Context. Synthetic spectra from 3D models of the solar atmosphere have become increasingly successful at reproducing observations, but there are still some outstanding discrepancies for chromospheric spectral lines, such as Ca II and Mg II, particularly regarding the width of the line cores. It has been demonstrated that using sufficiently high spatial resolution in the simulations significantly diminishes the differences in width between the mean spectra in observations and simulations, but a detailed investigation into how this impacts subgroups of individual profiles is currently lacking.

Aims. We compare and contrast the typical shapes of synthetic Ca II 854.2 nm spectra found in Bifrost simulations having different magnetic activity with the spectral shapes found in a quiet-Sun observation from the Swedish 1-m Solar Telescope (SST).

Methods. We used clustering techniques to extract the typical Ca II 854.2 nm profile shapes synthesized from Bifrost simulations with varying amounts of magnetic activity. We degraded the synthetic profiles to observational conditions and repeated the clustering, and we compared our synthetic results with actual observations. Subsequently, we examined the atmospheric structures in our models for some select sets of clusters, with the intention of uncovering why they do or do not resemble actual observations.

Results. While the mean spectra for our high resolution simulations compare reasonably well with the observations, we find that there are considerable differences between the clusters of observed and synthetic intensity profiles, even after the synthetic profiles have been degraded to match observational conditions. The typical absorption profiles from the simulations are both narrower and display a steeper transition from the inner wings to the line core. Furthermore, even in our most quiescent simulation, we find a far larger fraction of profiles with local emission around the core, or other exotic profile shapes, than in the quiet-Sun observations. Looking into the atmospheric structure for a selected set of synthetic clusters, we find distinct differences in the temperature stratification for the clusters most and least similar to the observations. The narrow and steep profiles are associated with either weak gradients in temperature or temperatures rising to a local maximum in the line wing forming region before sinking to a minimum in the line core forming region. The profiles that display less steep transitions show extended temperature gradients that are steeper in the range−3 ≲ log τ₅₀₀₀ ≲ −1.

Context. Determination of solar magnetic fields with a spatial resolution set by the diffraction limit of a telescope is difficult because the time required to measure the Stokes vector with sufficient signal-to-noise ratio is long compared to the solar evolution timescale. This difficulty becomes greater with increasing telescope size as the photon flux per diffraction-limited resolution element remains constant but the evolution timescale decreases linearly with the diffraction-limited resolution. Aims. We aim to improve magnetic field reconstruction at the diffraction limit without averaging the observations in time or space, and without applying noise filtering. Methods. The magnetic field vector tends to evolve more slowly than the temperature, velocity, or microturbulence. We exploit this by adding temporal regularisation terms for the magnetic field to the linear least-squares fitting used in the weak-field approximation, as well as to the Levenberg-Marquardt algorithm used in inversions. The other model parameters are allowed to change in time without constraints. We infer the chromospheric magnetic field from Ca II 854.2 nm observations using the weak field approximation and the photospheric magnetic field from Fe I 617.3 nm observations, both with and without temporal regularisation. Results. Temporal regularisation reduces the noise in the reconstructed maps of the magnetic field and provides a better coherency in time in both the weak-field approximation and Milne-Eddington inversions. Conclusions. Temporal regularisation markedly improves magnetic field determination from spatially and temporally resolved observations.

