ArticlePublisher preview available

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

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Figures

This content is subject to copyright. Terms and conditions apply.
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 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 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 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 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
... Sterling (2000) highlighted that high-resolution observations, due to the small width of the structures, are vital for a complete description of the spicule wave phenomena. Wedemeyer-Böhm et al. (2007) also note that the ability to detect oscillatory power at higher frequencies is influenced by the spatial resolution of the observations (see also the discussions provided by Jess et al. 2020Jess et al. , 2021. ...
Article
Full-text available
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 s ⁻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 km s ⁻¹ at ≈4900 km, and 168 ± 125 km and 26.3 ± 14.1 km s ⁻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 km s ⁻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.
... Sterling (2000) highlighted that high-resolution observations, due to the small width of the structures, are vital for a complete description of the spicule wave phenomena. Wedemeyer-Böhm et al. (2007) also note that the ability to detect oscillatory power at higher frequencies is influenced by the spatial resolution of the observations (see also the discussions provided by Jess et al. 2020Jess et al. , 2021. One of the major focuses of current solar physics research is the so-called 'coronal heating paradox'. ...
Preprint
Full-text available
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 s^-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 km s^-1 at 4900 km, and 168 +/- 125 km and 26.3 +/- 14.1 km s^-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 km s^-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.
... In recent decades, modern upgrades to existing observatories [e.g., the Dunn, Swedish, and Goode Solar Telescopes; [4][5][6], in addition to the construction and/or launch of new observing facilities [e.g., Hinode, the Interface Region Imaging Spectrograph, the National Science Foundation's Daniel K. Inouye Solar Telescope; [7][8][9], have paved the way for rapid advancements to be made in the field of lower atmospheric dynamics. In particular, the high spatial, temporal, and spectral resolutions now available from the cutting-edge observatories, in combination with polarimetric capabilities, we have at our disposal have made the studies of small-scale oscillatory phenomena possible, resulting in numerous high-impact publications in recent years [e.g., [10][11][12][13][14][15][16]. ...
Article
Full-text available
The magnetic and convective nature of the Sun’s photosphere provides a unique platform from which generated waves can be modelled, observed and interpreted across a wide breadth of spatial and temporal scales. As oscillations are generated in-situ or emerge through the photospheric layers, the interplay between the rapidly evolving densities, temperatures and magnetic field strengths provides dynamic evolution of the embedded wave modes as they propagate into the tenuous solar chromosphere. A focused science team was assembled to discuss the current challenges faced in wave studies in the lower solar atmosphere, including those related to spectropolarimetry and radiative transfer in the optically thick regions. Following the Theo Murphy international scientific meeting held at Chicheley Hall during February 2020, the scientific team worked collaboratively to produce 15 independent publications for the current Special Issue, which are introduced here. Implications from the current research efforts are discussed in terms of upcoming next-generation observing and high-performance computing facilities. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.
... In recent decades, modern upgrades to existing observatories [e.g., the Dunn, Swedish, and Goode Solar Telescopes; [4][5][6], in addition to the construction and/or launch of new observing facilities [e.g., Hinode, the Interface Region Imaging Spectrograph, the National Science Foundation's Daniel K. Inouye Solar Telescope; [7][8][9], have paved the way for rapid advancements to be made in the field of lower atmospheric dynamics. In particular, the high spatial, temporal, and spectral resolutions now available from the cutting-edge observatories, in combination with polarimetric capabilities, we have at our disposal have made the studies of small-scale oscillatory phenomena possible, resulting in numerous high-impact publications in recent years [e.g., [10][11][12][13][14][15][16]. ...
Preprint
Full-text available
The magnetic and convective nature of the Sun's photosphere provides a unique platform from which generated waves can be modelled, observed, and interpreted across a wide breadth of spatial and temporal scales. As oscillations are generated in-situ or emerge through the photospheric layers, the interplay between the rapidly evolving densities, temperatures, and magnetic field strengths provides dynamic evolution of the embedded wave modes as they propagate into the tenuous solar chromosphere. A focused science team was assembled to discuss the current challenges faced in wave studies in the lower solar atmosphere, including those related to spectropolarimetry and radiative transfer in the optically thick regions. Following the Theo Murphy international scientific meeting held at Chicheley Hall during February 2020, the scientific team worked collaboratively to produce 15 independent publications for the current Special Issue, which are introduced here. Implications from the current research efforts are discussed in terms of upcoming next-generation observing and high performance computing facilities.
... In this work, we have confirmed that in most cases the power spectra of the He I 10830 Å line do not exhibit such strong highfrequency peaks. Jess et al. (2020b) argued that this peak is only visible under ideal observational conditions. The upcoming data from the next generation of solar telescopes will clarify whether this peak is unusual or a common feature hidden in most observations up to date. ...
