Context. Full-Stokes polarimetric datasets, originating from slit-spectrograph or narrow-band filtergrams, are routinely acquired nowadays. The data rate is increasing with the advent of bi-dimensional spectropolarimeters and observing techniques that allow long-time sequences of high-quality observations. There is a clear need to go beyond the traditional pixel-by-pixel strategy in spectropolarimetric inversions by exploiting the spatiotemporal coherence of the inferred physical quantities that contain valuable information about the conditions of the solar atmosphere.

Aims. We explore the potential of neural networks as a continuous representation of the physical quantities over time and space (also known as neural fields), for spectropolarimetric inversions.

Methods. We have implemented and tested a neural field to perform one of the simplest forms of spectropolarimetric inversions, the inference of the magnetic field vector under the weak-field approximation (WFA). By using a neural field to describe the magnetic field vector, we regularized the solution in the spatial and temporal domain by assuming that the physical quantities are continuous functions of the coordinates. This technique can be trivially generalized to account for more complex inversion methods.

Results. We have tested the performance of the neural field to describe the magnetic field of a realistic 3D magnetohydrodynamic (MHD) simulation. We have also tested the neural field as a magnetic field inference tool (approach also known as physics-informed neural networks) using the WFA as our radiative transfer model. We investigated the results in synthetic and real observations of the Ca II 8542 Å line. We also explored the impact of other explicit regularizations, such as using the information of an extrapolated magnetic field, or the orientation of the chromospheric fibrils.

Conclusions. Compared to traditional pixel-by-pixel inversions, the neural field approach improves the fidelity of the reconstruction of the magnetic field vector, especially the transverse component. This implicit regularization is a way of increasing the effective signal to noise of the observations. Although it is slower than the pixel-wise WFA estimation, this approach shows a promising potential for depth-stratified inversions, by reducing the number of free parameters and inducing spatiotemporal constraints in the solution.

Context. Flux emergence in the solar atmosphere is a complex process that causes a release of magnetic energy as heat and acceleration of solar plasma on a variety of spatial scales.

Aims. We aim to investigate temperatures and velocities in small-scale reconnection episodes during flux emergence.

Methods. We analyzed imaging spectropolarimetric data taken in the He I 1083 nm line with a spatial resolution of 0.26″, a time cadence of 2.8 s, and a spectral range corresponding to ±220 km s⁻¹ around the line. This line is sensitive to temperatures higher than 15 kK, unlike diagnostics such as Mg II h&k, Ca II H&K, and Hα, which lose sensitivity already at 15 kK. The He I data is complemented by imaging spectropolarimetry in the Fe I 617.3 nm and Ca II 854.2 nm lines and imaging spectroscopy in Ca II K and Hα at a cadence between 12 s and 36 s. We employed inversions to determine the magnetic field and vertical velocity in the solar atmosphere. We computed He I 1083 nm profiles from a radiation-magneto-hydrodynamics simulation of the solar atmosphere to help in the interpretation of the observations.

Results. We find fast-evolving blob-like emission features in the He I 1083 nm triplet at locations where the magnetic field is rapidly changing direction, and these are likely sites of magnetic reconnection. We fit the line with a model consisting of an emitting layer located below a cold layer representing the fibril canopy. The modeling provides evidence that this model, while simple, catches the essential characteristics of the line formation. The morphology of the emission in the He I 1083 nm is localized and blob-like, unlike the emission in the Ca II K line, which is more filamentary.

Conclusions. The modeling shows that the He I 1083 nm emission features and their Doppler shifts can be caused by opposite-polarity reconnection and/or horizontal current sheets below the canopy layer in the chromosphere. Based on the high observed Doppler width and the blob-like appearance of the emission features, we conjecture that at least a fraction of them are produced by plasmoids. We conclude that transition-region-like temperatures in the deeper layers of the active region chromosphere are more common than previously thought.

Context. Fibrils in the solar chromosphere carry transverse oscillations as determined from non-spectroscopic imaging data. They are estimated to carry an energy flux of several kW m⁻², which is a significant fraction of the average chromospheric radiative energy losses.

Aims. We aim to determine the oscillation properties of fibrils not only in the plane-of-the-sky (horizontal) direction, but also along the line-of-sight (vertical) direction.

Methods. We obtained imaging-spectroscopy data in Fe I 6173 Å, Ca II 8542 Å, and Ca II K with the Swedish 1-m Solar Telescope. We created a sample of 605 bright Ca II K fibrils and measured their horizontal motions. Their vertical motion was determined through non-local thermodynamic equilibrium (non-LTE) inversion of the observed spectra. We determined the periods and velocity amplitudes of the fibril oscillations, as well as phase differences between vertical and horizontal oscillations in the fibrils.

Results. The bright Ca II K fibrils carry transverse waves with a mean period of 2.1 × 10² s, and a horizontal velocity amplitude of 1 km s⁻¹, consistent with earlier results. The mean vertical velocity amplitude is 1.1 km s⁻¹. We find that 77% of the fibrils carry waves in both the vertical and horizontal directions, and 80% of this subsample exhibit oscillations with similar periods in both horizontal and vertical directions. For the latter, we find that all phase differences between 0 and 2π occur with a mild but significant preference for linearly polarised waves (a phase difference of 0 or π).

Conclusions. The results are consistent with the scenario where transverse waves are excited by granular buffeting at the photospheric footpoints of the fibrils. Estimates of transverse wave flux based only on imaging data are too low because they ignore the contribution of the vertical velocity.

