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We investigated in detail the M5.8 class solar flare that occurred on 2023-03-06. This flare was one of the first strong flares observed by the Siberian Radioheliograph in the microwave range and the Advanced Space-based Solar Observatory in the X-ray range. The flare consisted of two separate flaring events (a "thermal" and a "cooler" ones), and was associated with (and probably triggered by) a filament eruption. During the first part of the flare, the microwave emission was produced in an arcade of relatively short and low flaring loops. During the second part of the flare, the microwave emission was produced by energetic electrons trapped near the top of a large-scale flaring loop; the evolution of the trapped electrons was mostly affected by the Coulomb collisions. Using the available observations and the GX Simulator tool, we created a 3D model of the flare, and estimated the parameters of the energetic electrons in it., Comment: Accepted for publication in Frontiers in Astronomy and Space Sciences - Stellar and Solar Physics

The origin of multiple peaks in lightcurves of various wavelengths remains illusive during flares. Here we discuss the flare of SOL2023-05-09T03:54M6.5 with six flux peaks as recorded by a tandem of new microwave and Hard X-ray instruments. According to its microwave spectra, the flare represents a high-turnover frequency (>15 GHz) event. The rather-complete microwave and HXR spectral coverage provides a rare opportunity to uncover the origin of such event together with simultaneous EUV images. We concluded that (1) the microwave sources originates around the top section of the flaring loops with a trend of source spatial dispersion with frequency;(2) the visible movement of the microwave source from peak to peak originates from the process of new flaring loops appearing sequentially along the magnetic neutral line; 3) the optically-thin microwave spectra are hard with the indices varying from -1.2 to -0.4, and the turnover frequency always exceeds 15 GHz; 4) higher turnover/peak frequency corresponds to stronger peak intensity and harder optically-thin spectra. Using the Fokker-Planck and GX simulator codes we obtained a good fit to the observed microwave spectra and spatial distribution of the sources at all peaks, if assuming the radiating energetic electrons have the same spatial distribution and single-power-law spectra but with the number density varying in a range of 30%. We conclude that the particle acceleration in this flare happens in a compact region nearing the looptop. These results provide new constraints on the acceleration of energetic electrons and the underlying flare intermittent reconnection process., Comment: 23 pages, 11 figures

To facilitate the study of solar active regions and flaring loops, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and non-thermal models of the chromosphere, transition region, and corona. The package has integrated tools to visualize the model data cubes, compute multi-wavelength emission maps from them, and quantitatively compare the resulting maps with observations. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers capabilities that include the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions to each individual voxel. The application integrates FORTRAN and C++ libraries for fast calculation of radio emission (free-free, gyroresonance, and gyrosynchrotron emission) along with soft and hard X-ray and EUV codes developed in IDL. To facilitate the creation of models, we have developed a fully automatic model production pipeline that downloads the required SDO/HMI vector magnetic field data and (optionally) the contextual SDO/AIA images, performs potential or nonlinear force free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through a set of interactive tools provided by the graphical user interface. Here we describe the GX Simulator framework and its applications.

Three- and five-minute oscillations are commonly found in any sunspot. As they are modulated by the internal thermal and magnetic structures of a sunspot, therehence, they could be used as an effective tool for sunspot seismology. In this paper, we investigate the properties of oscillations in sunspot groups with varying size and magnetic field, and aim to establish the relationships between sunspot oscillations and its internal structure comparatively. We selected three groups of unipolar sunspot with approximately axial-symmetric magnetic field and calculated their Fourier spectra based on the Ultraviolet(UV)/Extreme ultraviolet(EUV) emission intensity variations recorded by the Solar Dynamics Observatory/Atmospheric Imaging Assembly (SDO/AIA). We found that the distribution of three minute oscillation is defined by the joint effect of diverging magnetic field and the stratification of sunspot atmosphere. Its distribution could be modified by any invading magnetic structures in the umbra. Whereas the five minute oscillations are more prominent in small spots, it implies that five minute oscillation is very closely connected with umbral dynamics., Comment: 12 pages, 9 figures

We review novel data analysis techniques developed or adapted for the field of coronal seismology. We focus on methods from the last ten years that were developed for extreme ultraviolet (EUV) imaging observations of the solar corona, as well as for light curves from radio and X-ray. The review covers methods for the analysis of transverse and longitudinal waves; spectral analysis of oscillatory signals in time series; automated detection and processing of large data sets; empirical mode decomposition; motion magnification; and reliable detection, including the most common pitfalls causing artefacts and false detections. We also consider techniques for the detailed investigation of MHD waves and seismological inference of physical parameters of the coronal plasma, including restoration of the three-dimensional geometry of oscillating coronal loops, forward modelling and Bayesian parameter inference.

