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In this work, we study the accuracy that can be achieved when inferring the atmospheric information from realistic numerical magnetohydrodynamic simulations that reproduce the spatial resolution we will obtain with future observations made by the 4 m class telescopes DKIST and EST. We first study multiple inversion configurations using the SIR code and the Fe i transitions at 630 nm until we obtain minor differences between the input and the inferred atmosphere in a wide range of heights. Also, we examine how the inversion accuracy depends on the noise level of the Stokes profiles. The results indicate that when the majority of the inverted pixels come from strongly magnetised areas, there are almost no restrictions in terms of the noise, obtaining good results for noise amplitudes up to 1 x 10(-3) of I-c. At the same time, the situation is different for observations where the dominant magnetic structures are weak, and noise restraints are more demanding. Moreover, we find that the accuracy of the fits is almost the same as that obtained without noise when the noise levels are on the order of 1 x 10(-4) of I-c. We, therefore, advise aiming for noise values on the order of or lower than 5 x 10(-4) of I-c if observers seek reliable interpretations of the results for the magnetic field vector reliably. We expect those noise levels to be achievable by next-generation 4m class telescopes thanks to an optimised polarisation calibration and the large collecting area of the primary mirror.

In this work, we study the accuracy that can be achieved when inferring the atmospheric information from realistic numerical magneto-hydrodynamic simulations that reproduce the spatial resolution we will obtain with future observations made by the 4m class telescopes DKIST and EST. We first study multiple inversion configurations using the SIR code and the Fe I transitions at 630 nm until we obtain minor differences between the input and the inferred atmosphere in a wide range of heights. Also, we examine how the inversion accuracy depends on the noise level of the Stokes profiles. The results indicate that when the majority of the inverted pixels come from strongly magnetised areas, there are almost no restrictions in terms of the noise, obtaining good results for noise amplitudes up to 1 × 10−3 of Ic. At the same time, the situation is different for observations where the dominant magnetic structures are weak, and noise restraints are more demanding. Moreover, we find that the accuracy of the fits is almost the same as that obtained without noise when the noise levels are on the order of 1 × 10−4of Ic. We, therefore, advise aiming for noise values on the order of or lower than 5 × 10−4 of Ic if observers seek reliable interpretations of the results for the magnetic field vector reliably. We expect those noise levels to be achievable by next-generation 4m class telescopes thanks to an optimised polarisation calibration and the large collecting area of the primary mirror. © The Authors 2023.

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, the German Vacuum Tower Telescope and GREGOR, the French Télescope Héliographique pour l’Étude du Magnétisme et des Instabilités Solaires, and the Dutch Open Telescope. 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.

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, the German Vacuum Tower Telescope and GREGOR, the French Télescope Héliographique pour l’Étude du Magnétisme et des Instabilités Solaires, and the Dutch Open Telescope. 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. © C. Q. Noda et al. 2022.

Context. The Milne-Eddington approximation provides an analytic and simple solution to the radiative transfer equation. It can be easily implemented in inversion codes used to fit spectro-polarimetric observations and infer average values of the magnetic field vector and the line-of-sight velocity of the solar plasma. However, in principle, it is restricted to spectral lines that are formed under local thermodynamic conditions, namely, photospheric and optically thin lines. Aims. We show that a simple modification to the Milne-Eddington approximation is sufficient to infer relevant physical parameters from spectral lines that deviate from local thermodynamic equilibrium, such as those typically observed in the solar chromosphere. Methods. We modified the Milne-Eddington approximation by including several exponential terms in the source function to reproduce the prototypical shape of chromospheric spectral lines. To check the validity of such an approximation, we first studied the influence of these new terms on the profile shape by means of the response functions. Then we tested the performance of an inversion code including the modification against the presence of noise. The approximation was also tested with realistic spectral lines generated with the RH numerical radiative transfer code. Finally, we confronted the code with synthetic profiles generated from magneto-hydrodynamic simulations carried out with the Bifrost code. For the various tests, we focused on the vector magnetic field and the line-of-sight velocity. We compared our results with the weak-field approximation and center of gravity technique as well. Results. The response function corresponding to the new terms in the source function have no trade-offs with the response to the different components of the magnetic field vector and line-of-sight velocity. This allows us to perform a robust inference of the physical parameters from the interpretation of spectral line shapes. The strategy has been succe

Future ground-based telescopes, such as the 4-metre class facilities DKIST and EST, will dramatically improve on current capabilities for simultaneous multi-line polarimetric observations in a wide range of wavelength bands, from the near-ultraviolet to the near-infrared. As a result, there will be an increasing demand for fast diagnostic tools, i.e., inversion codes, that can infer the physical properties of the solar atmosphere from the vast amount of data these observatories will produce. The advent of substantially larger apertures, with the concomitant increase in polarimetric sensitivity, will drive an increased interest in observing chromospheric spectral lines. Accordingly, pertinent inversion codes will need to take account of line formation under general non-local thermodynamic equilibrium (NLTE) conditions. Several currently available codes can already accomplish this, but they have a common practical limitation that impairs the speed at which they can invert polarised spectra, namely that they employ numerical evaluation of the so-called response functions to changes in the atmospheric parameters, which makes them less suitable for the analysis of very large data volumes. Here we present DeSIRe (Departure coefficient aided Stokes Inversion based on Response functions), an inversion code that integrates the well-known inversion code SIR with the NLTE radiative transfer solver RH. The DeSIRe runtime benefits from employing analytical response functions computed in local thermodynamic equilibrium (through SIR), modified with fixed departure coefficients to incorporate NLTE effects in chromospheric spectral lines. This publication describes the operating fundamentals of DeSIRe and describes its behaviour, robustness, stability, and speed. The code is ready to be used by the solar community and is being made publicly available. © ESO 2022.

