telescope, we present an investigation of the statistical properties of transverse oscillations in spicules captured above the solar limb. At five equally separated atmospheric heights, spanning approximately 4900–7500 km, we have detected a total of 15,959 individual wave events, with a mean displacement amplitude of 151±124 km, a mean period of 54±45 s, and a mean projected velocity amplitude of 21±13 km^-1. We find that both the displacement and velocity amplitudes increase with height above the solar limb, ranging from 132±111 km and 17.7±10.6 kms^-1 at ≈4900 km, and 168±125 km and 26.3±14.1 kms^-1 at ≈7500 km, respectively. Following the examination of neighboring oscillations in time and space, we find 45% of the waves to be upwardly propagating, 49% to be downwardly propagating, and 6% to be standing, with mean absolute phase velocities for the propagating waves on the order of 75–150 kms^-1. While the energy flux of the waves propagating downwards does not appear to depend on height, we find the energy flux of the upwardly propagating waves decreases with atmospheric height at a rate of −13,200±6500 W m^-2/Mm. As a result, this decrease in energy flux as the waves propagate upwards may provide significant thermal input into the local plasma.

Figure: Upper-left panel: Hα line-core image from DST/ROSA acquired at 13:59:09 UT.
Upper-right panel: An Hα core subfield (67 × 16 Mm²) image acquired using HARDcam at 14:49:45 UT. Numerous spicules are clearly visible above the solar limb as narrow, straw-like structures. The two most extreme slits used to take the time–distance diagrams are shown by the white lines, at heights of 4890 and 7500 km.
Lower-left panel: Histograms of the wave properties identified at a height of 6850 km above the solar limb. See Figure 4 of the article for more statistical information.
Lower-right panel: Energy flux estimations as a function of atmospheric height for all propagating waves (upper panel), upwardly propagating waves (middle panel), and downwardly propagating waves (lower panel). The total energy flux provided by short/long-period waves is shown in black, while the energy fluxes for short- (<50 s) and long-period (>50 s) waves are shown in red and blue, respectively. The energy fluxes provided by the full set of waves (including upwardly and downwardly propagating) and for all upwardly propagating waves are depicted, using a linear line of best fit, as a dashed black line in the upper and middle panels.

Copyright: Bate, W., Jess, D. B., Nakariakov, V. M., Grant, S. D. T., Jafarzadeh, S., Stangalini, M., Keys, P. H., Christian, D. J., Keenan, F. P. 2022, The Astrophysical Journal, 930, 129 (doi: 10.3847/1538-4357/ac5c53) | ADS

Large scale coherent magnetohydrodynamic oscillations in a sunspot

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.

Figure: Upper panel: Example of an instantaneous map of the filtered Doppler velocity, derived from the IBIS Fe I 617.3 nm spectral imaging sequence, overlaid on a high-resolution intensity image acquired by IBIS in the continuum in proximity of the Fe I 617.3 nm spectral line.
Lower panel: Numerically modeled LOS velocities obtained by the superposition of 9 orthogonal eigenmodes assuming that the umbra-penumbra boundary is fixed, overlaid on the observational intensity image.
The pattern is extremely sensitive to the exact shape of the umbra, and this needs to be taken into account when generating the numerical model (see methods subsection Numerical modeling and modal reconstruction). Due to this, the oscillatory rings are distorted by the shape of the umbra, departing from the perfectly circular shape found in the case of the standard magnetic cylinder model. The numerical model incorporates the effect of superposition of several eigenmodes, which are simultaneously excited in the umbra. In relation to the standard magnetic cylinder model, the dominant modes are found to be sausage-like and contain both the fundamental and the first radial overtone.
See this Supplementary Movie to see the evolution of the eigenmodes.

Copyright: Stangalini, M., Verth, G., Fedun, V., Aldhafeeri, A. A., Jess, D. B., Jafarzadeh, S., Keys, P. H., Fleck, B., Terradas, J., Murabito, M., Ermolli, I., Soler, R., Giorgi, F., MacBride, C. D. 2022, Nature Communications, 13, 479 (doi: 10.1038/s41467-022-28136-8) | ADS

Slow magneto-acoustic waves in simulations of a solar plage region carry enough energy to heat the chromosphere

We study the properties of slow magneto-acoustic waves that are naturally excited as a result of turbulent convection and we investigate their role in the energy balance of a plage region using three dimensional radiation magnetohydrodynamic simulations. To follow slow magneto-acoustic waves traveling along the magnetic field lines, we selected 25 seed locations inside a strong magnetic element and tracked the associated magnetic field lines both in space and time. We calculate the longitudinal component (i.e., parallel to the field) of velocity at each grid point along the field line and compute the temporal power spectra at various heights above the mean solar surface. Additionally, the horizontally-averaged (over the whole domain) frequency power spectra for both longitudinal and vertical (i.e., the component perpendicular to the surface) components of velocity are calculated using time series at fixed locations.
Inside a plage region, there is on average a significant fraction of low frequency waves leaking into the chromosphere due to inclined magnetic field lines. Our results show that longitudinal waves carry (just) enough energy to heat the chromosphere in the solar plage.

Figure: Panels (a)-(f) on the top right illustrate magnetic field line (green) traced in the 3D cube from a seed point and correspond to snapshots at every 5 min starting from t = 0. The red vertical line corresponds to the initial location of the seed point. Saturated maps of magnetic field strength at the mean solar surface are also shown for each temporal snapshot.
Panels (a) and (b) on the bottom right show height-time map of the longitudinal and the vertical component of velocity, respectively. Local sound speed curves (solid) and a curve showing the height at which c_s = v_A (dotted) are also over-plotted on the panel (a).
The four panels on the left show power spectra of longitudinal velocity, i.e., velocity parallel to the field (black) and vertical velocity (red) at the full resolution of simulations, at different heights as mentioned in each panel. Power spectra of vertical velocity for degraded simulation data with an effective resolution of 100 km (blue) and 200 km (green). Dashed curve displays a power-law fit to the black curve in the frequency range 6–25 mHz in each panel. Here, “a” and “b” are the amplitude and the exponent for the power law.

