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Reply to: Signatures of sunspot oscillations and the case for chromospheric resonances

Authors:
David B. Jess at Queen's University Belfast
David B. Jess
Ben Snow at University of Exeter
Ben Snow
Bernhard Fleck at European Space Agency
Bernhard Fleck
Marco Stangalini
Marco Stangalini
Marco Stangalini
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Figures

The telescope pointing stability achieved on 2016 July 14 The rigid shifts in both the solar north–south (top) and east–west (middle) directions required to co-align consecutive ROSA 4170 Å continuum images, which were acquired contemporaneously with our He i 10830 Å spectra, are shown for the duration of the observations presented in ref. ¹. The image-by-image cross-correlation coefficients (bottom) are high, a result of solar north–south and east–west r.m.s. fluctuations on the order of 0.073″, demonstrating excellent seeing conditions. The increased fluctuations seen at times of ~2,835 s and ~5,100 s are caused by the passing of a thin cirrus cloud, with the latter resulting in the termination of the observing sequence.
The telescope pointing stability achieved on 2016 July 14 The rigid shifts in both the solar north–south (top) and east–west (middle) directions required to co-align consecutive ROSA 4170 Å continuum images, which were acquired contemporaneously with our He i 10830 Å spectra, are shown for the duration of the observations presented in ref. ¹. The image-by-image cross-correlation coefficients (bottom) are high, a result of solar north–south and east–west r.m.s. fluctuations on the order of 0.073″, demonstrating excellent seeing conditions. The increased fluctuations seen at times of ~2,835 s and ~5,100 s are caused by the passing of a thin cirrus cloud, with the latter resulting in the termination of the observing sequence.
… 
Spectral energies of the original and degraded He i 10830 Å observations a–d, The calculated He i 10830 Å spectral energies of the original data products (a), and those degraded by convolving time- and wavelength-dependent PSFs corresponding to 0.75″ (b), 1.00″ (c) and 1.50″ (d) seeing conditions. The coloured lines represent spectra derived across the entire sunspot umbral diameter (shaded blue to pink), whereas the solid black lines represent the average umbral spectral energies. It is clear that reduced image quality, caused by worsening seeing conditions and hence poorer spatial resolution, reduce the clarity of high-frequency fluctuations and promote a more rapid spectral energy decline after the dominant ~6 mHz peak.
Spectral energies of the original and degraded He i 10830 Å observations a–d, The calculated He i 10830 Å spectral energies of the original data products (a), and those degraded by convolving time- and wavelength-dependent PSFs corresponding to 0.75″ (b), 1.00″ (c) and 1.50″ (d) seeing conditions. The coloured lines represent spectra derived across the entire sunspot umbral diameter (shaded blue to pink), whereas the solid black lines represent the average umbral spectral energies. It is clear that reduced image quality, caused by worsening seeing conditions and hence poorer spatial resolution, reduce the clarity of high-frequency fluctuations and promote a more rapid spectral energy decline after the dominant ~6 mHz peak.
… 
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Matters arising
https://doi.org/10.1038/s41550-020-1158-4
1Astrophysics Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast, UK. 2Department of Physics and Astronomy,
California State University Northridge, Northridge, CA, USA. 3Centre for Geophysical and Astrophysical Fluid Dynamics, University of Exeter, Exeter, UK.
