arXiv subjects

Shahin Jafarzadeh

Publications and source records attributed to Shahin Jafarzadeh.

At least 19 recordsLinked to original sources

arXiv2026

Delayed, Line-dependent Reorganization of Pore Oscillations Following a Compact C8.2 Flare Observed by Sunrise III/SUSI

Magnetic oscillations permeating the solar atmosphere can be altered by flares. This could be due to changes in the atmospheric magnetic waveguide, the thermodynamic stratification, or both. To investigate this, we examine oscillations in a magnetic pore crossed in part by the ribbon of a C8.2 flare, using observations from the Sunrise Ultraviolet Spectropolarimeter and Imager (SUSI) aboard Sunrise III. We track the core intensities of eight spectral lines between 327-329 nm and show that oscillatory power in the 4.2-7.0 mHz range, measured around 30 minutes after the flare peak, exceeds the pre-event value in all eight lines by factors of 1.60-8.71. Conversely, in the 7.0-11.5 mHz band, the post-event intensity power is lower - approximately 0.13-0.41 of the original power in seven of the observed lines. Line-center velocity measurements support the lower-frequency enhancement. This delayed, line-dependent shift toward the lower-frequency band is consistent with flare-induced changes in wave transmission, reflection, or resonant response, although thermodynamic and magnetic effects cannot yet be separated.

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arXiv2026

The umbrella effect: Magnetic canopy topology modulates spatially averaged chromospheric three-minute power

Three-minute ($\sim$5 mHz) oscillations are a prominent signature of wave propagation in the solar chromosphere, but their measured power can vary substantially between full-disc observations and small, high-resolution fields of view. We investigate whether chromospheric magnetic canopy topology, particularly its lateral continuity and areal filling, modulates field-of-view-averaged three-minute power. We analyse H$α$ and Ca II 8542 Å spectral imaging from the Swedish 1-m Solar Telescope, comparing canopy-poor quiet-Sun scenes with canopy-dominated active-region environments, complemented by radiative-MHD Bifrost simulations of canopy-poor and canopy-rich atmospheres. We compute field-of-view-averaged power spectra from fixed-wavelength intensities and bisector-derived velocities in the observations, and from synthetic intensities, velocities, and temperature proxies in the simulations. We also quantify the relation between integrated 3-5 mHz excess power and canopy filling factor, using HMI-based magnetic-field extrapolations for the observations. In both observations and simulations, canopy-poor scenes show clear 3-5 mHz power enhancements, whereas canopy-dominated scenes show strongly reduced measured power. The trend is present in H$α$ and Ca II 8542 Å intensities and is supported by complementary velocity and temperature proxies. Integrated 3-5 mHz excess power decreases with increasing canopy filling factor. We conclude that chromospheric field-of-view-averaged three-minute power is a topology-weighted observable: dense, laterally continuous magnetic canopies can strongly reduce the measured large-scale three-minute signature without requiring the absence of local wave activity. This provides a practical criterion for interpreting chromospheric oscillation power as a proxy for atmospheric wave energy in the Sun and in magnetised cool-star atmospheres.

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arXiv2026

Height Dependent Phase Shifts of Wave Pulses in the Lower Solar Atmosphere Measured with SUNRISE III

We report on the measurement of the height-dependent time shifts of wave pulses in the lower solar atmosphere from high-resolution spectro-polarimetric observations obtained with the SUSI instrument on board the SUNRISE III balloon-borne solar observatory during its successful science flight in July 2024. The line-of-sight velocities derived from the line-core positions of 19 spectral lines in a 2 nm-wide window around the Ca II H line were used to determine the time shifts of propagating pulses at their respective formation heights. Our analysis reveals that these shifts are roughly ordered according to the computed formation heights of the respective spectral lines. A statistical analysis of the time shifts using sit-and-stare observations with a total duration of one hour reveals that wave pulses propagating upwards from near the solar surface to heights of approximately 500-700 km are most common, with average time lags of 20 s to 30 s between these heights. Also present are pulses with close-to-zero phase shifts, predominantly above intergranular lanes and areas of enhanced magnetic activity. Additionally, downward propagating wave pulses with negative time lags of 10 s to 15 s are seen, mostly above areas of enhanced magnetic activity. A common feature of all the observed pulses is that in the lower 250 km they show small time lags of zero to a few seconds, and only at higher layers do the propagating pulses become more dominant. This study demonstrates the potential of the many-line approach for investigating the height dependence of the physical conditions in the solar atmosphere.