Context. The calculation of the emerging radiation from a model atmosphere requires knowledge of the emissivity and absorption coefficients, which are proportional to the atomic level population densities of the levels involved in each transition. Due to the intricate interdependence of the radiation field and the physical state of the atoms, iterative methods are required in order to calculate the atomic level population densities. A variety of different methods have been proposed to solve this problem, which is known as the nonlocal thermodynamical equilibrium (NLTE) problem. Aims. Our goal is to develop an efficient and rapidly converging method to solve the NLTE problem under the assumption of statistical equilibrium. In particular, we explore whether the Jacobian-Free Newton-Krylov (JFNK) method can be used. This method does not require an explicit construction of the Jacobian matrix because it estimates the new correction with the Krylov-subspace method. Methods. We implemented an NLTE radiative transfer code with overlapping bound-bound and bound-free transitions. This solved the statistical equilibrium equations using a JFNK method, assuming a depth-stratified plane-parallel atmosphere. As a reference, we also implemented the Rybicki & Hummer (1992) method based on linearization and operator splitting. Results. Our tests with the Fontenla, Avrett and Loeser C model atmosphere (FAL-C) and two different six-level Ca II and H I atoms show that the JFNK method can converge faster than our reference case by up to a factor 2. This number is evaluated in terms of the total number of evaluations of the formal solution of the radiative transfer equation for all frequencies and directions. This method can also reach a lower residual error compared to the reference case. Conclusions. The JFNK method we developed poses a new alternative to solving the NLTE problem. Because it is not based on operator splitting with a local approximate operator, it can improve the convergence of the NLTE problem in highly scattering cases. One major advantage of this method is that it is expected to allow for a direct implementation of more complex problems, such as overlapping transitions from different active atoms, charge conservation, or a more efficient treatment of partial redistribution, without having to explicitly linearize the equations.

Context. The Mg II h&k lines are key diagnostics of the solar chromosphere. They are sensitive to the temperature, density, and nonthermal velocities in the chromosphere. The average Mg II h&k line profiles arising from previous 3D chromospheric simulations are too narrow compared to observations. Aims. We study the formation and properties of the Mg II h&k lines in a model atmosphere. We also compare the average spectrum, peak intensity, and peak separation of Mg II k with a representative observation taken by the Interface Region Imaging Spectrograph (IRIS). Methods. We use a model based on the recently developed nonequilibrium version of the radiative magneto-hydrodynamics code MURaM, the MURaM Chromospheric Extension (MURaM-ChE), in combination with forward modeling using the radiative transfer code RH1.5D to obtain synthetic spectra. Our model resembles an enhanced network region created using an evolved MURaM quiet Sun simulation and adding an imposed large-scale bipolar magnetic field similar to that in the public Bifrost snapshot of a bipolar magnetic feature. Results. The line width and the peak separation of the spatially averaged spectrum of the Mg II h&k lines from the MURaM-ChE simulation are close to a representative observation of the quiet Sun, which also includes network fields. However, we find the synthesized line width to be still slightly narrower than in the observation. We find that velocities in the chromosphere play a dominant role in the broadening of the spectral lines. While the average synthetic spectrum also shows a good match to the observations in the pseudo continuum between the two emission lines, the peak intensities are higher in the modeled spectrum. This discrepancy may be due in part to the larger magnetic flux density in the simulation than in the considered observations, but could also be a result of the 1.5D radiative transfer approximation. Conclusions. Our findings show that strong maximum-velocity differences or turbulent velocities in the chromosphere and lower atmosphere are necessary to reproduce the observed line widths of chromospheric spectral lines.

Measuring magnetic fields in the inner corona, the interface between the solar chromosphere and outer corona, is of paramount importance if we aim to understand the energetic transformations taking place there, and because it is at the origin of processes that lead to coronal heating, solar wind acceleration, and of most of the phenomena relevant to space weather. However, these measurements are more difficult than mere imaging because polarimetry requires differential photometry. The coronal magnetograph mission (CMAG) has been designed to map the vector magnetic field, line-of-sight velocities, and plane-of-the-sky velocities of the inner corona with unprecedented spatial and temporal resolutions from space. This will be achieved through full vector spectropolarimetric observations using a coronal magnetograph as the sole instrument on board a spacecraft, combined with an external occulter installed on another spacecraft. The two spacecraft will maintain a formation flight distance of 430 m for coronagraphic observations, which requires a 2.5 m occulter disk radius. The mission will be preferentially located at the Lagrangian L5 point, offering a significant advantage for solar physics and space weather research. Existing ground-based instruments face limitations such as atmospheric turbulence, solar scattered light, and long integration times when performing coronal magnetic field measurements. CMAG overcomes these limitations by performing spectropolarimetric measurements from space with an external occulter and high-image stability maintained over time. It achieves the necessary sensitivity and offers a spatial resolution of 2.5 '' and a temporal resolution of approximately one minute, in its nominal mode, covering the range from 1.02 solar radii to 2.5 radii. CMAG relies on proven European technologies and can be adapted to enhance any other solar mission, offering potential significant advancements in coronal physics and space weather modeling and monitoring.

