arXiv subjects

J. de la Cruz Rodríguez

Publications and source records attributed to J. de la Cruz Rodríguez.

At least 19 recordsLinked to original sources

arXiv2026

Operating the Fabry-Pérot systems of the European Solar Telescope in multi-aperture mode

We discuss how to optimise the science output of the European Solar Telescope (EST), when used without the wide-field compensation for high-altitude seeing that the EST multi conjugate adaptive optics (MCAO) system will offer. Without MCAO, in particular with the Sun at low elevations or when observing at short wavelengths, high-altitude seeing will strongly attenuate the signal at high spatial frequencies over almost the entire 1 arc min science field-of-view (FOV) of EST. We propose to provide EST with an optional multi-aperture mode, by optically segmenting the 4.2 m aperture into six 1.4 m sub-apertures. This pushes down the root mean square wavefront errors from the high altitude seeing to levels that can more reliably be compensated for with conventional ground-layer adaptive optics and post processing of restored images. This will provide the sustained stable high image quality over a large FOV, needed for obtaining time sequences of spectropolarimetric data. The multi-aperture mode is implemented with low-cost modifications of the camera lenses of the three Fabry-Perot systems that will be used to cover the wavelength range 380-860 nm. Switching between the full-aperture and multi-aperture modes can be done quickly and independently for the three FPI systems. This allows flexible optimisation of EST, taking into account the daily variability and wavelength dependence of seeing. Providing EST with a multi-aperture option represents a value-added aspect that has no negative impact on the EST optical systems or on the FPI systems. It provides a powerful and flexible option that has the potential of significantly improving the quality and amount of its science data before MCAO is operational. We perform simulations and image reconstructions of simulated data to demonstrate the benefits of the multi-aperture option, and provide an optical design to demonstrate its feasibility.

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arXiv2026

Jacobian-Free Newton-Krylov method for multilevel NLTE radiative transfer problems

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 interdependency 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 Non-Local Thermodynamical Equilibrium (NLTE) problem. In this study we have developed a Jacobian-Free Newton-Krylov method (JFNK) to solve multi-level NLTE radiative transfer problems. Using the Rybicki & Hummer (1992) method as a reference (Rybicki, G. B. & Hummer, D. G. 1992, A&A, 262, 209), our results show that our JFNK solver can achieve up to a factor two speed up when using local approximate operators / preconditioners, while also achieving a lower residual error in the statistical equilibrium equations. Another advantage of this method is that the addition of charge conservation and partial redistribution effects should be straight forward. Our method can help accelerating the calculation of the emerging spectra from numerical models and also the reconstruction of chromospheric datasets through NLTE inversions.

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arXiv2026

Chromospheric heating and magnetic topology above the shared penumbra of a delta-spot: Multi-line inversions and multi-height magnetic-field extrapolations

We analysed observations of the Fe I 617.3 nm, Ca II 854.2 nm, and Ca II H lines obtained with CRISP and CHROMIS at the SST. Spatially coupled non-LTE inversions constrained the chromospheric atmosphere, while the WFA provided estimates of the chromospheric line-of-sight magnetic field. We combined these photospheric and chromospheric constraints with an HMI magnetogram as input to a multi-height field extrapolation. We characterised the reconstructed topology using the twist number, squashing factor, current density, and field-line connectivity. Results. The Ca II H magnetic signal is concentrated mainly above the strongest photospheric field concentrations, whereas Ca II 854.2 nm yields stronger and more spatially extended line-of-sight fields. The chromosphere above the shared penumbra is approximately 300 K hotter than nearby quiet regions. The selected brightening follows a chromospheric loop, with enhanced temperature and a transition from blueshift to redshift along the structure. The extrapolation recovers field strengths broadly consistent with the inversions and reveals a left-handed, flux-rope-like core following the polarity inversion line. Enhanced currents and connectivity gradients occur near parts of its boundary, where field lines connect the twisted structure to overarching loops. Conclusions. The temperature and velocity patterns and magnetic topology are consistent with reconnection between the twisted polarity-inversion-line field and the surrounding loops, depositing energy in the chromosphere and driving plasma along reconfigured field lines. These signatures do not uniquely establish reconnection, but show that combining high-resolution spectropolarimetric inversions with multi-height extrapolations can relate chromospheric energy release to the local three-dimensional magnetic structure.