Copyright: Yadav, N., Cameron, R. H., Solanki, S. K. 2021, A&A, 652, A43 (doi: 10.1051/0004-6361/202039908) | ADS

The Nature of High-frequency Oscillations Associated with Short-lived Spicule-type Events

We investigate high-resolution spectroscopic and imaging observations from the CRisp Imaging SpectroPolarimeter (CRISP) instrument to study the dynamics of chromospheric spicule-type events. It is widely accepted that chromospheric fine structures are waveguides for several types of magnetohydrodynamic (MHD) oscillations, which can transport energy from the lower to upper layers of the Sun. We provide a statistical study of 30 high-frequency waves associated with spicule-type events. These high-frequency oscillations have two components of transverse motions: the plane-of-sky (POS) motion and the line-of-sight (LOS) motion. The composition of these two motions suggests that the wave has a helical structure. The oscillations do not have phase differences between points along the structure. We hypothesize that the compression and rarefaction of passing magnetoacoustic waves may influence the appearance of spicule-type events, not only by contributing to moving them in and out of the wing of the spectral line but also through the creation of density enhancements and an increase in opacity in the Hɑ line.

Figure: Panel (A): Evolution of a spicule-type event. White arrows show the location of the event, and the solid lines show the position of the slits.
Panel (B): Time– distance plots in the image-plane motion obtained at −774 mÅ.
Panel (C): Image offsets related to co-alignment of the images where the spicule-type event is observed.
Panel (D): Doppler velocity evolution.

Copyright: Shetye, J, Verwichte, E., Stangalini, M., Doyle, J. G. 2021, ApJ, 921, 30 (doi: 10.3847/1538-4357/ac1a12) | ADS

Magnetohydrodynamic wave mode identification in circular and elliptical sunspot umbrae: evidence for high order modes

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. While POD identifies modes based on orthogonality in space and it 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, from the National Solar Observatory’s Dunn Solar Telescope (DST), New Mexico, USA.

Figure: Panel (a): This figure displays 3D surface plot of POD (the first column) and DMD (the second column) modes obtained for the case of circular sunspot as well as volume rendering of the theoretical MHD wave model which uses the same color code as the POD and DMD modes (see the article). Rows refer to particular identified MHD modes, that is the fundamental slow body sausage mode (first row), the fundamental slow body kink mode (second row), the slow body sausage overtone (third row), the n = 2 slow body fluting mode (fourth row) and the n = 3 slow body fluting mode (last row).
Panel (b): The visualisation technique are same as Figure (a), but here rows refer to MHD wave mode recovered in the elliptical sunspot, that is the the fundamental slow body sausage (first row), the fundamental slow body kink mode (second row), the slow body overtone kink mode (third row), the n = 2 slow body fluting mode (fourth row) and the n = 3 slow body fluting mode (last row).

Copyright: Albidah, A. B., Fedun, V., Aldhafeeri, A. A., Ballai, I., Brevis, W., Jess, D. B., Higham, J., Stangalini, M., Silva, S. S. A., Verth, G. 2022, arXiv:2202.00624

Oscillations observed in umbra, plage, quiet-Sun and the polarity inversion line of AR 11158 using HMI/SDO

Using data from the Helioseismic Magnetic Imager (HMI), we report on the amplitudes and phase relations of oscillations in quiet-Sun, plage, umbra and the polarity inversion line (PIL) of an active region NOAA#11158. We employ Fourier, wavelet and cross correlation spectra analysis. Waves with 5 min periods are observed in umbra, PIL and plage with common phase values of φ(v,I)=π/2, φ(v,B_los)=−(π/2). In addition, φ(I,B_los)=π in plage are observed. These phase values are consistent with slow standing or fast standing surface sausage wave modes. The line width variations, and their phase relations with intensity and magnetic oscillations, show different values within the plage and PIL regions, which may offer a way to further differentiate wave mode mechanics. Significant Doppler velocity oscillations are present along the PIL, meaning that plasma motion is perpendicular to the magnetic ﬁeld lines, a signature of Alfvénic waves. A time–distance diagram along a section of the PIL shows Eastward propagating Doppler oscillations converting into magnetic oscillations; the propagation speeds range between 2 and 6 km s⁻¹. Lastly, a 3 min wave is observed in select regions of the umbra in the magnetogram data.

Figure: Histograms with 20 degrees bins are created for the phase values for oscillations of velocity and intensity, φ(v,I), velocity and magnetic flux, φ(v,|M|), velocity and line width, φ(v,Lw), intensity and line width, φ(I,Lw), and line width and magnetic flux, φ(Lw,|M|) for pixels in the quiet-Sun, PIL, umbra and plage regions. Lines are not plotted for the quiet-Sun and plage data for panels in which the data are very noisy.

Copyright: Norton, A. A., Stutz, R. B., Welsch, B. T. 2021, Phil. Trans. R. Soc. A 379: 2020.0175 (doi: 10.1098/rsta.2020.0175) | ADS

The effect of axisymmetric and spatially varying equilibria and flow on MHD wave modes: Cylindrical geometry

Realistic models of Magnetohydrodynamic (MHD) waves are required representing observed configurations such that plasma properties can be determined more accurately which can not be measured directly. This work utilises a previously developed numerical technique to find permittable eigenvalues under different non-uniform equilibrium conditions in a Cartesian magnetic slab geometry. Here we investigate the properties of magnetoacoustic waves under non-uniform equilibria in a cylindrical geometry. Previously obtained analytical results are retrieved to emphasise the power and applicability of this numerical technique. Further case studies investigate the effect that a radially non-uniform plasma density and non-uniform plasma flow, modelled as a series of Gaussian profiles, has on the properties of different MHD waves. For all cases the dispersion diagrams are obtained and spatial eigenfunctions calculated which display the effects of the equilibrium inhomogeneity. It is shown that as the equilibrium non-uniformity is increased, the radial spatial eigenfunctions are affected and extra nodes introduced, similar to the previous investigation of a magnetic slab. Furthermore, azimuthal perturbations are increased with increasing inhomogeneity introducing vortical motions inside the waveguide. Finally, 2D and 3D representations of the velocity fields are shown which may be useful for observers for wave mode identification under realistic magnetic waveguides with ever increasing instrument resolution.

Figure: 3D visualisation of the total pressure perturbation (P̂_T) and the perturbed velocity vector field in the presence of a uniform and non-uniform background plasma flow for the slow body kink mode with eigenfunctions shown in Figure 14d of this article. (a) Case for uniform plasma flow (W=10⁵; W is standard deviation (i.e. the width) of the density distribution). (b) case with Gaussian flow with W=0.6.
Movies of these 3D visualisations can be found online on the PDG visualisations web-page.

Copyright: Skirvin, S., Fedun, V., Silva, S., Verth, G. 2021, MNRAS, 510, 2689 (doi: 10.1093/mnras/stab3635)

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

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.

