Context. Penumbra formation occurs within hours and remains not fully understood. Two competing theories suggest either a top-down mechanism, whereby the chromospheric magnetic field becomes more horizontal, or a bottom-up process involving flux emergence near the sunspot umbra.

Aims. We investigate penumbra formation and test both hypotheses by inferring and analyzing the full magnetic field from the photosphere to the chromosphere above a forming sunspot.

Methods. We applied Milne-Eddington, weak field approximation, and the multiatom non-local thermodynamic equilibrium inversion code STiC to obtain the model atmosphere that reproduces the Stokes profiles of Fe I 6302 Å and Ca II 8542 Å observed at the Swedish Solar Telescope, complementing the analysis with images taken in Hβ.

Results. A penumbra formed only in the southern sector of a sunspot in AR 13010 on May 15, 2022. We find that a preexisting, strong (> 500 G) and nearly horizontal magnetic field in the chromosphere is a key prerequisite. Penumbral filaments grew southward where localized flux emergence was observed, accompanied by strong redshifts (2–3 km s⁻¹) throughout the atmospheric layers. These redshifts likely represent field-aligned horizontal flows, possibly combining the onset of the Evershed flow and a siphon-like flow driven by field-aligned pressure gradients.

Conclusions. Our findings indicate that penumbra formation results from both top-down and bottom-up processes. While strong horizontal chromospheric magnetic fields are a necessary boundary condition, flux emergence initiates filament growth. The fallen flux tube model is ruled out, based on clear bottom-up signatures, though it remains unclear why the chromospheric and photospheric fields become more horizontal concurrently. Extended spectropolarimetric data are needed to get a deeper insight.

We present spectropolarimetric observations of an on-disk condensation event obtained with Sunrise/SCIP in the Ca ii 854.2 nm line. The event occurred during the coalescence of two pores of the same magnetic polarity, accompanied by coronal brightenings that indicate magnetic activity in the loop system before the appearance of the condensations. We identify the material through red-wing absorption signatures and infer its properties using a two-stage approach that combines spectropolarimetric inversions and Doppler-velocity fitting. Good fits were obtained for about 1400 profiles (∼60% of the detected pixels), yielding chromospheric temperatures (5900–9100 K, mode near 7400 K) and line-of-sight velocities of 5–45 km s⁻¹ (mode near 14 km s⁻¹). We then apply the weak-field approximation in narrow spectral windows centered on the inferred Doppler shifts, obtaining B_LoS values from approximately −100 to −900 G in the coronal rain material. To interpret the large spatial variation of B_LoS, we compare the observations with a force-free magnetic field extrapolation and find a loop whose projected B_z variation reproduces the observed trend along the traced path. The inferred loop geometry also yields free-fall speeds consistent with the measured velocities. These results show that high-resolution spectropolarimetry of on-disk coronal rain can provide constraints on the thermodynamic and magnetic properties of cool plasma in coronal loops. The comparison with the extrapolated field also suggests that the observed B_LoS trend is compatible with a plausible loop geometry.

Context. Advancements in extreme-precision radial velocity (RV) observations for detecting low-mass exoplanets show that different spectral lines show different behaviours in response to stellar activity. Though this can be dealt with experimentally, why this is the case has not been studied. The Sun is a good test case for testing hypotheses as we can study spatially resolved observations with high-resolution spectropolarimetry to understand spectral line behaviour.

Aims. We aim to investigate whether the difference of spectral line behaviour can be attributed to the height of atoms in the solar atmosphere. It is expected that photospheric spectral lines will act differently from their chromospheric counterparts in response to magnetic fields.

Methods. We used a unique dataset using the CRisp Imaging SpectroPolarimeter (CRISP) looking at three spectral lines, two in the photosphere and one in the chromosphere, and measured their spatially resolved radial velocities, their transversal and longitudinal magnetic fields, their magnetic field strengths, and their source functions. We correlated the magnetic field measurements against the radial velocities and compared them against the case in which we destroyed the spatial resolution to mimic a normal stellar observation with high-resolution spectra.