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arXiv2026

Synthesizing Sun-as-a-star flare spectra from high-resolution solar observations

Spatially resolved observations of the Sun and the astronomical sample size of stellar bodies are the respective key strengths of solar and stellar observations. However, the large difference in object brightness between the Sun and other stars has led to distinctly different instrumentation and methodologies between the two fields. We produce and analyze synthetic full-disk spectra derived from 19 small area field-of-view optical observations of solar flares acquired by the Swedish 1-m Solar Telescope (SST) between 2011 and 2024. These are used to investigate what can and cannot be inferred about physical processes on the Sun from Sun-as-a-star observations. The recently released Numerical Empirical Sun-as-a-Star Integrator (NESSI) code provides synthetic full-disk integrated spectral line emission based on smaller field-of-view input, accounting for center-to-limb variations and differential rotation. We use this code to generate pseudo-Sun-as-a-star spectra from the SST observations. ...

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arXiv2026

Characterization of telecentric dual-etalon Fabry-Pérot systems from observational data. Properties of the CRISP2 instrument at the Swedish 1-m Solar Telescope

Imaging Fabry-Pérot Interferometer (FPI) observations are commonly used in solar physics to infer physical parameters in the photosphere and chromosphere through modeling of the observations. Such techniques require detailed knowledge of the spectral instrumental profile in order to produce accurate results. In this study we present a method to characterize the spatial variation of parameters of dual-etalon FPI instruments mounted in telecentric configuration: spatially-resolved cavity separation and reflectivities of both etalons, as well as the prefilter variation across the field-of-view. Here, we aim at characterizing the field-of-view dependence of the parameters of the new CRISP2 FPI. We have implemented a forward model of the FPI instrumental degradation combined with a template average quiet-Sun spectrum at disk center in order to model two sets of observational data. Our method does not require any change in the optical setup or the utilization of external sources of illumination. We assess the validity of several functional forms in the calculation of the FPI transmission profiles. Our results show that (generally) the inclusion of the secondary transmission peaks at 1 FSR and a detailed estimate of the prefilter curve is necessary to obtain accurate values of both etalon reflectivities. Our results show that the cavity separation of CRISP2 is very flat, with an RMS variation below 2 nm over the entire field-of-view for both etalons. Reflectivity RMS variations are 0.4% and 0.3% for the primary and secondary etalons at 617.3 nm. The methods described in this paper are relevant for the characterization of present and future FPI instruments and we have made them publicly available to the solar community.

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arXiv2025

The making of robust and highly performing imaging spectropolarimeters for large solar telescopes

We discuss the requirements, concepts, simulations, implementation, and calibration of two dual Fabry-Perot based imaging spectropolarimeters, CRISP and CHROMIS, at the Swedish 1-meter Solar Telescope, and CRISP2 that is under construction. These instruments 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, and by using a compact optical design that eliminates the need for folding mirrors. 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. Initial alignment, and maintaining that alignment over time, is greatly simplified. The telecentric design allows full calibration and/or modelling of essential system parameters to be carried out without interfering with the optical setup. 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 be of interest also outside the solar community.

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arXiv2025

Thermodynamic and magnetic evolution of an eruptive C-class solar flare observed with SST/TRIPPEL-SP

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 investigate 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 8542A line and nearby photospheric lines were obtained with the TRIPPEL-SP spectropolarimeter at the Swedish 1-m Solar Telescope. Using non-local 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 ($\sim2\times10^{30}$ erg). In this precursor phase, we detected persistent, localized heating (temperature increase of $\sim$2000 K) with strong downflows ($\sim$10-20 km/s) 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 larger than $\sim$70 km/s, when combining inversions and plane-of-sky motions. Following the eruption, the free energy decreased by $\sim$30$\%$ 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 $\sim$8500 K and downflows up to $\sim$10 km/s, consistent with energy deposition along reconnected loops.