A light bridge is a magnetic intrusion into a sunspot, it interacts with the main magnetic field and excites a variety of dynamical processes. In the letter, we studied magnetic connectivity between a light bridge and coronal loops rooted at the sunspot. We used the data of the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory (SDO) to study the features of sunspots with light bridges. It is found that if a light bridge anchors at the umbra-penumbra boundary, the coronal loops could not be formed around the anchoring point. If the a light bridge become detached from the penumbra, the coronal loop starts to form again. The vector magnetogram provided by the Helioseismic Magnetic Imager onboard SDO shows that the anchoring region of a light bridge usually have an accompanying opposite minor-polarities. We conjugate that the magnetic field line could connect to these opposite polarities and form short-range magnetic loops, and therefore, coronal loops that extend to long-range could not be formed. A model of light bridge is proposed to explain the magnetic connectivity between a light bridge and the coronal loops. This model could explain many physical processes associated with light bridges., Comment: MNRAS, 5 pages,3 figures

Quasi-periodic fast propagating (QFP) waves are often excited by solar flares, and could be trapped in the coronal structure with low Alfv\'en speed, so they could be used as a diagnosing tool for both the flaring core and magnetic waveguide. As the periodicity of a QFP wave could originate from a periodic source or be dispersively waveguided, it is a key parameter for diagnosing the flaring core and waveguide. In this paper, we study two QFP waves excited by a GOES-class C1.3 solar flare occurring at active region NOAA 12734 on 8 March 2019. Two QFP waves were guided by two oppositely oriented coronal funnel. The periods of two QFP waves were identical and were roughly equal to the period of the oscillatory signal in the X-ray and 17 GHz radio emission released by the flaring core. It is very likely that the two QFP waves could be periodically excited by the flaring core. Many features of this QFP wave event is consistent with the magnetic tuning fork model. We also investigated the seismological application with QFP waves, and found that the magnetic field inferred with magnetohydrodynamic seismology was consistent with that obtained in magnetic extrapolation model. Our study suggest that the QFP wave is a good tool for diagnosing both the flaring core and the magnetic waveguide., Comment: ApJL,10 pages,5 figures

The question why the solar corona is much hotter than the visible solar surface still puzzles solar researchers. Most theories of the coronal heating involve a tight coupling between the coronal magnetic field and the associated thermal structure. This coupling is based on two facts: (i) the magnetic field is the main source of the energy in the corona and (ii) the heat transfer preferentially happens along the magnetic field, while is suppressed across it. However, most of the information about the coronal heating is derived from analysis of EUV or soft X-ray emissions, which are not explicitly sensitive to the magnetic field. This paper employs another electromagnetic channel -- the sunspot-associated microwave gyroresonant emission, which is explicitly sensitive to both the magnetic field and thermal plasma. We use nonlinear force-free field reconstructions of the magnetic skeleton dressed with a thermal structure as prescribed by a field-aligned hydrodynamics to constrain the coronal heating model. We demonstrate that the microwave gyroresonant emission is extraordinarily sensitive to details of the coronal heating. We infer heating model parameters consistent with observations., Comment: Accepted to ApJ. 14 pages, 11 figures, 3 tables

We present the Solar Bayesian Analysis Toolkit (SoBAT) which is a new easy to use tool for Bayesian analysis of observational data, including parameter inference and model comparison. SoBAT is aimed (but not limited) to be used for the analysis of solar observational data. We describe a new Interactive Data Language (IDL) code designed to facilitate the comparison of user-supplied model with data. Bayesian inference allows prior information to be taken into account. The use of Markov chain Monte Carlo (MCMC) sampling allows efficient exploration of large parameter spaces and provides reliable estimation of model parameters and their uncertainties. The Bayesian evidence for different models can be used for quantitative comparison. The code is tested to demonstrate its ability to accurately recover a variety of parameter probability distributions. Its application to practical problems is demonstrated using studies of the structure and oscillation of coronal loops.