Context. Fabry–Pérot interferometers (FPIs) have become very popular in solar observations because they offer a balance between cadence, spatial resolution, and spectral resolution through a careful design of the spectral sampling scheme according to the observational requirements of a given target. However, an efficient balance requires knowledge of the expected target conditions, the properties of the chosen spectral line, and the instrumental characteristics.

Aims. Our aim is to find a method that allows the optimal spectral sampling of FPI observations in a given spectral region to be found. The selected line positions must maximize the information content in the observation with a minimal number of points.

Methods. In this study, we propose a technique based on a sequential selection approach in which a neural network is used to predict the spectrum (or physical quantities, if the model is known) from the information at a few points. Only those points that contain relevant information and improve the model prediction are included in the sampling scheme.

Results. We have quantified the performance of the new sampling schemes by showing the lower errors in the model parameter reconstructions. The method adapts the separation of the points according to the spectral resolution of the instrument, the typical broadening of the spectral shape, and the typical Doppler velocities. The experiments that use the Ca II 8542 Å line show that the resulting wavelength scheme naturally places more points in the core than in the wings (by almost a factor of 4), consistent with the sensitivity of the spectral line at each wavelength interval. As a result, observations focused on magnetic field analysis should prioritize a denser grid near the core, while those focused on thermodynamic properties would benefit from a larger coverage. The method can also be used as an accurate interpolator to improve the inference of the magnetic field when using the weak-field approximation.

Conclusions. Overall, this method offers an objective approach for designing new instrumentation or observing proposals with customized configurations for specific targets. This is particularly relevant when studying highly dynamic events in the solar atmosphere with a cadence that preserves spectral coherence without sacrificing much information.

Context. Rapid blue- and redshifted excursions (RBEs and RREs) may play an important role in mass-loading and heating the solar corona, but their nature and origin are still debatable.

Aims. We aim to model these features to learn more about their properties, formation, and origin.

Methods. We created a realistic three-dimensional (3D) magnetohydrodynamic model of a solar plage region. Synthetic Hα spectra were generated and the spectral signatures of these features identified. The magnetic field lines associated with these events were traced, and the underlying dynamic was studied.

Results. The model reproduces many properties of RBEs and RREs well, such as spatial distribution, lateral movement, length, and lifetimes. Synthetic Hα line profiles, similarly to observed ones, show a strong blue- or redshift as well as asymmetries. These line profiles are caused by the vertical component of velocities higher than 30 − 40 km s⁻¹, which mostly appear in the height range 2 − 4 Mm. By tracing magnetic field lines, we show that the vertical velocity that causes the appearance of RBEs or RREs is always associated with the component of velocity perpendicular to the magnetic field lines.

Conclusions. The study confirms the hypothesis that RBEs and RREs are signs of Alfvénic waves with, in some cases, a significant contribution from slow magneto-acoustic modes.

Context. The shapes of Stokes profiles contain a great deal of information about the atmospheric conditions that produced them. However, a variety of different atmospheric structures can produce very similar profiles. Thus, it is important for a proper interpretation of the observations to have a good understanding of how the shapes of Stokes profiles depend on the underlying atmosphere. An excellent tool in this regard is forward modeling, namely, computing and studying synthetic spectra from realistic simulations of the solar atmosphere. Modern simulations routinely produce several hundred thousand spectral profiles per snapshot. With such numbers, it becomes necessary to use automated procedures in order to organize the profiles according to their shape. Here, we illustrate the use of two complementary methods, k-means and k-Shape, to cluster similarly shaped profiles and demonstrate how the resulting clusters can be combined with knowledge of the simulation's atmosphere to interpret spectral shapes.