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arXiv2025

High flow speeds and transition-region like temperatures in the solar chromosphere during flux emergence

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 at a variety of spatial scales. Methods: We analysed imaging spectropolarimetric data taken in the He 1083 nm line. This line is sensitive to temperatures larger than 15 kK, unlike diagnostics such as \MgIIhk, \CaIIHK, and \Halpha, which lose sensitivity already at 15 kK. The He I data is complemented by imaging spectropolarimetry in the \CaIIK, \Feline, and \Caline\ lines. We employed inversions to determine the magnetic field and vertical velocity in the solar atmosphere. We computed He 1083 nm profiles from a radiation-MHD simulation of the solar atmosphere to help interpretation of the observations. Results: We find fast-evolving blob-like emission features in the He 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 modelling provides evidence that this model, while simple, catches the essential characteristics of the line formation. The morphology of the emission in the He 1083 nm line is localized and blob-like, unlike the emission in the \CaIIK\ line, which is more filamentary. Conclusions: The modelling shows that the \Heline\ 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.

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arXiv2024

Constraints on Acoustic Wave Energy Fluxes and Radiative Losses in the Solar Chromosphere from Non-LTE Inversions

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 (NLTE) inversions with the Stockholm Inversion Code (STiC). To achieve this, we utilize spectroscopic observations from the Interferometric BIdimensional Spectrometer (IBIS) in the Na I 5896 Å and Ca II 8542 Å lines and from the Interface Region Imaging Spectrograph (IRIS) in the Mg II 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 attenuation effect 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.

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arXiv2024

Exploring spectropolarimetric inversions using neural fields. Solar chromospheric magnetic field under the weak-field approximation

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. 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. We have implemented and tested a neural field to perform the inference of the magnetic field vector (approach also known as physics-informed neural networks) under the weak-field approximation (WFA). By using a neural field to describe the magnetic field vector, we can regularize the solution in the spatial and temporal domain by assuming that the physical quantities are continuous functions of the coordinates. We investigated the results in synthetic and real observations of the Ca II 8542 A 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. Compared to the traditional pixel-by-pixel inversion, 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 spatio-temporal constraints in the solution.

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arXiv2023

Designing wavelength sampling for Fabry-Pérot observations. Information-based spectral sampling

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. Our aim is to find a method that allows finding the optimal spectral sampling of FPI observations in a given spectral region. In this study, we propose a technique based on a sequential selection approach where 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. 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 using the CaII 8542 A line show that the resulting wavelength scheme naturally places more points in the core than in the wings, consistent with the sensitivity of the spectral line at each wavelength interval. The method can also be used as an accurate interpolator, to improve the inference of the magnetic field when using the weak-field approximation. 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.

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arXiv2023

A reconnection driven magnetic flux cancellation and a quiet Sun Ellerman bomb

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 H$α$ line, along with spectropolarimetry in the \ion{Fe}{I} 6173~Å and \ion{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 \ion{Fe}{I} 6173~Å line. We also found that, at times, the \ion{Fe}{I} line-core intensity reaches higher values than the quiet Sun continuum intensity. From FIRTEZ-dz inversions of the Stokes profiles in \ion{Fe}{I} and \ion{Ca}{II} lines, we found enhanced temperature, with respect to the quiet Sun values, at the photospheric ($\logτ_c$ = -1.5; $\sim$1000 K) and lower chromospheric heights ($\logτ_c$ = -4.5; $\sim$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.

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arXiv2023

Estimating the longitudinal magnetic field in the chromosphere of quiet-Sun magnetic concentrations

Details of the magnetic field in the quiet Sun chromosphere are key to our understanding of essential aspects of the solar atmosphere. We aim to determine the longitudinal magnetic field component (B_lon) of quiet Sun regions depending on their size. We estimated B_lon by applying the weak-field approximation (WFA) to high-spatial-resolution Ca II 854.2 nm data taken with the Swedish 1m Solar Telescope. Specifically, we analyzed the estimates inferred for different spectral ranges using the data at the original cadence and temporally integrated signals. The longitudinal magnetic field in each considered plasma structure correlates with its size. Using a spectral range restricted to the line core leads to chromospheric longitudinal fields varying from 50 G at the edges to 150-500 G at the center of the structure. These values increase as the spectral range widens due to the photospheric contribution. However, the difference between this contribution and the chromospheric one is not uniform for all structures. Small and medium-sized concentrations show a steeper height gradient in B_lon compared to their chromospheric values, so estimates for wider ranges are less trustworthy. Signal addition does not alleviate this situation as the height gradients in B_lon are consistent with time. Finally, despite the amplified noise levels that deconvolving processes may cause, data restored with the destretching technique show similar results, though are affected by smearing. We obtained B_lon estimates similar to those previously found, except for large concentrations and wide spectral ranges. In addition, we report a correlation between the height variation of B_lon compared to the chromospheric estimates and the concentration size. This correlation affects the difference between the photospheric and chromospheric magnetic flux values and the reliability of the estimates for wider spectral ranges.