Figure: Top row: Illustrated from left to right are, respectively, an intensity image (Fe I 617.3 nm line-core intensity), Doppler velocity, and magnetic-field maps of the solar pore under study.
Bottom row: B − ω diagram of the LoS velocity (left), CP (centre), where the vertical blue dashed line represents the approximate position of the boundary of the umbra as inferred from intensity images. Each column represents the average power spectrum across bins equal to 80 G. The global spectra for LoS velocities and CP fluctuations, both outside and inside the magnetic structure, are shown in the right panel. These are obtained bu integrating the B − ω diagram along the horizontal axis.

Copyright: Stangalini, M., Jess, D. B., Verth, G., Fedun, V., Fleck, B., Jafarzadeh, S., Keys, P. H., Murabito, M., Calchetti, D., Aldhafeeri, A. A., Berrilli, F., Del Moro, D., Jefferies, S. M., Terradas, J., Soler, R. 2021, A&A, 649, A169 (doi: 10.1051/0004-6361/202140429)

Finding the mechanism of wave energy flux damping in solar pores using numerical simulations

Solar magnetic pores are, due to their concentrated magnetic fields, suitable guides for magnetoacoustic waves. Recent observations (see the Image of the Month of July 2021) have shown that propagating energy flux in pores is subject to strong damping with height; however, the reason has been unclear.
While the analysis of the energy flux for ideal and non-ideal MHD simulations with a plane driver cannot reproduce the observed damping, the numerically predicted damping for a localized driver closely corresponds with the observations. The strong damping in simulations with localized driver was caused by two geometric effects, geometric spreading due to diverging field lines and lateral wave leakage.

Figure: Panel (a): Snapshot of the vertical velocity perturbation after two periods for the localized driver for ideal MHD. The gray lines show magnetic field lines. The red bar below the x-axis indicates the driver location.
Panel (b): Sound speed of the initial atmosphere. Contours for the sound speed are shown in thick black lines.
Panels (c) and (d): Snapshot of the wave energy flux parallel (c) and perpendicular (d) with respect to the magnetic field. The color range is saturated. The solid (dashed) green lines show the first theoretical wave fronts of the fast (slow) waves.

Copyright: Riedl, J. M., Gilchrist-Millar, C. A., Van Doorsselaere, T., Jess, D. B., Grant, S. D. T. 2021, A&A, 648, A77 (doi: 10.1051/0004-6361/202040163)

Solar inertial modes: Observations, identification, and diagnostic promise

The oscillations of a slowly rotating star have long been classified into spheroidal and toroidal modes. The spheroidal modes include the well-known 5-min acoustic modes used in helioseismology. Observations of the Sun's toroidal modes, for which the restoring force is the Coriolis force and whose periods are on the order of the solar rotation period, are reported in this article. By comparing the observations with the normal modes of a differentially rotating spherical shell, the authors were able to identify many of the observed modes. These are the high-latitude inertial modes, the critical-latitude inertial modes, and the equatorial Rossby modes.
Observed and model eigenfunctions for the modes are shown in the figure above. The left column shows the observed velocity (u^-_φ for the m=1 and m=2 modes, u⁺_θ for the m=3 mode). The middle columns show the corresponding eigenfunctions of the 2D model for ν_t=100 km² s^-1 and δ=0, at the surface and through the central meridian, together with the kinetic energy density. The thick black curves show the critical latitudes. The rightmost column shows the eigenfunctions of the 1D model at the surface. The retrograde propagation of these modes in the Carrington frame is illustrated as an online movie.

Copyright: Gizon, Laurent, Cameron, Robert H., Bekki, Yuto, Birch, Aaron C., Bogart, Richard S., Brun, Allan Sacha, Damiani, Cilia, Fournier, Damien, Hyest, Laura, Jain, Kiran, Lekshmi, B., Liang, Zhi-Chao, Proxauf, Bastian 2021, A&A, 652, L6 (doi: 10.1051/0004-6361/202141462)

Magnetic fields and the supply of low-frequency acoustic wave energy to the solar chromosphere

Maps of magnetic inclination angle (bottom panels), phase travel time (middle panels), and logarithm of energy flux (top panels) for a sunspot (left), plage region (middle), and quiet-network area (right). The phase travel time and energy flux are for acoustic waves of frequency 3 mHz propagating from 170 km (SDO/HMI line-core intensity) to 360 km (SDO/AIA 170 nm intensity).
It is found that the relatively less inclined magnetic field elements in the quiet Sun channel a significant amount of waves of frequency lower than the theoretical minimum acoustic cutoff frequency due to magnetic inclination. Indications that these waves steepen and start to dissipate within the height ranges probed were also derived. The flux of acoustic energy, in the 2-5 mHz frequency range, between the upper photosphere and lower chromosphere found to be in the range of 2.25-2.6 kW m^-2, which is about twice the previous estimates.

Copyright: Rajaguru, S. P., Sangeetha, C. R., Tripathi, Durgesh 2019, ApJ, 871, 155 (doi: 10.3847/1538-4357/aaf883)

Magnetoacoustic wave energy dissipation in the atmosphere of solar pores

(a) Five small pores as observed by the Dunn Solar Telescope (DST), Sacramento Peak, New Mexico. Panel (a) illustrates the pores in a DST/ROSA 4170 Å continuum image. The position of the FIRS (Facility Infrared Spectropolarimeter) slit is depicted by a dashed yellow line, with each of the five solar pores captured labelled by a number 1–5.
(b) Energy flux (due to propagating magnetoacoustic sausage mode waves) displayed as a function of both distance across the slit and atmospheric height. Pore boundaries are highlighted by the vertical white dashed lines. The solid green line displays the inclination angles of the magnetic field along the slit. High energy fluxes towards the edges of pore structures (i.e. pores 2, 3 and 4) may be the result of surface mode waves, while more uniform energy structuring (i.e. pores 1 and 5) may be related to the presence of body mode waves. Energy flux values seen in non-pore regions are likely a result of convective overshoots and not specifically propagating magnetoacoustic wave phenomena.