We report a quasi-periodic pulsation (QPP) event simultaneously detected from the spatial displacements of coronal loop at both EUV images and microwave emission during the preflare phase of a C1.1 flare on 2016 March 23. Using the motion magnification technique, a low-amplitude transverse oscillation with the growing period is discovered in a diffuse coronal loop in Atmospheric Imaging Assembly (AIA) image sequences at wavelength of 171 A, and the initial oscillation period is estimated to be ~397 s with a slow growth rate of 0.045. At the same time, a QPP with growing periods from roughly 300 s to nearly 500 s is discovered in the microwave flux in the same active region. Based on the imaging observations measured at EUV wavelengths by the AIA and at microwave 17 GHz by Nobeyama Radioheliograph, the diffuse coronal loop and the microwave radiation source are found to be connected through a hot loop seen in AIA images at wavelength of 94 A. The growing period of the QPP should be related to the modulation of LRC-circuit oscillating process in a current-carrying plasma loop. The existence of electric currents may imply the non-potentialities in the source region during the preflare phase., Comment: 13 pages, 4 figures, accepted by the ApJL

The ubiquity of recently discovered low-amplitude decayless kink oscillations of plasma loops allows for the seismological probing of the corona on a regular basis. In particular, in contrast to traditionally applied seismology which is based on the large-amplitude decaying kink oscillations excited by flares and eruptions, decayless oscillations can potentially provide the diagnostics necessary for their forecasting. We analysed decayless kink oscillations in several distinct loops belonging to active region NOAA 12107 on 10 July 2010 during its quiet time period, when it was observed on the West limb in EUV by the Atmospheric Imaging Assembly on-board Solar Dynamics Observatory. The oscillation periods were estimated with the use of the motion magnification technique. The lengths of the oscillating loops were determined within the assumption of its semicircular shape by measuring the position of their foot-points. The density contrast in the loops was estimated from the observed intensity contrast accounting for the unknown spatial scale of the background plasma. The combination of those measurements allows us to determine the distribution of kink and Alfv\'en speeds in the active region. Thus, we demonstrate the possibility to obtain seismological information about coronal active regions during the quiet periods of time.

At the Sun, the strongest magnetic fields are routinely detected at dark sunspots. The magnitude of the field is typically about 3000 G, with only a few exceptions that reported the magnetic field in excess of 5000 G. Given that the magnetic field decreases with height in the solar atmosphere, no coronal magnetic field above ~2000 G was ever reported. Here, we present imaging microwave observations of an anomalously strong magnetic field of about 4000 G at the base of the corona in solar active region NOAA 12673 on 06 September 2017. Combining the photospheric vector measurements of the magnetic field and the coronal probing, we created and validated a nonlinear force-free field coronal model, with which we quantify the record-breaking coronal magnetic field at various coronal heights.

We report hard X-ray and gamma-ray observations of the impulsive phase of the SOL2017-09-06T11:55 X9.3 solar flare. We focus on a high-energy part of the spectrum, >100 keV, and perform time resolved spectral analysis for a portion of the impulsive phase, recorded by the Konus-Wind experiment, that displayed prominent gamma-ray emission. Given a variety of possible emission components contributing to the gamma-ray emission, we employ a Bayesian inference to build the most probable fitting model. The analysis confidently revealed contributions from nuclear deexcitation lines, electron-positron annihilation line at 511 keV, and a neutron capture line at 2.223 MeV along with two components of the bremsstrahlung continuum. The revealed time evolution of the spectral components is particularly interesting. The low-energy bremsstrahlung continuum shows a soft-hard-soft pattern typical for impulsive flares, while the high-energy one shows a persistent hardening at the course of the flare. The neutron capture line emission shows an unusually short time delay relative to the nuclear deexcitation line component, which implies that the production of neutrons was significantly reduced soon after the event onset. This in turn may imply a prominent softening of the accelerated proton spectrum at the course of the flare, similar to the observed softening of the low-energy component of the accelerated electrons responsible for the low-energy bremsstrahlung continuum. We discuss possible physical scenarios, which might result in the obtained relationships between these gamma-ray components., Comment: Accepted for publication in ApJ

3D picture of the coronal magnetic field remains an outstanding problem in solar physics, particularly, in active regions. Nonlinear force-free field reconstructions that employ routinely available full-disk photospheric vector magnetograms represent state-of-the-art coronal magnetic field modeling. Such reconstructions, however, suffer from an inconsistency between a force-free coronal magnetic field and non-force-free photospheric boundary condition, from which the coronal reconstruction is performed. In this study we focus on integrating the additional chromospheric and / or coronal magnetic field data with the vector photospheric magnetograms with the goal of improving the reliability of the magnetic field reconstructions. We develop a corresponding modification of the available optimization codes described in Fleishman et al. (2017) and test their performance using a full-fledged MHD model obtained from the Bifrost code by performing a `voxel-by-voxel' comparison between the reconstructed and the model magnetic fields. We demonstrate that adding even an incomplete set of chromospheric magnetic field data can measurably improve the reconstruction of the coronal magnetic field, greatly improve reconstructions of the magnetic connectivity and of the coronal electric current., Comment: ApJ accepted; 22 pages, 11 figures, 10 tables