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arXiv2022

Radiative losses in the chromosphere during a C-class flare

Solar flares release an enormous amount of energy into the corona. A substantial fraction of this energy is transported to the lower atmosphere, which results in chromospheric heating. The mechanisms that transport energy to the lower solar atmosphere during a flare are still not fully understood. We aim to estimate the temporal evolution of the radiative losses in the chromosphere at the footpoints of a C-class flare, in order to set observational constraints on the electron beam parameters of a RADYN flare simulation. We estimated the radiative losses from hydrogen, and singly ionized Ca and Mg using semi-empirical model atmospheres. To estimate the integrated radiative losses in the chromosphere the net cooling rates were integrated between the temperature minimum and the height where the temperature reaches 10 kK. The stratification of the net cooling rate suggests that the Ca IR triplet lines are responsible for most of the radiative losses in the flaring atmosphere. During the flare peak time, the contribution from Ca II H & K and Mg II h & k lines are strong and comparable to the Ca IR triplet ($\sim$32 kW m$^{-2}$). Since our flare is a relatively weak event the chromosphere is not heated above 11 kK, which in turn yields a subdued Lyα contribution ($\sim$7 kW m$^{-2}$). The temporal evolution of total integrated radiative losses exhibits sharply-rising losses (0.4 kW m$^{-2}$ s$^{-1}$) and a relatively slow decay (0.23 kW~m$^{-2}$ s$^{-1}$). The maximum value of total radiative losses is reached around the flare peak time, and can go up to 175 kW m$^{-2}$ for a single pixel located at footpoint. After a small parameter study, we find the best model-data consistency in terms of the amplitude of radiative losses and the overall atmospheric structure with a RADYN flare simulation in the injected energy flux of $5\times10^{10}$ erg s$^{-1}$ cm$^{-2}$.

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arXiv2022

The European Solar Telescope

The European Solar Telescope (EST) is a project aimed at studying the magnetic connectivity of the solar atmosphere, from the deep photosphere to the upper chromosphere. Its design combines the knowledge and expertise gathered by the European solar physics community during the construction and operation of state-of-the-art solar telescopes operating in visible and near-infrared wavelengths: the Swedish 1m Solar Telescope (SST), the German Vacuum Tower Telescope (VTT) and GREGOR, the French Télescope Héliographique pour l'Étude du Magnétisme et des Instabilités Solaires (THÉMIS), and the Dutch Open Telescope (DOT). With its 4.2 m primary mirror and an open configuration, EST will become the most powerful European ground-based facility to study the Sun in the coming decades in the visible and near-infrared bands. EST uses the most innovative technological advances: the first adaptive secondary mirror ever used in a solar telescope, a complex multi-conjugate adaptive optics with deformable mirrors that form part of the optical design in a natural way, a polarimetrically compensated telescope design that eliminates the complex temporal variation and wavelength dependence of the telescope Mueller matrix, and an instrument suite containing several (etalon-based) tunable imaging spectropolarimeters and several integral field unit spectropolarimeters. This publication summarises some fundamental science questions that can be addressed with the telescope, together with a complete description of its major subsystems.