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arXiv2026

Multi-height Identification of Sausage and Fluting Eigenmodes in a Solar Pore

Magnetic pores are compact, strongly magnetised waveguides in the lower solar atmosphere and therefore provide favourable conditions for identifying magnetohydrodynamic (MHD) wave modes. Earlier seeing-free observations revealed concurrent sausage, kink, and fluting modes in photospheric pores, but only at a single sampled layer. In this Letter, we exploit the dense spectral sampling of the near-ultraviolet 327-329 nm window observed by the Sunrise-III UV Spectropolarimeter and Imager (SUSI) to investigate how pore wave modes behave across multiple photospheric and low-chromospheric heights spanning roughly 500 km. We analyse ~75 min of a Sunrise-III/SUSI time series containing a small solar pore. From eight selected spectral lines sampling different estimated formation heights, we identify the pore boundary at each line and time step and apply proper orthogonal decomposition (POD) to the boundary oscillations. In all eight lines, the first POD mode is consistently identified as an axisymmetric sausage mode, with dominant power at ~1-2 mHz, and carries the dominant normalised eigenvalue fraction, typically about 66-86%, while the second mode is a fluting mode with azimuthal wave number m = 2, dominant at ~2-3.5 mHz, and contributes about 4-10%. Cross-line wavelet phase analysis of the temporal coefficients shows that the sausage mode remains close to zero phase difference across the sampled heights, consistent with standing or near-standing behaviour, whereas the fluting mode displays a modest but systematic increase in phase with height, reaching about 50 degrees, indicative of an upward-propagating component. These observations provide the first multi-height identification and phase characterisation of sausage and fluting modes inferred from pore-boundary oscillations.

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arXiv2026

Standing oscillations in a resonant sunspot atmosphere captured by integral field spectroscopy

The solar atmosphere is replete with magnetohydrodynamic wave activity, with magnetic structures such as sunspots channelling wave energy flux efficiently into the outer atmosphere. Steep density and temperature gradients between the photosphere and chromosphere provide ideal conditions for magnetoacoustic resonance cavities, amplifying $\sim 5$ mHz oscillatory power in sunspot atmospheres. However, diagnosis of such cavities has largely been limited to lines such as Ca II H/K and He I 10830 Å, with no evidence yet from layers probed by the Na I D$_1$/D$_2$ doublet. Here we use the newly commissioned integral field unit FRANCIS to examine oscillations spanning the formation heights of the Na I D$_1$/D$_2$ lines and determine whether propagating and/or standing modes are present within a sunspot umbra. The RH1.5D code estimated formation heights for three windows: the Na I D$_1$ wing (core $-300$ mÅ; $\approx 355$ km), the Na I D$_1$ core ($\approx 750$ km), and the Na I D$_2$ core ($\approx 850$ km). Wavelet cross-correlation of line-core and bisector Doppler velocities yielded phase spectra versus height, classifying the dominant $\sim 5.5$ mHz oscillations as propagating or standing-like. At the umbra-penumbra boundary we find propagating modes with energy fluxes of $\sim 1.3 \times 10^{4}$ W m$^{-2}$ in the upper photosphere, falling to $\sim 3.1 \times 10^{3}$ W m$^{-2}$ in the lower chromosphere, implying a damping length $L_d \approx 363$ km, comparable to the local density scale height. In contrast, near-zero phase differences dominate regions of enhanced chromospheric power at the umbral centre, evidencing standing-wave behaviour and resonance-cavity dynamics. These results demonstrate the suitability of solar integral field units for mapping sunspot wave properties, with the Na I D$_1$/D$_2$ lines offering a novel diagnostic of resonance cavities and energy flux.