4Science and Operations Department, ESA, Greenbelt, MD, USA. 5Italian Space Agency (ASI), Rome, Italy. 6INAF-OAR National Institute for Astrophysics,
Monte Porzio Catone (RM), Italy. 7Institute of Theoretical Astrophysics, University of Oslo, Oslo, Norway. 8Rosseland Centre for Solar Physics, University
of Oslo, Oslo, Norway. ✉e-mail: d.jess@qub.ac.uk
In our paper1, we studied a fully formed active region that was
approximately halfway through its evolutionary lifecycle, and exam-
ination of the Fourier-derived spectral energies of the sunspot umbra
revealed a spectral ‘bump’ at ~20 mHz. Furthermore, the spectral
gradients following the ~20 mHz energy enhancement changed
progressively across the umbral diameter, implying that they may
reflect the intrinsic characteristics of the underlying umbral atmo-
sphere. Numerical simulations of the sunspot atmosphere, harness-
ing the Lagrangian–Eulerian remap2 (LareXd) code, also revealed
spectral energy variability at ~20 mHz (including changing spectral
slopes). These results were consistent with the pioneering theoreti-
cal work of Botha etal.3 and Snow etal.4, allowing us to interpret
these as a signature of wave resonance arising from the temperature
gradients naturally occurring in the solar photosphere and transi-
tion region. At the time of publication, we recognized that we had
observed strong evidence of resonance behaviour in a single, iso-
lated sunspot structure. As a result, in the supplementary informa-
tion of our paper1, we openly posed a number of key outstanding
questions, and requested that the community examine sunspot
wave phenomena on a statistical basis to verify how commonplace
resonance signatures are.
The Matters Arising by Felipe5 highlights the observational and
modelling challenges facing solar physicists in the modern era of
high temporal, spatial and spectral resolutions. We welcome this
particular side of his communication, as it directly reflects the open
questions we posed in the supplementary information of our Letter.
Considering our paper, Felipe remarks that: (1) the observational
power spectra of sunspots do not always demonstrate consistent sig-
natures that can be used as an indicator for the presence of a reso-
nance cavity; (2) theoretical time series can generate spectral energy
enhancements that are not solely linked to resonance effects; and (3)
the interplay between linear and nonlinear effects is likely to play a
role in the features observed in both simulated and observed power
spectra. In the following, we address the points raised by Felipe to
highlight the importance of ongoing research in this challenging
scientific field.
He
i
10830Å sunspot observations
Felipe highlighted that the observations we presented were
“extraordinary”. The quality of the atmospheric seeing can be esti-
mated by the root mean squared (r.m.s.) fluctuations required to
co-align (on a sub-pixel level) successive image from our time
series. For this task, the contemporaneous 4170 Å blue continuum
imaging observations obtained with the Rapid Oscillations in the
Solar Atmosphere6 (ROSA) instrument were employed, as these
were acquired with short exposure times (5 ms) to prevent any
seeing-induced smearing from effecting the cross-correlations, and
the highest cadence (2.11 s after image reconstruction). In total,
there were 2,468 ROSA frames, spanning 5,207.48 s (~87 min).
Figure 1 documents the absolute sub-pixel shifts in both solar
north–south and east–west directions, calculated from the
cross-correlation coefficients. At a time of ~2,835 s into the observ-
ing sequence, there is a degradation of the image quality caused
by a passing cirrus cloud. However, the original adaptive optics
(AO) lock point was restored once this had completely passed (at
~3,060 s) and the pointing accuracy continued to be excellent until
5,100 s, when the seeing degraded and we terminated the observa-
tions. On the basis of the raw (sub-pixel) shifts, the r.m.s. fluctua-
tions are 0.070″ and 0.073″ for the solar east–west and north–south
directions, respectively. These r.m.s. pointing fluctuations are less
than half of our He 10830 Å pixel sampling (0.15″ per pixel),
showing the high image stability achieved during our observations.