Results. We find that the unsigned magnetic field is strongly correlated to the RV for both the photospheric and chromospheric spectral lines in the case where the observation is spatially resolved. When the spatial resolution is destroyed, this correlation changes. We find that for the photospheric spectral lines there still exists a correlation to both components of the magnetic field, but the chromospheric spectral lines do not show any significant correlation.

We introduce an improved and fast inversion tool that is able to provide the thermodynamics of the solar atmosphere from the photosphere to the top of the chromosphere, as well as the integrated radiative losses (IRLs) in the chromosphere for data observed by the Interface Region Imaging Spectrograph (IRIS). This NASA mission has been observing the Sun and providing, among other kinds of data, multiline spectral observations sensitive to changes in the lower solar atmosphere since 2013. In this paper, we explain the new inversion tool IRIS²⁺ based on the IRIS²⁺ database, which is based on 135,472 synthetic representative profiles (RPs), each of them consisting of six chromospheric lines and six photospheric lines, their corresponding representative model atmospheres (RMA), and the IRL associated with these atmospheres. A nearest neighbor (k-nn) model algorithm is trained with the synthetic representative profiles to predict the closest RP in the database to the one observed, at which point IRIS²⁺ assigns the RMA and the IRL to the location of that observed profile. We have compared the results obtained by IRIS²⁺ with results obtained from the state-of-the-art inversion code STiC, which is also used to build the IRIS²⁺ database. We find that the thermodynamics and the IRL obtained with both methods are comparable in most cases. Therefore, IRIS²⁺ is a fast and reliable inversion tool that provides approximate values of the thermodynamic state and the radiative losses in the lower solar atmosphere for a large variety of solar scenes observed with IRIS.

Context. The solar chromosphere is a transition layer between the cool, dense photosphere and the hot, rarefied corona. This boundary region plays a key role in regulating energy transport and structuring the magnetic field throughout the solar atmosphere. Understanding its thermodynamic and magnetic properties is essential to model and interpret solar phenomena.

Aims. This study investigates the theoretical properties and diagnostic potential of the polarisation signals in the Ca II H & K lines, with particular emphasis on their capability to probe magnetic fields in the upper chromosphere with the CHROMIS instrument at the Swedish 1-m solar telescope.

Methods. We combine semi-empirical atmospheric models with high-resolution solar observations to model the formation of the Ca II H & K lines using non-local thermodynamic equilibrium radiative transfer calculations. The sensitivity of the lines to the magnetic field is examined through response functions and synthetic inversions, enabling an assessment of their diagnostic performance under realistic chromospheric conditions.

Results. For typical chromospheric field strengths, the linear polarisation of the Ca II H & K lines is less than 1.7%, below the expected detection threshold of CHROMIS. However, their circular polarisation reaches more than 10% in strong-field regions, which is detectable by CHROMIS. Both lines are sensitive to magnetic fields in the upper chromosphere, with the K line forming slightly higher due to its larger opacity, and the H line exhibiting a somewhat stronger Zeeman sensitivity owing to its higher effective Landé factor and longer wavelength. Using the weak-field approximation, the line of sight magnetic field can be reliably inferred around log ξ ≈ −4. These results confirm that the Ca II H & K lines constitute powerful diagnostics for studying the magnetic structure of the upper solar chromosphere.

We discuss the requirements, concepts, simulations, implementation, and calibration of two dual Fabry-Perot (FPI)-based imaging spectropolarimeters, CRISP and CHROMIS, at the Swedish 1-m Solar Telescope, and CRISP2, which is under construction. These instruments are optimised for a large field of view and high cadence at the expense of a moderate spectral resolution, and use a combination of a high-resolution and a low-resolution etalon together with an order-sorting prefilter to define the bandpass. The overall design is made robust and stable by tailoring the low-resolution etalon reflectivity to accommodate expected cavity errors from both etalons, by using a compact optical design that eliminates the need for folding mirrors, and enclosing the entire system within a single container sealed by lenses. By using a telecentric design based on lenses rather than mirrors, image degradation by the FPI system is negligible, as shown in a previous publication, and the throughput of the system is maximised. The initial alignment, and maintaining that alignment over time, is greatly simplified. Moreover, the telecentric design allows the full calibration and/or modelling of essential system parameters to be carried out without interfering with the optical set-up or the cameras. We also discuss briefly the polarimeters developed for CRISP and CHROMIS. The high performance of CRISP and CHROMIS has been demonstrated in an earlier publication through measurements of the granulation contrast and comparisons with similar measurements simultaneously made through broadband continuum filters. Here, we focus on the aspects of the design that are central to enabling high performance and robustness, but also discuss the calibration and processing of the data, and use a few examples of processed data to demonstrate the achievable image and data quality. We put forward a proposal for a similar conceptual design for the European Solar Telescope and conclude by discussing potential problems of the proposed approach to designs of this type. Some aspects of these FPI systems may also be of interest outside the solar community.