Copyright: Gilchrist-Millar, Caitlin A., Jess, David B., Grant, Samuel D. T., Keys, Peter H., Beck, Christian, Jafarzadeh, Shahin, Riedl, Julia M., Van Doorsselaere, Tom, Ruiz Cobo, Basilio 2021, Phil. Trans. R. Soc. A 379: 20200172 (doi: 10.1098/rsta.2020.0172)

Transverse motions in sunspot super-penumbral fibrils

(a) The sunspot as observed in Ca II 8542 Å. The upper left image shows the chromospheric emission at the nominal line centre wavelength. Super-penumbral fibrils are seen to extend near-radially from the chromospheric umbra in the upper half, while those in the lower half are more curvilinear. The upper right-hand image shows the photospheric section of the sunspot as observed in the wings of the Ca II line (−0.942 Å). The lower two panels show the temporally averaged line width (left) and Doppler velocity (right) data products. The width and Doppler components of the fibrils can be seen in both data product images.
(b) An isolated set of fibrils in the CaII sunspot super-penumbra. The figure shows the outline of the fibril’s central axis along with the cross-cuts normal to the guide-line. For clarity, a small number of guide points and a large separation distance is chosen.
(c) Wave properties as a function of distance from the umbral centre. The figure displays the mean values for velocity and period, with the error bars denoting the standard errors on the mean.

Copyright: Morton, R. J., Mooroogen, K., Henriques, V. M. J. 2021, Phil. Trans. R. Soc. A 379: 20200183 (doi: 10.1098/rsta.2020.0183)

Torsional oscillations within a magnetic pore in the solar photosphere

Alfvén waves have proven to be important in a range of physical systems due to their ability to transport non-thermal energy over long distances in a magnetized plasma. This property is of specific interest in solar physics, where the extreme heating of the atmosphere of the Sun remains unexplained. In an inhomogeneous plasma such as a flux tube in the solar atmosphere, they manifest as incompressible torsional perturbations. However, despite evidence in the upper atmosphere, they have not been directly observed in the photosphere. Here, we report the detection of antiphase incompressible torsional oscillations observed in a magnetic pore in the photosphere by the Interferometric Bidimensional Spectropolarimeter (IBIS) at the Dunn Solar Telescope (DST). State-of-the-art numerical simulations suggest that a kink mode is a possible excitation mechanism of these waves.
Panel b: Measured angular rotation oscillations of the two lobes of the magnetic pore, as obtained from a cross-correlation tracking analysis at the edges of the flux tube.
Panel d: Schematic depicting the m = 1 antisymmetric torsional Alfvén oscillations in the magnetic structure.

Copyright: Marco Stangalini, Robertus Erdélyi, Callum Boocock, David Tsiklauri, Christopher J. Nelson, Dario Del Moro, Francesco Berrilli, and Marianna B. Korsós 2021, Nature Astronomy, advance online publications (doi: 10.1038/s41550-021-01354-8)

Wave phenomena in sunspots

Wave dynamics in a sunspot, observed with the ground-based Dunn Solar Telescope (DST) in New Mexico, has been illustrated. The simultaneous scanning of multiple spectral lines in the visible to near-infrared range has allowed a ﬁne sampling of the photosphere and chromosphere above the sunspot. Sunspot waves are detected throughout all atmospheric layers, from the lower photosphere to the upper transition region and corona. Umbral ﬂashes and running penumbral waves are most prominent in the sunspot chromosphere. All oscillations in spectral intensity and Doppler velocity occur unceasingly at periods of a few minutes for the observational timespan. The most likely driving mechanism is the absorption of p-modes by the sunspot in the upper convection zone and lower photosphere. Magnetoacoustic waves are also driven by perturbations of the magnetic ﬁeld lines.

Copyright: Johannes Löhner-Böttcher 2015, PhD thesis

The Effects of Transients on Photospheric and Chromospheric Power Distributions

Left: Images of a quiet region as seen in different layers of the solar atmosphere along with the corresponding magnetogram from photosphere at the bottom. Bottom to top: line-of-sight (LOS) magnetogram obtained by using Fe 6302 Å Stokes V profiles, visible continuum, and narrow-band filter images taken at different positions across the Hɑ line profile as indicated (Hɑ + 0.906 Å, Hɑ + 0.543 Å, Hɑ + 0.362 Å and Hɑ core). The long tick marks on the magnetogram represent 10 Mm intervals.
Right: Distribution of dominant periods (of intensity oscillations) in different layers along with the corresponding magnetogram at the bottom. The green, red, and yellow colors roughly represent periods around 3, 5, and 7 minutes, respectively.

Copyright: Tanmoy Samanta, Vasco M. J. Henriques, Dipankar Banerjee, Sayamanthula Krishna Prasad, Mihalis Mathioudakis, David B. Jess, and Vaibhav Pant 2016, The Astrophysical Journal, 828, 23

An overall view of temperature oscillations in the solar chromosphere with ALMA

Global oscillations in one of the most magnetically quiescent datasets studied in this research article.
Top left: A brightness-temperature map from the ALMA’s Band-3 observations from 12 April 2018. The blue ellipse on the bottom-left corner of the panel represents the beam size of the observations. Top right: Spatially averaged brightness-temperature power spectra from fast Fourier (dash-dotted black line) and Lomb– Scargle (solid red line) transforms. The purple and yellow stripes have been depicted to mark period ranges corresponding to the 3 and 5 min windows (each with a width of 1 min), respectively. The chromospheric characteristic frequencies of the global p-mode oscillations (i.e., around 3-5~mHz) is evident. Bottom left: Line-of-sight photospheric magnetic fields (Blos) from SDO/HMI with a factor of two larger FOV than that of ALMA. The range of Blos values has been indicated in the upper left corner. The ALMA’s FOV is marked with the dashed square. Bottom right: Top view of field extrapolation of the surface magnetic field (from SDO/HMI) at the chromosphere heights (for the ALMA’s FOV). The colours represent inclination, from vertical (blue) to horizontal (red).

Copyright: S. Jafarzadeh, S. Wedemeyer, B. Fleck, M. Stangalini, D. B. Jess, R. J. Morton, M. Szydlarski, V. M. J. Henriques, X. Zhu, T. Wiegelmann, J. C. Guevara Gómez, S. D. T. Grant, B. Chen9, K. Reardon and S. M. White 2021, Phil. Trans. R. Soc. A 379: 20200174

Evolution of Complex 3D Motions in Spicules

Three dimensional visualization of coupled MHD wave modes are illustrated in a spicule, obtained from high-resolution observations with the Swedish 1-m Solar Telescope. The four columns illustrate the 3D structure at different time steps indicated on the top. Top row: coupled transverse and width with intensity. Bottom row: transverse and azimuthal shear components. The azimuthal shear/torsion component magnitude exhibits field-aligned upward and downward motions, possibly due to perturbed Lorentz forces.