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arXiv2026

Multi-line Wave Signatures in a Sunspot from Near-UV Sunrise III/SUSI Observations

Magnetohydrodynamic waves redistribute energy in magnetic structures of the lower solar atmosphere, yet constraints on how wave power and dominant frequencies are organised above sunspots remain limited because most studies use only a few well-separated diagnostics. Here we present multiline wave signatures in a sunspot from near-UV spectroscopy with the Sunrise-III UV Spectropolarimeter and Imager (SUSI). We analyse a two-hour time series of repeated raster scans of a sunspot near disc centre in the 327-329 nm spectral window (> 100 lines). From these, we select 44 lines that radiative-transfer calculations suggest sample effective formation heights within the umbral core from deep photosphere toward the low chromosphere. For each line, we extract line-core intensity and line-of-sight velocity time series using a dedicated multi-line fitting routine and compute Morlet-wavelet power spectra. The refined global wavelet spectra show that most lines (in both intensity and velocity) are genuinely multi-frequency, with a dominant peak and substantial statistically significant power up to 12 mHz. Unsupervised clustering of the normalised spectra groups lines into families with similar spectral shapes and reveals a progression of dominant frequencies from ~2 to ~10 mHz across the ensemble, for both intensity and velocity (not necessarily in the same lines). This behaviour is not reproduced by a simple formation-height ranking, suggesting that uncertainties in the formation-height estimates and line-dependent diagnostic response together shape the ordering. These Sunrise-III/SUSI observations open a new regime for near-UV multi-line wave studies and provide the first systematic characterisation of frequency-structured sunspot wave behaviour in this spectral region.

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arXiv2026

Magnetically Structured Oscillatory Power Along an Active-Region Transect in Near-UV Sunrise-III/SUSI Spectroscopy

We present a multi-line characterisation of how oscillatory power is organised across distinct magnetic environments in an active region using seeing-free, stratospheric near-ultraviolet spectroscopy from the Sunrise-III UV Spectropolarimeter and Imager (SUSI). A two-hour time series of short raster scans in the line-rich 327-329 nm window samples along a single transect that contains the following regions: weak magnetic-field surroundings, a plage, a sunspot, and a pore. From a set of 30 selected, relatively unblended absorption lines, we extract line-core Doppler-velocity time series and compute Morlet-wavelet refined global spectra from which we form band-integrated power maps for three frequency bands (2-4, 4-6, and 6-12 mHz). The stacked, line-resolved maps reveal a clear environment-dependent redistribution of power: 2-4 mHz power is strongest in the weak-field/plage segments but is commonly suppressed in the umbra and pore cores, while 4-6 mHz and 6-12 mHz power becomes relatively enhanced in the strongest-field regions, with line-dependent behaviour in the penumbra and plage. Across the line ensemble, this broad frequency structuring is coherent, but the detailed spatial distribution and relative band ranking are not identical from line to line - even among spectral lines with comparable effective formation depths - demonstrating clear line dependence. This novel result implies that single-line measurements may miss secondary components of the local wave spectrum because different lines weight co-existing perturbations and modes differently; therefore, the SUSI near-UV window provides a uniquely diagnostic-rich mapping of oscillations, offering leverage that is difficult to obtain with traditional one- or two-line approaches.