We believe that the excellent seeing conditions are responsible for
the clarity of the heightened spectral energy bump at ~20 mHz. To
test this hypothesis, we generated time- and wavelength-dependent
point spread functions (PSFs) corresponding to 0.75″, 1.00″ and
1.50″ seeing conditions. The PSFs model the AO residual aberra-
tions at the Dunn Solar Telescope focal plane for the three different
seeing conditions. These were obtained from simple closed-loop
AO numerical simulations carried out with the PAOLA simulation
code7. These PSFs, specific to the He  10830 Å line, were convolved
with the original spectra to degrade its spatial resolution, before
recomputing the corresponding spectral energy densities. Figure 2
reveals the importance of seeing conditions when exploring the
high-frequency regime, with the secondary bump at ~20 mHz
reduced with 0.75″ seeing, barely visible with 1.00″ seeing and com-
pletely suppressed with 1.50″ seeing conditions. Furthermore, it can
be seen from Fig. 2 that the steepness of the spectral slope following
the dominant peak at ~6 mHz is dependent on the quality of the
local seeing conditions, with higher frequency fluctuations heavily
damped (by more than an order of magnitude) as the seeing con-
ditions degrade. Therefore, spectral energy spectra showing very
steep gradients immediately after the universal ~6 mHz dominant
peak may not be suitable for such resonance studies, which require
prolonged periods of excellent seeing conditions. Hence, the impor-
tance of spatial resolution, which is often intrinsically coupled
Reply to: Signatures of sunspot oscillations and
the case for chromospheric resonances
David B. Jess 1,2 ✉ , Ben Snow 3, Bernhard Fleck 4, Marco Stangalini 5,6 and Shahin Jafarzadeh 7,8
replying to T. Felipe Nature Astronomy https://doi.org/10.1038/s41550-020-1157-5 (2020)
NATURE ASTRONOMY | VOL 5 | JANUARY 2021 | 5–8 | www.nature.com/natureastronomy 5
Content courtesy of Springer Nature, terms of use apply. Rights reserved
... This model is based on the presence of a resonant cavity in sunspot chromospheres that is produced by waves that are trapped between the temperature gradients of the transition region and the photosphere (Zhugzhda & Locans 1981;Zhugzhda 2008). The existence of this cavity above sunspot umbrae was recently confirmed (see Jess et al. 2020Jess et al. , 2021Felipe et al. 2020;Felipe 2021). ...
Observations of umbral flashes in the resonant sunspot chromosphere
Article
Full-text available
  • Dec 2024
  • ASTRON ASTROPHYS
Context. In sunspot umbrae, the core of some chromospheric lines exhibits periodic brightness enhancements known as umbral flashes. The consensus is that they are produced by the upward propagation of shock waves. This view has recently been challenged by the detection of downflowing umbral flashes and the confirmation of a resonant cavity above sunspots. Aims. We aim to determine the propagating or standing nature of the waves in the low umbral chromosphere and confirm or refute the existence of downflowing umbral flashes. Methods. Spectroscopic temporal series of Ca II 8542 Å, Ca II H, and H α in a sunspot were acquired with the Swedish Solar Telescope. The H α velocity was inferred using bisectors. Simultaneous inversions of the Ca II 8542 Å line and the Ca II H core were performed using the code NICOLE. The nature of the oscillations were determined and insights into the resonant oscillatory pattern were gained by analyzing the phase shift between the velocity signals and examining the temporal evolution. Results. Propagating waves in the low chromosphere are more common in regions with frequent umbral flashes, where the transition region is shifted upward, making resonant cavity signatures less noticeable. In contrast, areas with fewer umbral flashes show velocity fluctuations that align with standing oscillations. Evidence suggests dynamic changes in the location of velocity-resonant nodes due to variations in the transition region height. Downflowing profiles appear at the onset of some umbral flashes, but upflowing motion dominates during most of the flash. These downflowing flashes are more common in standing umbral flashes. Conclusions. We confirm the existence of a chromospheric resonant cavity above sunspot umbrae. It is produced by wave reflections at the transition region. The oscillatory pattern depends on the transition region height, which exhibits spatial and temporal variations due to the impact of the waves.
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... Besides depending on the size of the structure and spatial resolution of the observations, the identification of wave modes is affected by the variable seeing due to the Earth's atmosphere (Jess et al. 2021b). As such, seeing-free observations of (spatially resolved) small-scale magnetic structures from space can better guarantee the absence of spurious signals and/or disturbances arising from the Earth atmospheric turbulence. ...