Copyright: Rahul Sharma, Gary Verth, and Robertus Erdélyi 2018, The Astrophysical Journal, 853, 61

The Sun at millimeter wavelengths — II. Small-scale dynamic events in ALMA Band 3

Detailed study of an event. a-e) The top panels show a close up of the surroundings at different time steps, t1 to t5 from left to right, through the shock wave event. The time of the Tb peak is marked by t3 = 14:46:38. t1 and t2 mark 70 s and 26 s prior the peak and t4 and t5 mark 26 s and 70 s after the peak. The center location is marked by a blue cross. The contour lines marks the half maximum of the maximum ∆Tb peak. f-g) Space-time diagrams for a vertical and horizontal slit across the FOV at the center location, which is marked with blue dots for the time steps t1 to t5 . Velocity slopes for 10 and 20 km s −1 are indicated by blue dotted and white dashed lines, respectively. The color code is the same in all panels. h) The time evolution of the brightness temperature of the center location, where the time steps t1 to t5 are indicated by blue dotted vertical lines. Both the original data (black) and the averaged data (green) are shown. The horizontal and vertical black dashed lines mark the event lifetime and brightness temperature excess.

Copyright: Henrik Eklund, Sven Wedemeyer, Mikolaj Szydlarski, Shahin Jafarzadeh, and Juan Camilo Guevara Gómez 2020, Astronomy & Astrophysics, 644, A152

Numerical Simulations of Quiet Sun Oscillations

A comparison between oscillations in a quiet Sun background model from the three-dimensional Semi-spectral Linear MHD (SLiM) code, and observations with SOHO/MDI.

"The azimuthally averaged power spectrum (on a log scale where black is high and white low) of 8 hours of vertical velocity data from the SLiM simulation (top) and 24 hours of SOHO/MDI full-disk, line-of-sight Doppler observations (bottom). The eigenfrequencies of Model S (Christensen-Dalsgaard et al. 1996) are overplotted as dashed lines. Modes with a horizontal phase speed ω/k greater than c(zb)/(1+ zb/R_☉) (solid line in top panel) encounter the bottom sponge layer before reaching their lower turning point."

Copyright: Hannah Schunker, Robert Cameron, and Laurent Gizon 2009, ASP Conference Series, Vol. 416, 49

Collisional ionisation, recombination and ionisation potential in two-fluid slow-mode shocks: analytical and numerical results

Close-up of the slow mode shock for the IRIP (Collisional ionisation, recombination and ionisation potential) model showing vx velocity (top left), temperature (top right) and density (lower left) for plasma (blue) and neutral (red) species. The lower right panel shows the ionisation (orange) and recombination (green) rates.

Copyright: Ben Snow & Andrew Hillier 2021, Astronomy & Astrophysics, 645, A81

The dynamics of 3-minute wavefronts and their relation to sunspot magnetic fields

The frequency distribution of oscillation power corresponding to the instantaneous wavefront visible at 00:14:33 UT (panel a). The contours show a broadband ∼3-minute wavefront superimposed on the narrowband power distributions corresponding to periods in the range of 1.8 – 3.8 minutes. The corresponding power spectra for the selected points on the wavefront ridge, as a function of period. The coloured lines reflect the locations marked by the coloured dots in the upper-left panel. The first area is associated with a pulsating source.

Copyright: Sych, Robert, Jess, David B., Su, Jiangtao 2021, Phil. Trans. R. Soc. A, 379, 20200180

High-frequency oscillations in small chromospheric bright features observed with ALMA

Fluctuations in brightness temperature (black) and size (red) of three small bright features. The horizontal black, dotted line in the top panel marks the size of the major axis of the synthetic elliptical median beam (i.e., the spatial-resolution element). An anti-correlation between oscillations of the two quantities is evident.

Copyright: Guevara Gómez, J. C., Jafarzadeh, S., Wedemeyer, S., Szydlarski, M., Stangalini, M., Fleck, B., Keys, P. 2021, Phil. Trans. R. Soc. A, 379, 20200184

Acoustic-gravity wave propagation characteristics in 3D radiation hydrodynamic simulations of the solar atmosphere

Frequency-height phase diagrams (cuts at constant wave numbers at approximately 2 (top) and 4 Mm^-1 (bottom) through the stacks of the layer-by-layer 2D k-ω phase difference diagrams) for the MANCHA3D model (left) and comparison to a MURaM (middle) and Bifrost (right) model. This works reveals considerable differences between the various models.

Copyright: Fleck, B., Carlsson, M., Khomenko, E., Rempel, M., Steiner, O., Vigeesh, G. 2020, Phil. Trans. R. Soc. A, 379, 20200170

Oscillations on Width and Intensity of Slender Ca ii H Fibrils from Sunrise/SuFI

Example of intensity maxima and width detections along cuts perpendicular to the axis of an SCF. Plotted are vertically stacked images of a fibril recorded in Ca ii H observed at different times. Individual images, recorded every 7 s, are separated by horizontal black lines. The red dots within a given image represent the locations of the fibril's maximum intensity along a series of cuts roughly perpendicular to the backbone of the fibril, while the vertical black lines indicate the width of the fibril at the same locations. The color represents intensity, normalized to the mean value of the quiet region in the SUFI frame. An anti-correlation between width and intensity oscillations suggests the presence of fast sausage mode.

Copyright: Gafeira, R., Jafarzadeh, S., Solanki, S. K., Lagg, A., van Noort, M., Barthol, P., Blanco Rodríguez, J.,del Toro Iniesta, J. C., Gandorfer, A., Gizon, L., Hirzberger, J., Knölker, M., Orozco Suárez, D., Riethmüller, T. L.,Schmidt, W. 2017, The Astrophysical Journal Supplement Series, 229, 7 (doi: 10.3847/1538-4365/229/1/7)

Vortices evolution in the solar atmosphere

Co-spatial images revealing the structure of a sunspot observed at 13:00 UT on 24 August 2014. The lower image shows the magnitude of the photospheric magnetic field from HMI/SDO, revealing high umbral field strengths (colour bar relates to the field strengths in gauss). The image above is taken from the blue wing of the Ca II 8542 Å spectral line from DST, displaying the photospheric representation of the sunspot. Above this is the photospheric plasma temperature of the region derived from CAISAR at log(τ 500nm) ~ −2 (or ~ 250 km above the photosphere), showing the clear temperature distinction between the umbra, penumbra and surrounding quiet Sun (colour bar in units of kelvin). The upper image shows the chromospheric core of the Ca II 8542 Å spectral line from DST, highlighting the strong intensity gradient between the umbra and penumbra at these heights. In each of these images, the red contours represent the inner and outer boundaries of the plasma-β = 1 region at the height where shocks first begin to manifest (~ 250 km), where magneto-acoustic and Alfvén waves can readily convert.