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arXiv2026

The Influence of Opacity on Inferred MHD Wave Signatures in the Lower Solar Atmosphere

Magnetohydrodynamic wave activity in small-scale magnetic structures, such as solar pores, provides key insights into energy transport in the lower solar atmosphere. This study presents high-resolution observations of ten solar pores contained within a 43 x 43 Mm$^2$ field of view, obtained with the CRISP instrument at the Swedish 1-m Solar Telescope. We investigate the temporal behaviour of the line-of-sight velocity (vlos) and magnetic field (blos) oscillations within the pore structures. Using SIR inversions, we analyse the oscillatory signals at multiple optical depths (log $τ$ levels) to assess how variations in geometric height (z) and temperature relate to the observed blos fluctuations. Our results reveal that higher-frequency oscillations (> 6 mHz) exhibit strong coherences with in-phase fluctuations between blos and z across atmospheric layers, consistent with upward-propagating magneto-acoustic waves. In contrast, coherent lower-frequency oscillations display significant phase differences, which may arise from opacity effects contaminating the inversion response. These findings highlight the importance of accounting for opacity effects when interpreting magnetic oscillations, with direct implications for forthcoming high-precision magnetic diagnostics from facilities such as DKIST.

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arXiv2026

Adaptive multi-line fitting for stable line-core intensity and Doppler velocity

Next-generation solar spectrographs increasingly record dense wavelength windows in which tens to hundreds of spectral lines are sampled at each spatial location and time step. This expands the scope for multi-line, multi-height diagnostics of magnetohydrodynamic motions, but also raises a practical challenge: deriving stable line-core intensity and line-of-sight velocity time series when profiles evolve rapidly, become asymmetric, blend, or develop multi-lobed cores. Common fast estimators can perform well for simple, isolated absorption lines, yet can intermittently misidentify the core in crowded or morphologically complex cases. Even infrequent mis-tracking can leave step-like artefacts that redistribute power and bias spectral, phase, and coherence measures used in wave and dynamics analyses. We introduce LineFit, a fully reproducible adaptive multi-line fitting approach tailored to dense-window spectroscopy. LineFit models each line locally with bounded non-linear least-squares fits to a Voigt-family profile, including an asymmetric-Voigt option to accommodate unequal wing broadening, and incorporates close-pair ownership control together with conservative, per-line window adaptation and split-core-aware handling. Using a synthetic time series with unambiguous ground truth, we benchmark LineFit against four widely used fast baselines and assess both instantaneous centre errors and downstream time-series diagnostics. Several fast methods remain competitive for many lines, whereas LineFit is most robust in key stress cases involving intermittently split-core profiles and correspondingly yields power spectra that agree most closely with the truth. We also demonstrate a proof-of-principle that benchmarks hybrid acceleration of the LineFit software via supervised emulation, offering at least three orders-of-magnitude improvement in processing time.

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arXiv2025

Science Requirement Document (SRD) for the European Solar Telescope (EST) (3rd Edition, December 2025)

The European Strategy Forum on Research Infrastructures (ESFRI) included the European Solar Telescope (EST) as an ESFRI Project in its 2016 Roadmap and confirmed this status in 2021. During the Preparatory Phase (2017 to 2022), the EST Science Advisory Group (SAG) was established in 2017. Its first task was to revise the Science Requirements Document (SRD), originally formulated in 2011. This second edition of the SRD was published in December 2019 (Schlichenmaier et al. 2019, 2019arXiv191208650S). Since 2019, the EST Project Office has advanced the telescope design and developed the Science Instrumentation Suite (SIS). All telescope subsystems and the SIS have now passed their Design Reviews. Aligned with the discussions and resolutions of the SAG, the SIS comprises three categories of first-generation instruments: (1) Tunable Imaging Spectropolarimeters coupled with Fixed Band Imagers (TIS/FBIs), employing large-aperture Fabry-Pérot etalons; (2) Integral Field Spectropolarimeters based on microlens arrays (IFS-M); (3) The near-infrared spectropolarimeter EMBER (spectropolariMeter Based on slicEr-mirrors for the near-infraRed), using image-slicing technology. This configuration enables simultaneous observations of the same two-dimensional solar region across a broad wavelength range (380-2200 nm), giving EST a uniquely powerful multi-wavelength observing capability. This has made it necessary to revise the Observing Programmes so that they accurately reflect the capabilities of the SIS and ensure that all science objectives can be met. This third edition of the EST SRD integrates the outcomes of numerous SAG meetings held between 2020 and 2025 and incorporates all design developments up to 2025. It updates the Observing Programmes accordingly and assesses their alignment with the scientific objectives defined by the SAG.