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arXiv2022

Spatio-temporal analysis of chromospheric heating in a plage region

Our knowledge of the heating mechanisms that are at work in the chromosphere of plage regions remains highly unconstrained from observational studies. The purpose of our study is to estimate the chromospheric heating terms from a plage dataset, characterize their spatio-temporal distribution and set constraints on the heating processes that are at work. We make use of NLTE inversions to infer a model of the photosphere and chromosphere of a plage dataset acquired with the Swedish 1-m Solar Telescope. We use this model atmosphere to calculate the chromospheric radiative losses from H i, Ca ii and Mg ii atoms. We approximate the chromospheric heating terms by the net radiative losses predicted by the inverted model. In order to make the analysis of time-series over a large field-of-view computationally tractable, we make use of a neural network. In the lower chromosphere, the contribution from the Ca ii lines is dominant and located in the surroundings of the photospheric footpoints. In the upper chromosphere, the H i contribution is dominant. Radiative losses in the upper chromosphere form an homogeneous patch that covers the plage region. The net radiative losses can be split in a periodic component with an average amplitude of ampQ = 7.6 kW m^{-2} and a static (or very slowly evolving) component with a mean value of -26.1 kW m^{-2}. Our interpretation is that in the lower chromosphere, the radiative losses are tracing the sharp lower edge of the hot magnetic canopy, where the electric current is expected to be large. In the upper chromosphere, both the magnetic field and the distribution of net radiative losses are room-filling, whereas the amplitude of the periodic component is largest. Our results suggest that acoustic wave heating may be responsible for one third of the energy deposition in the upper chromosphere, whereas other heating mechanisms must be responsible for the rest.

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arXiv2022

Heating of the solar chromosphere through current dissipation

The solar chromosphere is heated to temperatures higher than predicted by radiative equilibrium. This excess heating is greater in active regions where the magnetic field is stronger. We aim to investigate the magnetic topology associated with an area of enhanced millimeter (mm) brightness temperatures in a solar active region mapped by the Atacama Large Millimeter/submillimeter Array (ALMA) using spectropolarimetric co-observations with the 1-m Swedish Solar Telescope (SST). We used Milne-Eddington inversions, nonlocal thermodynamic equilibrium (non-LTE) inversions, and a magnetohydrostatic extrapolation to obtain constraints on the three-dimensional stratification of temperature, magnetic field, and radiative energy losses. We compared the observations to a snapshot of a magnetohydrodynamics simulation and investigate the formation of the thermal continuum at 3 mm using contribution functions. We find enhanced heating rates in the upper chromosphere of up to $\sim 5\rm\,kW\,m^{-2}$, where small-scale emerging loops interact with the overlying magnetic canopy leading to current sheets as shown by the magnetic field extrapolation. Our estimates are about a factor of two higher than canonical values, but they are limited by the ALMA spatial resolution ($\sim 1.2^{\prime\prime}$). Band 3 brightness temperatures reach about $\sim10^{4}\,$K in the region, and the transverse magnetic field strength inferred from the non-LTE inversions is on the order of $\sim 500\,$G in the chromosphere. We are able to quantitatively reproduce many of the observed features, including the integrated radiative losses in our numerical simulation. We conclude that the heating is caused by dissipation in current sheets. However, the simulation shows a complex stratification in the flux emergence region where distinct layers may contribute significantly to the emission in the mm continuum.

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arXiv2021

Bayesian Stokes inversion with Normalizing flows

Stokes inversion techniques are very powerful methods for obtaining information on the thermodynamic and magnetic properties of solar and stellar atmospheres. In recent years, very sophisticated inversion codes have been developed that are now routinely applied to spectro-polarimetric observations. Most of these inversion codes are designed for finding an optimum solution to the nonlinear inverse problem. However, to obtain the location of potentially multimodal cases (ambiguities), the degeneracies, and the uncertainties of each parameter inferred from the inversions, algorithms such as Markov chain Monte Carlo (MCMC), require to evaluate the likelihood of the model thousand of times and are computationally costly. Variational methods are a quick alternative to Monte Carlo methods by approximating the posterior distribution by a parametrized distribution. In this study, we introduce a highly flexible variational inference method to perform fast Bayesian inference, known as normalizing flows. Normalizing flows are a set of invertible, differentiable, and parametric transformations that convert a simple distribution into an approximation of any other complex distribution. If the transformations are conditioned on observations, the normalizing flows can be trained to return Bayesian posterior probability estimates for any observation. We illustrate the ability of the method using a simple Milne-Eddington model and a complex non-LTE inversion. However, the method is extremely general and other more complex forward models can be applied. The training procedure need only be performed once for a given prior parameter space and the resulting network can then generate samples describing the posterior distribution several orders of magnitude faster than existing techniques.

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