Quantifying coronal magnetic field remains a central problem in solar physics. Nowadays the coronal magnetic field is often modelled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as pi-disambiguation, photospheric field preprocessing, and volume reconstruction methods using a 3D snapshot of the publicly available full-fledged radiative MHD model. Specifically, from the MHD model we know the magnetic field vector in the entire 3D domain, which enables us to perform "voxel-by-voxel" comparison of the restored and the true magnetic field in the 3D model volume. Our tests show that the available pi-disambiguation methods often fail at the quiet sun areas dominated by small-scale magnetic elements, while they work well at the AR photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although does produce a more force-free boundary condition, also results in some effective `elevation' of the magnetic field components. This `elevation' height is different for the longitudinal and transverse components, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolations performed starting from actual AR photospheric magnetogram are free from this systematic error, while have other metrics comparable with those for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing. Our tests further suggest that extrapolations from a force-free chromospheric boundary produce measurably better results, than those from the photospheric boundary., Comment: Replaces the previous submission to fix minor errors in a few figures and Tables 12 and 14. No conclusion is affected by the identified errors. 26 pages, 18 Figures, 14 Tables; 6 animated Figures are published in the journal version

We introduce a new method for the investigation of low-amplitude transverse oscillations of solar plasma non-uniformities, such as coronal loops, individual strands in coronal arcades, jets, prominence fibrils, polar plumes, and other contrast features, observed with imaging instruments. The method is based on the two-dimensional dual tree complex wavelet transform (DT$\mathbb{C}$WT). It allows us to magnify transverse, in the plane-of-the-sky, quasi-periodic motions of contrast features in image sequences. The tests performed on the artificial data cubes imitating exponentially decaying, multi-periodic and frequency-modulated kink oscillations of coronal loops showed the effectiveness, reliability and robustness of this technique. The algorithm was found to give linear scaling of the magnified amplitudes with the original amplitudes provided they are sufficiently small. Also, the magnification is independent of the oscillation period in a broad range of the periods. The application of this technique to SDO/AIA EUV data cubes of a non-flaring active region allowed for the improved detection of low-amplitude decay-less oscillations in the majority of loops., Comment: Accepted for publication in Solar Physics

Magnetic helicity is a conserved quantity of ideal magneto-hydrodynamics characterized by an inverse turbulent cascade. Accordingly, it is often invoked as one of the basic physical quantities driving the generation and structuring of magnetic fields in a variety of astrophysical and laboratory plasmas. We provide here the first systematic comparison of six existing methods for the estimation of the helicity of magnetic fields known in a finite volume. All such methods are reviewed, benchmarked, and compared with each other, and specifically tested for accuracy and sensitivity to errors. To that purpose, we consider four groups of numerical tests, ranging from solutions of the three-dimensional, force-free equilibrium, to magneto-hydrodynamical numerical simulations. Almost all methods are found to produce the same value of magnetic helicity within few percent in all tests. In the more solar-relevant and realistic of the tests employed here, the simulation of an eruptive flux rope, the spread in the computed values obtained by all but one method is only 3%, indicating the reliability and mutual consistency of such methods in appropriate parameter ranges. However, methods show differences in the sensitivity to numerical resolution and to errors in the solenoidal property of the input fields. In addition to finite volume methods, we also briefly discuss a method that estimates helicity from the field lines' twist, and one that exploits the field's value at one boundary and a coronal minimal connectivity instead of a pre-defined three-dimensional magnetic-field solution., Comment: Accepted for publication in Space Science Reviews. First paper by the ISSI International Team on 'Magnetic Helicity estimations in models and observations of the solar magnetic field', 54 pages, 12 figure. Data available at http://www.issibern.ch/teams/magnetichelicity/

The Siberian Solar Radio Telescope (SSRT) is a solar-dedicated directly-imaging interferometer observing the Sun at 5.7 GHz. The SSRT operates in the two-dimensional mode since 1996. The imaging principle of the SSRT restricts its opportunities in observations of very bright flare sources, while it is possible to use `dirty' images in studies of low brightness features, which do not overlap with side lobes from bright sources. The interactive CLEAN technique routinely used for the SSRT data provides imaging of active regions but consumes much time and efforts and does not reveal low-brightness features below the CLEAN threshold. The newly developed technique combines the CLEAN routine with the directly imaging capability of the SSRT and provides clean images with an enhanced dynamic range automatically. These elaborations considerably extend the range of tasks, which can be solved with the SSRT. We show some examples of the present opportunities of the SSRT and compare its data with the images produced by the Nobeyama Radioheliograph at 17 GHz as well as observations in different spectral ranges., Comment: 12 pages, 8 figures, 1 table. Submitted to PASJ