Copyright: José R. Canivete Cuissa and Oskar Steiner 2020, Astronomy & Astrophysics, 639, A118 (doi: 10.1051/0004-6361/202038060)

Unveiling the magnetic nature of chromospheric vortices

Perturbations in intensity (left), LOS Doppler velocity (middle), and Circular Polarisation (right) as a function of angle and time in a polar grid centered one of the events and averaged over radius. The line highlights the phase propagation of the wave patterns with their corresponding periodicity.

Copyright: Murabito, M., Shetye, J., Stangalini, M., Verwichte, E., Arber, T., Ermolli, I., Giorgi, F., Goffrey, T. 2020, Astronomy & Astrophysics, 639, A59 (doi: 10.1051/0004-6361/202038360)

Magnetohydrodynamic Nonlinearities in Sunspot Atmospheres: Chromospheric Detections of Intermediate Shocks

Left: shock LOS Doppler velocities plotted as a function of their quiescent (i.e., pre-shock) Doppler velocities for the same pixel location. The background blue–red color scheme helps visualize the Doppler velocities corresponding to each quadrant of the plot, with progressively more blue and red colors representing larger up- and downflowing material, respectively. Right: shock temperature changes displayed as a function of the pre-shock background temperature. The background blue–red color scheme provides a visual representation of temperature, with more red colors corresponding to both hotter quiescent and shock-induced temperatures. In both panels the colored data points correspond to the optical depths at which the plasma parameters are extracted, as defined in the legends located in the upper left corner of each panel.

Copyright: Houston, S. J., Jess, D. B., Keppens, R., Stangalini, M., Keys, P. H., Grant, S. D. T., Jafarzadeh, S., McFetridge, L. M., Murabito, M., Ermolli, I., Giorgi, F. 2020, The Astrophysical Journal, 892, 49 (doi: 10.3847/1538-4357/ab7a90)

Third meeting of the WaLSA Team / Theo Murphy international scientific meeting
Chicheley Hall of The Royal Society, UK, 10-11 February 2020

Long-period magnetic field oscillations and motions in isolated sunspots

Penumbral distribution of the wavelet power of a sunspot, NOAA AR12218, and its comparison to the spatial distribution of the magnetic field and coronal emission. The upper left panel represents the spatial distribution of events, where the penumbra is divided into four 90 degrees sectors (north, east, south, and west). The upper and lower right panels show the HMI line-of-sight magnetogram (saturated between -200 and 200 gauss) and the corresponding coronal image in the AIA 171 Å filter (with the area denoted with a white square zoomed in the lower left corner of the image). Both display an extended field of view at the time the sunspot was crossing the central meridian. Finally, the lower left panel represents a histogram of the integrated azimuthal distribution of magnetic fluxes and wavelet power. The black and red lines show the magnetic flux around the target sunspot of the same and opposite polarity, respectively, and the blue line corresponds to the wavelet power of the studied sunspot.

Copyright: A. B. Griñón-Marín, A. Pastor Yabar, H. Socas-Navarro, & Rebecca Centeno 2020, Astronomy & Astrophysics, 635, A64 (doi: 10.1051/0004-6361/201936589)

A chromospheric resonance cavity in a sunspot mapped with seismology

Three-dimensional visualization of the geometric extent of the chromosphere above active region NoAA 12565. The geometric extent of the chromosphere, visualized here as the pink isocontours extending upwards from the photospheric (ROSA 4170 Å continuum) umbra and through the chromospheric (IBIS 8542 Å line core). It can be seen that the depth of the resonance cavity is suppressed in the immediate vicinity of the trans-umbral filamentary structure, providing geometric heights of approximately 1,300 km, which is consistent with the depth measured at the outermost edges of the umbra. The cores of the umbrae display the largest resonance cavity depths, often with geometric heights on the order of 2,300 km. An image of the Earth is added to provide a sense of scale. Note that the pink resonance cavity depth contours are not to scale. Credit: Earth image, NOAA.

Copyright: David B. Jess, Ben Snow, Scott J. Houston, Gert J. J. Botha, Bernhard Fleck, S. Krishna Prasad, Andrés Asensio Ramos, Richard J. Morton, Peter H. Keys, Shahin Jafarzadeh, Marco Stangalini, Samuel D. T. Grant & Damian J. Christian 2020, Nature Astronomy, 4, 220 (doi: 10.1038/s41550-019-0945-2)

The Magnetic Response of the Solar Atmosphere to Umbral Flashes

Top left: ROSA 4170 Å continuum image of active region NOAA 12565. Middle left: IBIS blue-wing snapshot acquired at 8540.82 Å (line core −1.3 Å). Bottom left: IBIS Ca II 8542 Å line-core image, where the green contour represents the location of the outer umbral boundary. In each panel, the solid red line represents the orientation and position of the FIRS spectral slit. Right panel: velocity–time image showing the spectral and temporal evolution of the He I 10830 Å Stokes I line profile, where the black-to-white color scale represents the inverse spectral intensities to aid visual clarity. The vertical dashed red line represents the rest position of the He I 10830 Å line core.

Copyright: S. J. Houston, D. B. Jess, A. Asensio Ramos, S. D. T. Grant, C. Beck, A. A. Norton, and S. Krishna Prasad 2018, The Astrophysical Journal, 860, 28 (doi: 10.3847/1538-4357/aab366)

Two-fluid simulations of waves in the solar chromosphere

Simulations of acoustic wave propagation in a homogeneous plasma. Numerically (red dashed line) and analytically (green solid line) calculated time evolution of the velocity of neutrals and charges as a function of time. Below the panels showing the velocity of neutrals, the difference (Δ) between the numerical solution and the analytical solution for unz is given. Time is measured in units of the wave period, 2π/ωR. Panels from left to right and from top to bottom: simulations for different values of the wavenumber k.

Copyright: B. Popescu Braileanu, V. S. Lukin, E. Khomenko and Á. de Vicente 2019, Astronomy & Astrophysics, 627, A25 (doi: 10.1051/0004-6361/201834154)

Spiral-shaped wavefronts in a sunspot umbra

Temporal evolution of the Doppler velocity, inferred from the GFPI Fe I 5435 Å restored images (from observations with GREGOR; a 1.5 m solar telescope), during the appearance of a two-armed spiral wavefront, filtered in frequency bands. From left to right columns: 2–8 mHz, 2–3.5 mHz, 3.5–4.7 mHz, 4.7–8 mHz. T The black lines mark the umbral and penumbral boundaries. The green circles highlight the location of the spiral wavefronts.