Solar flares are complex phenomena driven by the release of magnetic energy, but a large energy reservoir is not sufficient to determine their eruptive potential; the magnetic topology and plasma dynamics play a key role. We investigated the thermodynamic and magnetic properties of the solar atmosphere during the rise, peak, and decay phases of a C5.1-class flare and filament eruption in active region NOAA 12561 on 2016 July 7 to understand the origin and atmospheric response of this event. High spatial and spectral resolution spectropolarimetric observations of the chromospheric Ca II 8542 Å line and nearby photospheric lines were obtained with the TRIPPEL-SP spectropolarimeter at the Swedish 1-m Solar Telescope. Using nonlocal thermodynamic equilibrium (NLTE) inversions and non-force-free field (NFFF) magnetic extrapolations, we followed the event’s evolution from its precursor to its decay. Before the flare, our analysis reveals a complex, sheared magnetic topology with a high free energy content (∼2 × 10³⁰ erg). In this precursor phase, we detected persistent localized heating (temperature increase of ∼2000 K) with strong downflows (∼10–20 km s⁻¹) deep in the atmosphere. This heating was co-spatial with a bald-patch region, suggesting that low-altitude magnetic reconnection could destabilize the filament of the region. The flare’s rise phase was marked by the filament’s eruption, with a total speed greater than ∼70 km s⁻¹, when combining inversions and plane-of-sky motions. Following the eruption, the free energy decreased by ∼30% as post-flare loops formed, connecting the flare ribbons and channeling the released energy into the lower atmosphere. The flare ribbons exhibited significant heating to ∼8500 K and downflows up to ∼10 km s⁻¹, consistent with energy deposition along reconnected loops.

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. The physical conditions in stellar atmospheres, such as temperature, velocity, and magnetic fields, can be obtained from the interpretation of solar spectro-polarimetric observations. However, traditional inversion codes, while successful, are computationally demanding, especially for lines whose formation is complex and dictated by non-local thermodynamical equilibrium effects. The necessity of faster alternatives, particularly with the the increasing volume of data coming from large solar telescopes, has motivated the emergence of machine learning solutions.

Aims. This paper introduces an approach to the inversion and synthesis of Stokes profiles inspired by neural machine translation. Our aim is to develop a generative model that treats Stokes profiles and atmospheric models as two distinct “languages” encoding the same physical reality. We build a model that learns how to translate between them, also providing estimates of the uncertainty.

Methods. We employ a tokenization strategy for both Stokes parameters and model atmospheres, which is learned using Vector Quantized Variational Autoencoders (VQ-VAE), a neural model used to compress the data into a lower dimensionality form. The core of our inversion code utilizes a transformer encoder-decoder architecture, akin to those used in natural language processing, to perform the translation between these tokenized representations. The model is trained on a comprehensive database of synthetic Stokes profiles derived from perturbations to various semi-empirical solar atmospheric models, ensuring a wide range of expected solar physical conditions.

Results. The method effectively reconstructs atmospheric models from observed Stokes profiles, showing better constrained models within the region of sensitivity of the considered spectral lines. The latent representation induced by the VQ-VAE helps accelerate the inversion by compressing the length of the Stokes profiles and model atmospheres. Additionally, it helps regularize the solution by reducing the chances of obtaining unphysical models. As a final and crucial advantage, the method described in this paper provides the generative nature of our model, which naturally yields an estimate of the uncertainty in the solution.