Sausage, kink, and fluting magnetohydrodynamic wave modes identified in solar magnetic pores by Solar Orbiter/PHI
Article
Full-text available
  • May 2024
Solar pores are intense concentrations of magnetic flux that emerge through the solar photosphere. When compared to sunspots, they are much smaller in diameter and can therefore be affected and buffeted by neighbouring granular activity to generate significant magnetohydrodynamic (MHD) wave energy flux within their confines. However, observations of solar pores from ground-based telescope facilities may struggle to capture subtle motions that are synonymous with higher-order MHD wave signatures because of the seeing effects that are produced in the Earth's atmosphere. Hence, we exploited timely seeing-free and high-quality observations of four small magnetic pores from the High Resolution Telescope (HRT) of the Polarimetric and Helioseismic Imager (PHI) on board the Solar Orbiter spacecraft during its first close perihelion passage in March 2022 (at a distance of 0.5 au from the Sun). Through acquisition of data under stable observing conditions, we were able to measure the area fluctuations and horizontal displacements of the solar pores. Cross correlations between perturbations in intensity, area, line-of-sight velocity, and magnetic fields, coupled with the first-time application of novel proper orthogonal decomposition techniques on the boundary oscillations, provided a comprehensive diagnosis of the embedded MHD waves as sausage and kink modes. Additionally, the previously elusive m=2 fluting mode is identified in the most magnetically isolated of the four pores. An important consideration lies in how the identified wave modes contribute to the transfer of energy into the upper solar atmosphere. Approximately 56 , 72 , 52 , and 34 of the total wave energy of the four pores we examined is associated with the identified sausage modes and about 23 , 17 , 39 , and 49 with their kink modes, while the first pore also receives a contribution of about 11 linked to the fluting mode. This study reports the first-time identification of concurrent sausage, kink, and fluting MHD wave modes in solar magnetic pores.
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... Different temperature profiles of the sunspot's umbra would lead to different peaks in the spectrum of the chromospheric resonator, explaining the frequency variation in the sunspot oscillation. The existence of a chromospheric resonator is a matter of some debate (Felipe & Sangeetha 2020;Jess et al. 2020Jess et al. , 2021Felipe et al. 2021) but opinion seems to be moving in its favor. Recent numerical modeling by Felipe & Sangeetha (2020) reveals that different profiles of the chromospheric temperature and density lead to variations in the cutoff frequency (that are quite different from analytic model predictions) so we would expect this to affect the observed frequency of oscillation. ...
Enhanced Three-minute Oscillation above a Sunspot during a Solar Flare
Article
Full-text available
  • Jan 2024
Three-minute oscillations are a common phenomenon in the solar chromosphere above a sunspot. Oscillations can be affected by the energy release process related to solar flares. In this paper, we report on an enhanced oscillation in flare event SOL2012-07-05T21:42 with a period of around 3 minutes that occurred at the location of a flare ribbon at a sunspot umbral–penumbral boundary and was observed in both chromospheric and coronal passbands. An analysis of this oscillation was carried out using simultaneous ground-based observations from the Goode Solar Telescope at the Big Bear Solar Observatory and space-based observations from the Solar Dynamics Observatory. A frequency shift was observed before and after the flare, with the running penumbral wave that was present with a period of about 200 s before the flare coexisting with a strengthened oscillation with a period of 180 s at the same locations after the flare. We also found a phase difference between different passbands, with the oscillation occurring from high-temperature to low-temperature passbands. Theoretically, the change in frequency was strongly dependent on the variation of the inclination of the magnetic field and the chromospheric temperature. Following an analysis of the properties of the region, we found the frequency change was caused by a slight decrease of the magnetic inclination angle with respect to the local vertical. In addition, we suggest that the enhanced 3 minute oscillation was related to the additional heating, maybe due to the downflow, during the EUV late phase of the flare.
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... Equation (13) characterizes very nicely the impact spatial resolution has on the visible wave characteristics, whereby when the resolution element is larger than the characteristic physical scale of the observed process in the solar atmosphere (i.e., FWHM [ s 0 ), then the oscillatory signal is strongly suppressed. This may result in weak oscillatory amplitudes being lost from the final data products, a process that was recently discussed by Jess et al. (2021b) in the context of sunspot oscillations. The dashed red line displays an exponential fit (using Eq. (13)), with the fit parameters shown in the figure legend. ...
Waves in the lower solar atmosphere: the dawn of next-generation solar telescopes
Article
Full-text available
  • Jan 2023
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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... The angular resolution affects the detection and identification of small-scale features in the spatial domain, but it also affects variations and oscillations in the temporal domain of the data (Jess et al. 2021;Eklund et al. 2021b;Jafarzadeh et al. 2021). The degree of the degradation of a particular feature is dependent on the angular resolution, but also the distribution and spatial scales of the surrounding intensities. ...