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arXiv2025

Small-scale bright point characteristics at high-resolution with the Daniel K. Inouye Solar Telescope

Bright points (BPs) are small-scale, dynamic features that are ubiquitous across the solar disc and are often associated with the underlying magnetic field. Using broadband photospheric images obtained with the Visible Broadband Imager at the National Science Foundation's Daniel K. Inouye Solar Telescope (DKIST), the properties of BPs have been analyzed with DKIST for the first time at the highest spatial resolutions achievable. BPs were observed to have an average lifetime of 95$\pm$29 s and a mean transverse velocity of 1.60$\pm$0.41 km/s. The BPs had a log-normal area distribution with a peak at 2300 km$^2$. Transverse velocity and lifetimes across the DKIST images were comparable and consistent with previous studies. The area distribution of the DKIST data peaked in areas significantly lower than those from the literature. This was explored further and was observed to be due to an overestimation of BP areas due to the merging of close features when the spatial resolution is reduced, in tandem with possible over-splitting of features in the DKIST images. Furthermore, the effect of variable seeing within the data was determined. This showed that the average spatial resolution of the data was around 0.''034$\pm$0.''007 in comparison to the theoretical diffraction-limit of 0.''022. Accounting for the influence of seeing, the peak of the area distribution of BPs in the DKIST data was estimated as 4800 km$^2$, which is still significantly lower than previously observed.

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arXiv2025

Solar Vortices as Conduits for Magnetoacoustic Waves: Multi-Layer Coupling and Their Role in Atmospheric Heating

The Sun's atmosphere hosts swirling plasma structures, known as solar vortices, which have long been thought to channel wave energy into higher layers. Until now, no direct observations have confirmed their role in the heating of the atmosphere. Here, we present the first direct evidence that solar vortices act as structured waveguides, carrying magnetoacoustic modes (waves that behave like sound waves but travel through magnetized plasma) that leave clear wave-heating signatures. By mapping vortex regions at multiple heights and analysing the waves they contain, we show that magnetoacoustic waves efficiently transfer energy, offset losses from radiation, and dominate energy transport in the lower chromosphere. These results challenge the long-standing assumption that vortices primarily support twisting disturbances traveling along magnetic field lines (Alfven waves), revealing instead that magnetoacoustic modes play the leading role in the lower atmosphere. This redefines the role of vortices in magnetized plasmas and has broader implications for wave-plasma interactions in regions of strong magnetic fields.

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arXiv2024

The Sun at millimeter wavelengths V. Magnetohydrodynamic waves in a fibrillar structure

Magnetohydrodynamic (MHD) waves, playing a crucial role in transporting energy through the solar atmosphere, manifest in various chromospheric structures. Here, we investigated MHD waves in a long-lasting dark fibril using high-temporal-resolution (2~s cadence) Atacama Large Millimeter/submillimeter Array (ALMA) observations in Band 6 (centered at 1.25~mm). We detected oscillations in brightness temperature, horizontal displacement, and width at multiple locations along the fibril, with median periods and standard deviations of $240\pm114$~s, $225\pm102$~s, and $272\pm118$~s, respectively. Wavelet analysis revealed a combination of standing and propagating waves, suggesting the presence of both MHD kink and sausage modes. Less dominant than standing waves, oppositely propagating waves exhibit phase speeds (median and standard deviation of distributions) of $74\pm204$~km/s, $52\pm197$~km/s, and $28\pm254$~km/s for the three observables, respectively. This work demonstrates ALMA's capability to effectively sample dynamic fibrillar structures, despite previous doubts, and provides valuable insights into wave dynamics in the upper chromosphere.