Accurately assessing the balance between acoustic wave energy fluxes and radiative losses is critical for understanding how the solar chromosphere is thermally regulated. We investigate the energy balance in the chromosphere by comparing deposited acoustic flux and radiative losses under quiet and active solar conditions using non–local thermodynamic equilibrium inversions with the Stockholm Inversion Code. To achieve this, we utilize spectroscopic observations from the Interferometric BIdimensional Spectrometer in the Na ɪ 5896 Å and Ca ɪɪ 8542 Å lines and from the Interface Region Imaging Spectrograph in the Mg ɪɪ h and k lines to self-consistently derive spatially resolved velocity power spectra and cooling rates across different heights in the atmosphere. Additionally, we use snapshots of a three-dimensional radiative magnetohydrodynamics simulation to investigate the systematic effects of the inversion approach, particularly the effect of attenuation on the velocity power spectra and the determination of the cooling rates. The results indicate that inversions potentially underestimate acoustic fluxes at all chromospheric heights while slightly overestimating the radiative losses when fitting these spectral lines. However, even after accounting for these biases, the ratio of acoustic flux to radiative losses remains below unity in most observed regions, particularly in the higher layers of the chromosphere. We also observe a correlation between the magnetic field inclination in the photosphere and radiative losses in the low chromosphere in plage, which is evidence that the field topology plays a role in the chromospheric losses.

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. One-dimensional, semi-empirical models of the solar atmosphere are widely employed in numerous contexts within solar physics, ranging from the determination of element abundances and atomic parameters to studies of the solar irradiance and from Stokes inversions to coronal extrapolations. These models provide the physical parameters (i.e. temperature, gas pressure, etc.) in the solar atmosphere as a function of the continuum optical depth τc. The transformation to the geometrical z scale (i.e. vertical coordinate) is provided via vertical hydrostatic equilibrium. Aims. Our aim is to provide updated, one-dimensional, semi-empirical models of the solar atmosphere as a function of z, but employing the more general case of three-dimensional magneto-hydrostatic equilibrium (MHS) instead of vertical hydrostatic equilibrium (HE). Methods. We employed a recently developed Stokes inversion code that, along with non-local thermodynamic equilibrium effects, considers MHS instead of HE. This code is applied to spatially and temporally resolved spectropolarimetric observations of the quiet Sun obtained with the CRISP instrument attached to the Swedish Solar Telescope. Results. We provide average models for granules, intergranules, dark magnetic elements, and overall quiet-Sun as a function of both τc and z from the photosphere to the lower chromosphere. Conclusions. We demonstrate that, in these quiet-Sun models, the effect of considering MHS instead of HE is negligible. However, employing MHS increases the consistency of the inversion results before averaging. We surmise that in regions with stronger magnetic fields (i.e. pores, sunspots, network) the benefits of employing the magneto-hydrostatic approximation will be much more palpable.

Context. Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied.

Aims. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model.

Methods. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630 nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution.

Results. The results show a significant decrease in the mean magnetic flux density – related to the open flux observed at the disk center – with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20 cm aperture telescope yields a 30% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface.

Conclusions. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle.

The focus of this investigation is to quantify the conversion of magnetic to thermal energy initiated by a quiet Sun cancellation event and to explore the resulting dynamics from the interaction of the opposite-polarity magnetic features. We used imaging spectroscopy in the Hα line, along with spectropolarimetry in the Fe I 6173 Å and Ca II 8542 Å lines from the Swedish Solar Telescope (SST) to study a reconnection-related cancellation and the appearance of a quiet Sun Ellerman bomb (QSEB). We observed, for the first time, QSEB signature in both the wings and core of the Fe I 6173 Å line. We also found that, at times, the Fe I line-core intensity reaches higher values than the quiet Sun continuum intensity. From FIRTEZ-dz inversions of the Stokes profiles in Fe I and Ca II lines, we found enhanced temperature, with respect to the quiet Sun values, at the photospheric (log τ_c  = −1.5; ∼1000 K) and lower chromospheric heights (log τ_c  = −4.5; ∼360 K). From the calculation of total magnetic energy and thermal energy within these two layers, it was confirmed that the magnetic energy released during the flux cancellation can support heating in the aforesaid height range. Further, the temperature stratification maps enabled us to identify cumulative effects of successive reconnection on temperature pattern, including recurring temperature enhancements. Similarly, Doppler velocity stratification maps revealed impacts on plasma flow pattern, such as a sudden change in the flow direction. 

The heating of the chromosphere in internetwork regions remains one of the foremost open questions in solar physics. In the present study, we tackle this old problem by using a very-high-spatial-resolution simulation of quiet-Sun conditions performed with radiative MHD numerical models and interface region imaging spectrograph (IRIS) observations. We have expanded a previously existing 3D radiative MHD numerical model of the solar atmosphere, which included self-consistently locally driven magnetic amplification in the chromosphere, by adding ambipolar diffusion and time-dependent nonequilibrium hydrogen ionization to the model. The energy of the magnetic field is dissipated in the upper chromosphere, providing a large temperature increase due to ambipolar diffusion and nonequilibrium ionization (NEQI). At the same time, we find that adding the ambipolar diffusion and NEQI in the simulation has a minor impact on the local growth of the magnetic field in the lower chromosphere and its dynamics. Our comparison between synthesized Mg ii profiles from these high-spatial-resolution models, with and without ambipolar diffusion and NEQI, and quiet-Sun and coronal hole observations from IRIS now reveal a slightly better correspondence. The intensity of profiles is increased, and the line cores are slightly broader when ambipolar diffusion and NEQI effects are included. Therefore, the Mg ii profiles are closer to those observed than in previous models, though some differences still remain.