Deep solar ALMA neural network estimator for image refinement and estimates of small-scale dynamics
Article
Full-text available
  • Jan 2023
Context. The solar atmosphere is highly dynamic, and observing the small-scale features is valuable for interpretations of the underlying physical processes. The contrasts and magnitude of the observable signatures of small-scale features degrade as angular resolution decreases. Aims. The estimates of the degradation associated with the observational angular resolution allows a more accurate analysis of the data. Methods. High-cadence time-series of synthetic observable maps at λ = 1.25 mm were produced from three-dimensional magnetohydrodynamic Bifrost simulations of the solar atmosphere and degraded to the angular resolution corresponding to observational data with the Atacama Large Millimeter/sub-millimeter Array (ALMA). The deep solar ALMA neural network estimator (Deep-SANNE) is an artificial neural network trained to improve the resolution and contrast of solar observations. This is done by recognizing dynamic patterns in both the spatial and temporal domains of small-scale features at an angular resolution corresponding to observational data and correlated them to highly resolved nondegraded data from the magnetohydrodynamic simulations. A second simulation, previously never seen by Deep-SANNE, was used to validate the performance. Results. Deep-SANNE provides maps of the estimated degradation of the brightness temperature across the field of view, which can be used to filter for locations that most probably show a high accuracy and as correction factors in order to construct refined images that show higher contrast and more accurate brightness temperatures than at the observational resolution. Deep-SANNE reveals more small-scale features in the data and achieves a good performance in estimating the excess temperature of brightening events with an average of 94.0% relative to the highly resolved data, compared to 43.7% at the observational resolution. By using the additional information of the temporal domain, Deep-SANNE can restore high contrasts better than a standard two-dimensional deconvolver technique. In addition, Deep-SANNE is applied on observational solar ALMA data, for which it also reveals eventual artifacts that were introduced during the image reconstruction process, in addition to improving the contrast. It is important to account for eventual artifacts in the analysis. Conclusions. The Deep-SANNE estimates and refined images are useful for an analysis of small-scale and dynamic features. They can identify locations in the data with high accuracy for an in-depth analysis and allow a more meaningful interpretation of solar observations.
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... Indeed, including the standard errors, each line-depth interval straddles the zero degree phase threshold, suggesting the presence of standing mode waves in the pores at chromospheric heights. Standing compressible modes have previously been observed in chromospheric magnetic flux tubes, with Freij et al. (2016) postulating that the reflection occurs at the transition region boundary, and could be indicative of a chromospheric resonator Jess et al. 2020;Felipe 2021;Jess et al. 2021). The viability of this reflection region can be assessed through calculating the typical wavelength of these standing modes. ...
The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores
Article
Full-text available
  • Oct 2022
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.
View
Spatial Structure of Resonance Cavities in Sunspots
Article
Full-text available
  • Feb 2024
  • MON NOT R ASTRON SOC
We present a study of wave processes in sunspots from active regions NOAA 11131 on 10 December 2010 and NOAA 12565 on 14 July 2016 observed by SDO/AIA in the 1600Å, 304Å and 171Å temperature channels. To study the spatial structure of the resonance cavities previously found by Jess et al. (2020), we applied spectral data processing techniques such as pixelised wavelet filtering (PWF) and mode decomposition (PMD). For the first time, we found stable regions as waveguides of the oscillations in the sunspot umbra, occupying specific frequency ranges without spatial overlap. The sizes of these regions depend on the frequency oscillations, and the maximum frequency coincides with the values of the harmonics of the main oscillation mode. Frequency drifts were observed in the band occupied by these regions, with different spectral slopes depending on the location of the sources in the sunspot umbra. We suggest that the observed distribution of wave sources in the umbra is a set of resonant cavities where successive amplification of oscillations at selected multiple harmonics is observed. The distribution of sources at low frequencies indicates the influence of the atmospheric cutoff due to the inclinations of the magnetic field lines.