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arXiv2024

ALMA Memo 628 -- High-cadence observations of the Sun

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic capabilities for studying the Sun, providing complementary insights through high spatial and temporal resolution at millimeter wavelengths. ALMA acts as a linear thermometer for atmospheric gas, aiding in understanding the solar atmosphere's structure, dynamics, and energy balance. Given the Sun's complex emission patterns and rapid evolution, high-cadence imaging is essential for solar observations. Snapshot imaging is required, though it limits available visibility data, making full exploitation of ALMA's capabilities non-trivial. Challenges in processing solar ALMA data highlight the need for revising and enhancing the solar observing mode. The ALMA development study High-Cadence Imaging of the Sun demonstrated the potential benefits of high cadence observations through a forward modelling approach. The resulting report provides initial recommendations for improved post-processing solar ALMA data and explores increasing the observing cadence to sub-second intervals to improve image reliability.

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arXiv2024

Observation of Alfvén Wave Reflection in the Solar Chromosphere: Ponderomotive Force and First Ionization Potential Effect

We investigate the propagation of Alfvén waves in the solar chromosphere, distinguishing between upward and downward propagating waves. We find clear evidence for the reflection of waves in the chromosphere and differences in propagation between cases with waves interpreted to be resonant or nonresonant with the overlying coronal structures. This establishes the wave connection to coronal element abundance anomalies through the action of the wave ponderomotive force on the chromospheric plasma, which interacts with chromospheric ions but not neutrals, thereby providing a novel mechanism of ion-neutral separation. This is seen as a "First Ionization Potential Effect" when this plasma is lifted into the corona, with implications elsewhere on the Sun for the origin of the slow speed solar wind and its elemental composition.

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arXiv2022

The Sun at millimeter wavelengths IV. Magnetohydrodynamic waves in small-scale bright features

We used solar observations of a plage/enhanced network with the Atacama Large Millimeter/sub-millimeter Array (ALMA) in Band 3 and Band 6 together with synthetic continuum maps from numerical simulations with Bifrost at the same bands to carry out a detailed study of bright small-scale magnetic features. To this end, we have used an algorithm to automatically identify and trace the features within the field of view (FoV) of the observations and the simulation. We found 193 and 293 features in the Bands 3 and 6 observations, respectively. In the degraded simulation, the total number of features were 24 for Band 3 and 204 for Band 6. In the original simulation, the total number of features were 36 for Band 3 and 392 for Band 6. Based on the simulation, we confirm the magnetic nature of the features which exhibit an oscillatory behaviour in temperature, size and horizontal velocity. The average oscillation periods were of 30-99\,s for temperature, 37-92\,s for size and 37-78\,s for horizontal velocity. There are indications for the possible presence of transverse (kink) waves with average amplitude velocities of 2.1-5.0\,km\,s$^{-1}$. An anti-phase behaviour between temperature and size oscillations suggest the presence of compressible fast-sausage Magnetohydrodynamics (MHD) modes. Finally, we have estimated the flux of energy of the fast-sausage waves at the chromospheric heights sampled by ALMA as 453-1838\,W\,m$^{-2}$ for Band 3 and 3640-5485\,W\,m$^{-2}$ for Band 6. The decrease of wave energy-flux with height (from Band 6 to Band 3) could possibly suggest energy dissipation at chromospheric heights, thus wave heating, with the assumptions that the identified small-scale waves are typical at each band and they propagate upward through the chromosphere.

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arXiv2022

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.

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arXiv2022

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 $73\pm16$~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 $\approx96$~km/s, resulting in a mean energy flux of $3800$\,W/m$^2$.

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