Aims. We aim to showcase the use of clustering analysis for forward modeling. In particular, we wish to introduce the k-Shape clustering method to the solar physics community as a complement to the well-known k-means method.

Methods. We generated synthetic Stokes profiles for the Ca II 854.2 nm line using the Multi3D code from a Bifrost simulation snapshot. We then applied the k-means and k-Shape clustering techniques to group the profiles together according to their shape and investigated the within-group correlations of temperature, line-of-sight velocity, and line-of-sight magnetic field strengths.

Results. We show and compare the classes of profile shapes we retrieved from applying both k-means and k-Shape to our synthetic intensity spectra. We then show the structure of the underlying atmosphere for two particular classes of profile shapes retrieved by the clustering and demonstrate how this leads to an interpretation for the formation of those profile shapes. We applied both methods to the subset of our profiles containing the strongest Stokes V signals and we demonstrate how k-Shape can be qualitatively better than k-means at retrieving complex profile shapes when using a small number of clusters.

Context. Recent observations have revealed loop-like structures at very small scales visible in observables that sample the transition region (TR) and even coronal temperatures. These structures are referred to as either ‘unresolved fine structures’, ‘dynamic cool loops’, ‘miniature hot loops’ or ‘campfires’ depending on the observables in which they are detected. Their formation remains unclear.

Aims. Realistic magnetohydrodynamic simulations and forward synthesis of spectral lines are used to investigate how these features occur.

Methods. Computations were carried out using the MURaM code to generate model atmospheres. The synthetic Hα and Si IV spectra are calculated at two angles (μ = 1, μ = 0.66) using the Multi3D code. We traced magnetic field lines in the model and examined the evolution of the underlying field topology.

Results. The synthetic Hα Dopplergrams reveal loops that evolve dramatically within a few minutes. The synthetic Hα line profiles show observed asymmetries and Doppler shifts in the line core. However, they also show strong emission peaks in the line wings, even at the slanted view. The synthetic Si IV emission features partly coincide with structures visible in Hα Dopplergrams and partly follow separate magnetic field threads. Some are even visible in the emission measure maps for the lg(T/K) = [5.8, 6.2] temperature interval. The emission areas trace out the magnetic field lines rooted in opposite polarities in a bipolar region.

Conclusions. The model shows that a loop-like structure in a bipolar system with footpoints undergoing rapid movement and shuffling can produce many small-scale recurrent events heated to high temperatures. It demonstrates that heating to different temperatures occurs and can be confined to a small part of the loop, at the location where resistive and viscous heating increases. The model largely reproduces the observed features in terms of size, lifetime and morphology in chromospheric, TR and coronal observables. The morphology and evolution of the resulting observable features can vary depending on the viewing angle.

We investigate the thermal, kinematic, and magnetic structure of small-scale heating events in an emerging flux region (EFR). We use high-resolution multiline observations (including Ca ii 8542 angstrom, Ca ii K, and the Fe i 6301 angstrom line pair) of an EFR located close to the disk center from the CRISP and CHROMIS instruments at the Swedish 1 m Solar Telescope. We perform non-LTE inversions of multiple spectral lines to infer the temperature, velocity, and magnetic field structure of the heating events. Additionally, we use the data-driven Coronal Global Evolutionary Model to simulate the evolution of the 3D magnetic field configuration above the events and understand their dynamics. Furthermore, we analyze the differential emission measure to gain insights into the heating of the coronal plasma in the EFR. Our analysis reveals the presence of numerous small-scale heating events in the EFR, primarily located at polarity inversion lines of bipolar structures. These events not only heat the lower atmosphere but also significantly heat the corona. The data-driven simulations, along with the observed enhancement of currents and Poynting flux, suggest that magnetic reconnection in the lower atmosphere is likely responsible for the observed heating at these sites.