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Impact of opacity effects on chromospheric oscillations inferred from NLTE inversions
Article
Full-text available
  • Jan 2023
Context. Spectropolarimetric inversions are a fundamental tool for diagnosing the solar atmosphere. Chromospheric inferences rely on the interpretation of spectral lines that are formed under nonlocal thermodynamic equilibrium (NLTE) conditions. In the presence of oscillations, changes in the opacity impact the response height of the spectral lines and hinder the determination of the real properties of the fluctuations. Aims. We aim to explore the relationship between the chromospheric oscillations inferred by NLTE inversion codes and the intrinsic fluctuations in velocity and temperature produced by the waves. Methods. We computed numerical simulations of wave propagation in a sunspot umbra with the code MANCHA. We used the NLTE synthesis and inversion code NICOLE to compute spectropolarimetric Ca II 8542 Å line profiles for the atmospheric models obtained as the output from the simulations. We then inverted the synthetic profiles and compared the inferences from the inversions with the known atmospheres from the simulations. Results. NLTE inversions of the Ca II 8542 Å line capture low-frequency oscillations, including those in the main band of chromospheric oscillations around 6 mHz. In contrast, waves with frequencies above 9 mHz are poorly characterized by the inversion results. Velocity oscillations at those higher frequencies exhibit clear signs of opacity fluctuations; namely the power of the signal at constant optical depth greatly departs from the power of the oscillations at constant geometrical height. The main response of the line to velocity fluctuations comes from low chromospheric heights, whereas the response to temperature shows sudden jumps between the high photosphere and the low chromosphere. This strong variation in the height where the line is sensitive to temperature is revealed as a strong oscillatory power in the inferred fluctuations, which is much stronger than the actual power from the intrinsic temperature oscillations. Conclusions. Our results validate the use of NLTE inversions to study chromospheric oscillations with frequencies below ∼9 mHz. However, the interpretation of higher-frequency oscillations and the power of temperature oscillations must be addressed with care, as these exhibit signatures of opacity oscillations.
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The dynamic chromosphere at millimeter wavelengths
Article
  • Oct 2022
The chromosphere is one of the most complex and dynamic layers of the solar atmosphere. The dynamic phenomena occur on different spatial and temporal scales, not only in active regions but also in the so-called quiet Sun. In this paper we review recent advances in our understanding of these phenomena that stem from the analysis of observations with the Atacama Large Millimeter/submillimeter Array (ALMA). The unprecedented sensitivity as well as spatial and temporal resolution of ALMA at millimeter wavelengths have advanced the study of diverse phenomena such as chromospheric p-mode-like and high-frequency oscillations, as well as small-scale, weak episodes of energy release, including shock waves. We review the most important results of these studies by highlighting the new aspects of the phenomena that have revealed as well as the new questions and challenges that have generated.
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The Propagation of Coherent Waves Across Multiple Solar Magnetic Pores
Preprint
Full-text available
  • Sep 2022
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 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 bi-sector Doppler velocity analysis of the Ca II 8542 {\AA} 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 bi-sectors 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 wave guides, 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.
View
View
Modelling the solar transition region using an adaptive conduction method
Article
Full-text available
  • Mar 2020
Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and transition region, when the corona undergoes impulsive heating. The TRAC method eliminates the need for highly resolved numerical grids in the transition region and the commensurate very short time steps that are required for numerical stability. When employed with coarse spatial resolutions, typically achieved in multi-dimensional magnetohydrodynamic codes, the errors at peak density are less than 5% and the computation time is three orders of magnitude faster than fully resolved field-aligned models. This paper presents further examples that demonstrate the versatility and robustness of the method over a range of heating events, including impulsive and quasi-steady footpoint heating. A detailed analytical assessment of the TRAC method is also presented, showing that the approach works through all phases of an impulsive heating event because (i) the total radiative losses and (ii) the total heating when integrated over the transition region are both preserved at all temperatures under the broadening modifications of the method. The results from the numerical simulations complement this conclusion.
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A chromospheric resonance cavity in a sunspot mapped with seismology
Article
Full-text available
  • Mar 2020
  • Nat. Astron.