Copyright: Tobías Felipe, C. Kuckein, Elena Khomenko, and I. Thaler 2019, Astronomy & Astrophysics, 621, A43 (doi: 10.1051/0004-6361/201834367)

Second meeting of the WaLSA Team
Oslo, Norway, 12-16 August 2019

Semi-empirical model atmospheres for the chromosphere of the sunspot penumbra and umbral flashes

Columns showing the observed (black dots; from the Swedish 1- Solar Telescope, SST) and synthetic (red) full Stokes spectra in units of normalized HSRA (Gingerich et al. 1971) continuum intensity at disk center at a wavelength in the middle of the spectral range, and their atmospheric parameters such as temperature, LOS magnetic field, velocity, and microturbulent velocity for three different models: hot penumbra (asterisk), cool penumbra ('cross') and umbral flash ('plus sign'), respectively. The continuous line overplotted on the dashed line for the LOS magnetic field, shows the variation of the magnetic field in the region log(tau) = [-6,-2] where the Ca 8542 spectra is most sensitive.

Copyright: S. Bose, Vasco M.J. Henriques, L. Rouppe van der Voort, and T.M.D. Pereira 2019, Astronomy & Astrophysics, 627, A46 (doi: 10.1051/0004-6361/201935289)

Transverse Oscillations in Slender Ca ii H Fibrils Observed with Sunrise/SuFI

Left: A dense forest of slender bright fibrils near a small solar active region seen in high-quality narrowband Ca ii H images from the SuFI instrument onboard the Sunrise balloon-borne solar observatory.
Right: Phase speeds in an example slender Ca ii H fibril (SCF) with an indication of wave propagation. The curves in panels (a)–(e) represent displacement of the SCF along a series of cuts across the fibril shown in the upper panel, from left to right, respectively. The red triple-dot–dashed lines are the centroids of a Gaussian fit to the oscillations smoothed by convolving with a boxcar filter of 0.05 arcsec width. The green lines indicate waves propagation in the SCF in a direction corresponding to from right to left in the top panel.

Copyright: Shahin Jafarzadeh, Sami K. Solanki, Ricardo Gafeira, Michiel van Noort, et al. 2017, The Astrophysical Journal Supplement Series, 229, 1, 9 (doi: 10.3847/1538-4365/229/1/9)

Observations of ubiquitous compressive waves in the Sun’s chromosphere

(a) Typical ROSA Hɑ example of a pair of relatively large dark flux tubes at t=1,536 s measured from the beginning of the data series. (b) Time-distance plot revealing the dynamic motion. The position of the cross-cut is shown in (a), with the given distance starting at the top of the cross-cut. Times are given in seconds from the start of the data set. The results from a Gaussian fitting are over-plotted and show the nonlinear fast MHD kink wave (red line shows the central axis of the structure) and the fast MHD sausage mode (yellow bars show the measured width of structure). The transverse motion has a period of 232±8 s and we detect multi-directional propagating transversal wave trains in the MFT travelling with speeds of 71±22 km/s upwards and 87±26 km/s downwards. The typical velocity amplitudes are 5 km/s. The fast MHD sausage mode has a period of 197±8 s, a phase speed of 67±15 km/s and apparent velocity amplitudes of 1–2 km/s. (c) Comparison of MFTs intensity (blue) and width (red) perturbations from the Gaussian fitting. The data points have been fitted with a smoothed 3-point box-car function. The observed out-of-phase behaviour is typical of fast MHD sausage waves. The error bars plotted are the one-sigma errors on each data point calculated from the Gaussian fitting.

Copyright: Richard J. Morton, Gary Verth, David B. Jess, David Kuridze, Michael S. Ruderman, Mihalis Mathioudakis, and Robertus Erdélyi 2012, Nature Communications, 3, 1315 (doi: 10.1038/ncomms2324)

Signatures of running penumbral waves in sunspot photospheres

Three-dimensional view of intensities and peak periods of intensity wave power of a sunspot at various wavelength positions. The intensities (left) show the sunspot at August 21st 2013 at 15:00:06 UTC (±3 s). The images along the z-axis belong to several line core and wing positions of Fe I 630.15 nm, Na I 589.6 nm, and Ca II 854.2 nm. The corresponding time-averaged (≈1h) distribution of peak periods TPEAK of the intensity wave power is shown on the right. The periods are scaled from 2.5 min (dark blue) to 8 min (dark red). The black contours indicate the location of the umbra (inner) and penumbra (outer) in continuum intensity (bottom panel). Whereas the length of the axis arrows represent distances around 1.5 Mm, the image positions along the z-axis are not to scale.

Copyright: J. Löhner-Böttcher and N. Bello González 2018, Astronomy & Astrophysics, 580, A53 (doi: 10.1051/0004-6361/201526230)

Photospheric observations of surface and body modes in solar magnetic pores

This stack image shows the basis of designation of a sausage surface mode in a pore. The bottom panel shows the LOS magnetogram from HMI indicating the magnetic field of the pore and the sharp boundary in terms of magnetic field at the pore's edge. Above this is the full FOV ROSA G-band image showing the photospheric appearance of the pore taken on 2011 December 10. The blue box indicates the expanded region shown in the top three panels. The expanded G-band image has blue contours indicating the pore boundary established for that particular frame. Above this is the time-averaged pore boundary map showing the variation in boundary location during this observation sequence, where the arrows indicate the sausage mode oscillations present. The top panel is a two-dimensional power plot of the power across the pore obtained with wavelet transforms of the data filtered at a frequency of ~4.6 mHz. The blue contour shows the time average pore boundary location. Peaks in power at this boundary indicate that a sausage mode is observed at this frequency.

Copyright: Keys, P. H., Morton, R. J., Jess, D. B., Verth, G., et al. 2018, The Astrophysical Journal, 857, 28 (doi: 10.3847/1538-4357/aab432)

Alfvén wave dissipation in the solar chromosphere

Co-spatial images revealing the structure of a sunspot observed at 13:00 UT on 24 August 2014. The lower image shows the magnitude of the photospheric magnetic field from HMI/SDO, revealing high umbral field strengths (colour bar relates to the field strengths in gauss). The image above is taken from the blue wing of the Ca II 8542 Å spectral line from DST, displaying the photospheric representation of the sunspot. Above this is the photospheric plasma temperature of the region derived from CAISAR at log(τ 500nm) ~ −2 (or ~ 250 km above the photosphere), showing the clear temperature distinction between the umbra, penumbra and surrounding quiet Sun (colour bar in units of kelvin). The upper image shows the chromospheric core of the Ca II 8542 Å spectral line from DST, highlighting the strong intensity gradient between the umbra and penumbra at these heights. In each of these images, the red contours represent the inner and outer boundaries of the plasma-β = 1 region at the height where shocks first begin to manifest (~ 250 km), where magneto-acoustic and Alfvén waves can readily convert.