... In this work, we have confirmed that in most cases the power spectra of the He i 10830Å line do not exhibit such strong high-frequency peaks. Jess et al. (2020b) argued that this peak is only visible under ideal observational conditions. The upcoming data from the next generation of solar telescopes will clarify whether this peak is unusual or a common feature hidden in most observations up to date. ...
Preprint
Full-text available
Oscillations in sunspot umbrae exhibit remarkable differences between the photosphere and chromosphere. We evaluate two competing scenarios proposed for explaining those observations: a chromospheric resonant cavity and waves traveling from the photosphere to upper atmospheric layers. We have employed numerical simulations to analyze the oscillations in both models. They have been compared with observations in the low (Na I D2) and high (He I 10830 \AA) chromosphere. The nodes of the resonant cavity can be detected as phase jumps or power dips, although the identification of the latter is not sufficient to claim the existence of resonances. In contrast, phase differences between velocity and temperature fluctuations reveal standing waves and unequivocally prove the presence of an acoustic resonator above umbrae. Our findings offer a new seismic method to probe active region chromospheres through the detection of resonant nodes.
Article
Context. Interferometric observations of the Sun with the Atacama Large Millimeter/sub-millimeter Array (ALMA) provide valuable diagnostic tools for studying the small-scale dynamics of the solar atmosphere. Aims. The aims are to perform estimations of the observability of the small-scale dynamics as a function of spatial resolution for regions with different characteristic magnetic field topology facilitate a more robust analysis of ALMA observations of the Sun. Methods. A three-dimensional model of the solar atmosphere from the radiation-magnetohydrodynamic code Bifrost was used to produce high-cadence observables at millimeter and submillimeter wavelengths. The synthetic observables for receiver bands 3–10 were degraded to the angular resolution corresponding to ALMA observations with different configurations of the interferometric array from the most compact, C1, to the more extended, C7. The observability of the small-scale dynamics was analyzed in each case. The analysis was thus also performed for receiver bands and resolutions that are not commissioned so far for solar observations as a means for predicting the potential of future capabilities. Results. The minimum resolution required to study the typical small spatial scales in the solar chromosphere depends on the characteristic properties of the target region. Here, a range from quiet Sun to enhanced network loops is considered. Limited spatial resolution affects the observable signatures of dynamic small-scale brightening events in the form of reduced brightness temperature amplitudes, potentially leaving them undetectable, and even shifts in the times at which the peaks occur of up to tens of seconds. Conversion factors between the observable brightness amplitude and the original amplitude in the fully resolved simulation are provided that can be applied to observational data in principle, but are subject to wavelength-dependent uncertainties. Predictions of the typical appearance at the different combinations of receiver band, array configuration, and properties of the target region are conducted. Conclusions. The simulation results demonstrate the high scientific potential that ALMA already has with the currently offered capabilities for solar observations. For the study of small-scale dynamic events, however, the spatial resolution is still crucial, and wide array configurations are preferable. In any case, it is essential to take the effects due to limited spatial resolution into account in the analysis of observational data. Finally, the further development of observing capabilities including wider array configurations and advanced imaging procedures yields a high potential for future ALMA observations of the Sun.
Article
Context. Umbral flashes are sudden brightenings commonly visible in the core of some chromospheric lines. Theoretical and numerical modeling suggests that they are produced by the propagation of shock waves. According to these models and early observations, umbral flashes are associated with upflows. However, recent studies have reported umbral flashes in downflowing atmospheres. Aims. We aim to understand the origin of downflowing umbral flashes. We explore how the existence of standing waves in the umbral chromosphere impacts the generation of flashed profiles. Methods. We performed numerical simulations of wave propagation in a sunspot umbra with the code MANCHA. The Stokes profiles of the Ca II 8542 Å line were synthesized with the NICOLE code. Results. For freely propagating waves, the chromospheric temperature enhancements of the oscillations are in phase with velocity upflows. In this case, the intensity core of the Ca II 8542 Å atmosphere is heated during the upflowing stage of the oscillation. However, a different scenario with a resonant cavity produced by the sharp temperature gradient of the transition region leads to chromospheric standing oscillations. In this situation, temperature fluctuations are shifted backward and temperature enhancements partially coincide with the downflowing stage of the oscillation. In umbral flash events produced by standing oscillations, the reversal of the emission feature is produced when the oscillation is downflowing. The chromospheric temperature keeps increasing while the atmosphere is changing from a downflow to an upflow. During the appearance of flashed Ca II 8542 Å cores, the atmosphere is upflowing most of the time, and only 38% of the flashed profiles are associated with downflows. Conclusions. We find a scenario that remarkably explains the recent empirical findings of downflowing umbral flashes as a natural consequence of the presence of standing oscillations above sunspot umbrae.
Article
Full-text available
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.
Article
Full-text available
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.
Article
Full-text available
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)
Article
Full-text available
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.
Article
Full-text available
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.
Article
Full-text available
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.
Article
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.
Article
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.
Article
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'.