Sunspots are intense collections of magnetic fields that pierce through the Sun’s photosphere, with their signatures extending upwards into the outermost extremities of the solar corona¹. Cutting-edge observations and simulations are providing insights into the underlying wave generation², configuration3,4 and damping⁵ mechanisms found in sunspot atmospheres. However, the in situ amplification of magnetohydrodynamic waves⁶, rising from a few hundreds of metres per second in the photosphere to several kilometres per second in the chromosphere⁷, has, until now, proved difficult to explain. Theory predicts that the enhanced umbral wave power found at chromospheric heights may come from the existence of an acoustic resonator8,9,10, which is created due to the substantial temperature gradients experienced at photospheric and transition region heights¹¹. Here, we provide strong observational evidence of a resonance cavity existing above a highly magnetic sunspot. Through a combination of spectropolarimetric inversions and comparisons with high-resolution numerical simulations, we provide a new seismological approach to mapping the geometry of the inherent temperature stratifications across the diameter of the underlying sunspot, with the upper boundaries of the chromosphere ranging between 1,300 ± 200 km and 2,300 ± 250 km. Our findings will allow the three-dimensional structure of solar active regions to be conclusively determined from relatively commonplace two-dimensional Fourier power spectra. The techniques presented are also readily suitable for investigating temperature-dependent resonance effects in other areas of astrophysics, including the examination of Earth–ionosphere wave cavities¹².
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Daniel K. Inouye Solar Telescope: High-resolution observing of the dynamic Sun
Article
Full-text available
  • Nov 2016
  • ASTRON NACHR
The 4-m aperture Daniel K. Inouye Solar Telescope (DKIST) formerly known as the Advanced Technology Solar Telescope (ATST) is currently under construction on Haleakalā (Maui, Hawai'i) projected to start operations in 2019. At the time of completion, DKIST will be the largest ground-based solar telescope providing unprecedented resolution and photon collecting power. The DKIST will be equipped with a set of first-light facility-class instruments offering unique imaging, spectroscopic and spectropolarimetric observing opportunities covering the visible to infrared wavelength range. This first-light instrumentation suite will include: a Visible Broadband Imager (VBI) for high-spatial and -temporal resolution imaging of the solar atmosphere; a Visible Spectro-Polarimeter (ViSP) for sensitive and accurate multi-line spectropolarimetry; a Fabry-Pérot based Visible Tunable Filter (VTF) for high-spatial resolution spectropolarimetry; a fiber-fed Diffraction-Limited Near Infra-Red Spectro-Polarimeter (DL-NIRSP) for two-dimensional high-spatial resolution spectropolarimetry (simultaneous spatial and spectral information); and a Cryogenic Near Infra-Red Spectro-Polarimeter (Cryo-NIRSP) for coronal magnetic field measurements and on-disk observations of, e.g., the CO lines at 4.7 μm. We will provide an overview of the DKISTs unique capabilities with strong focus on the first-light instrumentation suite, highlight some of the additional properties supporting observations of transient and dynamic solar phenomena, and touch on some operational strategies and the DKIST critical science plan. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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A new approach for modelling chromospheric evaporation in response to enhanced coronal heating: I. The method
Article
Full-text available
  • Sep 2016
  • ASTRON ASTROPHYS
We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region in response to rapid heating events. In the coupled corona, transition region and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation). However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux jumps across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved one-dimensional model, we present field-aligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both one-dimensional hydrodynamic and three-dimensional magnetohydrodynamic simulations are discussed.