Copyright: Grant, S. D. T., Jess, D. B., Zaqarashvili, T. V., et al. 2018, Nature Physics, 14, 480 (doi: 10.1038/s41567-018-0058-3)

Image of the Month

Research Illustrations

Select month and/or year for previous images:

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

Alfvén Waves in the Lower Solar Atmosphere

Magnetohydrodynamic Poynting Flux Vortices in the Solar Atmosphere and Their Role in Concentrating Energy

Alfvén wave dissipation in the solar chromosphere

Are There Alfvén Waves in the Solar Atmosphere?

The Fibre Resolved OpticAl and Near-Ultraviolet Czerny–Turner Imaging Spectropolarimeter (FRANCIS)

Sixth meeting of the WaLSA Team Rosseland Centre for Solar Physics, University of Oslo, Norway, 8-12 January 2024

The Temporal and Spatial Evolution of Magnetohydrodynamic Wave Modes in Sunspots

Numerical Simulations of Conversion to Alfvén Waves in Sunspots

On the propagation of gravity waves in the lower solar atmosphere in different magnetic configurations

Waves in the lower solar atmosphere: the dawn of next-generation solar telescopes

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

High-frequency Oscillations in Small Magnetic Elements Observed with Sunrise/SuFI

Numerical Modeling of Magnetohydrodynamic Wave Propagation and Refraction in Sunspots

The Influence of the Magnetic Field on Running Penumbral Waves in the Solar Chromosphere

Theory of solar oscillations in the inertial frequency range:Amplitudes of equatorial modes from a nonlinear rotating convection simulation

The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores

Propagating Spectropolarimetric Disturbances in a Large Sunspot

The effect of linear background rotational flows on magnetoacoustic modes of a photospheric magnetic flux tube

Phase Shifts Measured in Evanescent Acoustic Waves above the Solar Photosphere and Their Possible Impacts on Local Helioseismology

Propagation of transverse waves in the solar chromosphere probed at different heights with ALMA sub-bands

Polarized Kink Waves in Magnetic Elements: Evidence for Chromospheric Helical Waves

Photospheric Observations of Surface and Body Modes in Solar Magnetic Pores

Alfvénic Perturbations in a Sunspot Chromosphere Linked to Fractionated Plasma in the Corona

Wave Damping Observed in Upwardly Propagating Sausage-mode Oscillations Contained within a Magnetic Pore

High-frequency Waves in Chromospheric Spicules

Large scale coherent magnetohydrodynamic oscillations in a sunspot

Slow magneto-acoustic waves in simulations of a solar plage region carry enough energy to heat the chromosphere

The Nature of High-frequency Oscillations Associated with Short-lived Spicule-type Events

Magnetohydrodynamic wave mode identification in circular and elliptical sunspot umbrae: evidence for high order modes

Oscillations observed in umbra, plage, quiet-Sun and the polarity inversion line of AR 11158 using HMI/SDO

The effect of axisymmetric and spatially varying equilibria and flow on MHD wave modes: Cylindrical geometry

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

Finding the mechanism of wave energy flux damping in solar pores using numerical simulations

Solar inertial modes: Observations, identification, and diagnostic promise

Magnetic fields and the supply of low-frequency acoustic wave energy to the solar chromosphere

Magnetoacoustic wave energy dissipation in the atmosphere of solar pores

Transverse motions in sunspot super-penumbral fibrils

Torsional oscillations within a magnetic pore in the solar photosphere

Wave phenomena in sunspots

The Effects of Transients on Photospheric and Chromospheric Power Distributions

An overall view of temperature oscillations in the solar chromosphere with ALMA

Evolution of Complex 3D Motions in Spicules

The Sun at millimeter wavelengths — II. Small-scale dynamic events in ALMA Band 3

Numerical Simulations of Quiet Sun Oscillations

Collisional ionisation, recombination and ionisation potential in two-fluid slow-mode shocks: analytical and numerical results

The dynamics of 3-minute wavefronts and their relation to sunspot magnetic fields

High-frequency oscillations in small chromospheric bright features observed with ALMA

Acoustic-gravity wave propagation characteristics in 3D radiation hydrodynamic simulations of the solar atmosphere

Oscillations on Width and Intensity of Slender Ca ii H Fibrils from Sunrise/SuFI

Vortices evolution in the solar atmosphere

Unveiling the magnetic nature of chromospheric vortices

Magnetohydrodynamic Nonlinearities in Sunspot Atmospheres: Chromospheric Detections of Intermediate Shocks

Third meeting of the WaLSA Team / Theo Murphy international scientific meeting Chicheley Hall of The Royal Society, UK, 10-11 February 2020

Long-period magnetic field oscillations and motions in isolated sunspots

A chromospheric resonance cavity in a sunspot mapped with seismology

The Magnetic Response of the Solar Atmosphere to Umbral Flashes

Two-fluid simulations of waves in the solar chromosphere

Spiral-shaped wavefronts in a sunspot umbra

Second meeting of the WaLSA Team Oslo, Norway, 12-16 August 2019

Semi-empirical model atmospheres for the chromosphere of the sunspot penumbra and umbral flashes

Transverse Oscillations in Slender Ca ii H Fibrils Observed with Sunrise/SuFI

Observations of ubiquitous compressive waves in the Sun’s chromosphere

Signatures of running penumbral waves in sunspot photospheres

Photospheric observations of surface and body modes in solar magnetic pores

Alfvén wave dissipation in the solar chromosphere

Kickoff meeting of the WaLSA Team Oslo, Norway, 7-11 January 2019

Sixth meeting of the WaLSA Team
Rosseland Centre for Solar Physics, University of Oslo, Norway, 8-12 January 2024

Theory of solar oscillations in the inertial frequency range:
Amplitudes of equatorial modes from a nonlinear rotating convection simulation

Third meeting of the WaLSA Team / Theo Murphy international scientific meeting
Chicheley Hall of The Royal Society, UK, 10-11 February 2020

Second meeting of the WaLSA Team
Oslo, Norway, 12-16 August 2019

Kickoff meeting of the WaLSA Team
Oslo, Norway, 7-11 January 2019