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Chromospheric seismology above sunspot umbrae
Article
Full-text available
  • Jul 2015
The acoustic resonator is an important model for explaining the three-minute oscillations in the chromosphere above sunspot umbrae. The steep temperature gradients at the photosphere and transition region provide the cavity for the acoustic resonator, which allows waves to be both partially transmitted and partially reflected. In this paper, a new method of estimating the size and temperature profile of the chromospheric cavity above a sunspot umbra is developed. The magnetic field above umbrae is modelled numerically in 1.5D with slow magnetoacoustic wave trains travelling along magnetic fieldlines. Resonances are driven by applying the random noise of three different colours---white, pink and brown---as small velocity perturbations to the upper convection zone. Energy escapes the resonating cavity and generates wave trains moving into the corona. Line of sight (LOS) integration is also performed to determine the observable spectra through SDO/AIA. The numerical results show that the gradient of the coronal spectra is directly correlated with the chromosperic temperature configuration. As the chromospheric cavity size increases, the spectral gradient becomes shallower. When LOS integrations is performed, the resulting spectra demonstrate a broadband of excited frequencies that is correlated with the chromospheric cavity size. The broadband of excited frequencies becomes narrower as the chromospheric cavity size increases. These two results provide a potentially useful diagnostic for the chromospheric temperature profile by considering coronal velocity oscillations.
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The stellar atmosphere simulation code Bifrost
Article
Full-text available
  • Jul 2011
Context. Numerical simulations of stellar convection and photospheres have been developed to the point where detailed shapes of observed spectral lines can be explained. Stellar atmospheres are very complex, and very different physical regimes are present in the convection zone, photosphere, chromosphere, transition region and corona. To understand the details of the atmosphere it is necessary to simulate the whole atmosphere since the different layers interact strongly. These physical regimes are very diverse and it takes a highly efficient massively parallel numerical code to solve the associated equations. Aims: The design, implementation and validation of the massively parallel numerical code Bifrost for simulating stellar atmospheres from the convection zone to the corona. Methods: The code is subjected to a number of validation tests, among them the Sod shock tube test, the Orzag-Tang colliding shock test, boundary condition tests and tests of how the code treats magnetic field advection, chromospheric radiation, radiative transfer in an isothermal scattering atmosphere, hydrogen ionization and thermal conduction. Results.Bifrost completes the tests with good results and shows near linear efficiency scaling to thousands of computing cores.
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Analyses of three shock interactions in magnetohydrodynamics: Aligned‐field case
Article
  • Aug 1996
The paper deals with the confluence of three shock waves at a point, in a magnetohydrodynamic (MHD) fluid. Based on the three‐shock theory, the equations governing the flow field in the vicinity of the intersection point are obtained. The three shock confluences in field‐aligned cases are studied here using shock polars, revealing that only seven combinations of three shock types are possible. The relations among (a) the combinations of incident and reflected shock types, (b) the angle between incident and reflected shocks, and (c) the streamline deflection angle across the reflected shock are shown. As an example of application, the flow field induced by a supersonic MHD flow over a concave double wedge is studied both analytically and numerically.
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A Staggered Grid, Lagrangian-Eulerian Remap Code for 3-D MHD Simulations
Article
  • Jul 2001
In this paper an approach to multidimensional magnetohydrodynamics (MHD) which correctly handles shocks but does not use an approximate Riemann solver is proposed. This approach is simple and is based on control volume averaging with a staggered grid. The method builds on the older and often overlooked technique of on each step taking a fully 3-D Lagrangian step and then conservatively remapping onto the original grid. At the remap step gradient limiters are applied so that the scheme is monotonicity-preserving. For Euler's equations this technique, combined with an appropriately staggered grid and Wilkins artificial viscosity, can give results comparable to those from approximate Riemann solvers. We show how this can be extended to include a magnetic field, maintaining the divergence-free condition and pressure positivity and then present numerical test results. Where possible a comparison with other shock capturing techniques is presented and the advantages and disadvantages of the proposed scheme are clearly explained.
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First local helioseismic experiments with CO(5)BOLD
Article
  • Mar 2007
With numerical experiments we explore the feasibility of using high frequency waves for probing the magnetic fields in the photosphere and the chromosphere of the Sun. We track a plane-parallel, monochromatic wave that propagates through a non-stationary, realistic atmosphere, from the convection-zone through the photosphere into the magnetically dominated chromosphere, where it gets refracted and reflected. We compare the wave travel time between two fixed geometrical height levels in the atmosphere (representing the formation height of two spectral lines) with the topography of the surface of equal magnetic and thermal energy density (the magnetic canopy or beta=1 contour) and find good correspondence between the two. We conclude that high frequency waves indeed bear information on the topography of the `magnetic canopy'.
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