Context. Despite their importance, routine and direct measurements of electric currents, j, in the solar atmosphere have generally not been possible. Aims. We aim at demonstrating the capabilities of a newly developed method for determining electric currents in the solar photosphere. Methods. We employ three-dimensional radiative magneto-hydrodynamic (MHD) simulations to produce synthetic Stokes profiles in several spectral lines with a spatial resolution similar to what the newly operational 4-meter Daniel K. Inouye Solar Telescope solar telescope should achieve. We apply a newly developed inversion method of the polarized radiative transfer equation with magneto-hydrostatic (MHS) constraints to infer the magnetic field vector in the three-dimensional Cartesian domain, B(x,y,z), from the synthetic Stokes profiles. We then apply Ampere's law to determine the electric currents, j, from the inferred magnetic field, B(x,z), and compare the results with the electric currents present in the original MHD simulation. Results. We show that the method employed here is able to attain reasonable reliability (close to 50% of the cases are within a factor of two, and this increases to 60%-70% for pixels with B300 G) in the inference of electric currents for low atmospheric heights (optical depths at 500 nm tau(5)is an element of[1, 0.1]) regardless of whether a small or large number of spectral lines are inverted. Above these photospheric layers, the method's accuracy strongly deteriorates as magnetic fields become weaker and as the MHS approximation becomes less accurate. We also find that the inferred electric currents have a floor value that is related to low-magnetized plasma, where the uncertainty in the magnetic field inference prevents a sufficiently accurate determination of the spatial derivatives. Conclusions. We present a method that allows the inference of the three components of the electric current vector at deep atmospheric layers (photospheric layers) from spectr

Future ground-based telescopes will expand our capabilities for simultaneous multi-line polarimetric observations in a wide range of wavelengths, from the near-ultraviolet to the near-infrared. This creates a strong demand to compare candidate spectral lines to establish a guideline of the lines that are most appropriate for each observation target. We focused in this first work on Zeeman-sensitive photospheric lines in the visible and infrared. We first examined their polarisation signals and response functions using a 1D semi-empirical atmosphere. Then we studied the spatial distribution of the line core intensity and linear and circular polarisation signals using a realistic 3D numerical simulation. We ran inversions of synthetic profiles, and we compared the heights at which we obtain a high correlation between the input and the inferred atmosphere. We also used this opportunity to revisit the atomic information we have on these lines and computed the broadening cross-sections due to collisions with neutral hydrogen atoms for all the studied spectral lines. The results reveal that four spectral lines stand out from the rest for quiet-Sun and network conditions: Fe» I 5250.2, 6302, 8468, and 15 648 A. The first three form higher in the atmosphere, and the last line is mainly sensitive to the atmospheric parameters at the bottom of the photosphere. However, as they reach different heights, we strongly recommend using at least one of the first three candidates together with the Fe» I 15 648 A line to optimise our capabilities for inferring the thermal and magnetic properties of the lower atmosphere. © ESO 2021.

Context. At present, an exponential growth in scientific data from current and upcoming solar observatories is expected. Most of the data consist of high spatial and temporal resolution cubes of Stokes profiles taken in both local thermodynamic equilibrium (LTE) and non-LTE spectral lines. The analysis of such solar observations requires complex inversion codes. Hence, it is necessary to develop new tools to boost the speed and efficiency of inversions and reduce computation times and costs. Aims. In this work we discuss the application of convolutional neural networks (CNNs) as a tool to advantageously initialize Stokes profile inversions. Methods. To demonstrate the usefulness of CNNs, we concentrate in this paper on the inversion of LTE Stokes profiles. We use observations taken with the spectropolarimeter on board the Hinode spacecraft as a test bench mark. First, we carefully analyse the data with the SIR inversion code using a given initial atmospheric model. The code provides a set of atmospheric models that reproduce the observations well. These models are then used to train a CNN. Afterwards, the same data are again inverted with SIR but using the trained CNN to provide the initial guess atmospheric models for SIR. Results. The CNNs allow us to significantly reduce the number of inversion cycles when used to compute initial guess model atmospheres ('assisted inversions'), therefore decreasing the computational time for LTE inversions by a factor of two to four. CNNs alone are much faster than assisted inversions, but the latter are more robust and accurate. CNNs also help to automatically cluster pixels with similar physical properties, allowing the association with different solar features on the solar surface, which is useful when inverting huge datasets where completely different regimes are present. The advantages and limitations of machine learning techniques for estimating optimum initial atmospheric models for spectral line inversions are discussed.

We investigate the diagnostic potential of the spectral lines at 850 nm for understanding the magnetism of the lower atmosphere. For that purpose, we use a newly developed 3D simulation of a chromospheric jet to check the sensitivity of the spectral lines to this phenomenon as well as our ability to infer the atmospheric information through spectropolarimetric inversions of noisy synthetic data. We start comparing the benefits of inverting the entire spectrum at 850 nm versus only the Ca II 8542 angstrom spectral line. We found a better match of the input atmosphere for the former case, mainly at lower heights. However, the results at higher layers were not accurate. After several tests, we determined that we need to weight more the chromospheric lines than the photospheric ones in the computation of the goodness of the fit. The new inversion configuration allows us to obtain better fits and consequently more accurate physical parameters. Therefore, to extract the most from multiline inversions, a proper set of weights needs to be estimated. Besides that, we conclude again that the lines at 850 nm, or a similar arrangement with Ca II 8542 angstrom plus Zeeman-sensitive photospheric lines, pose the best-observing configuration for examining the thermal and magnetic properties of the lower solar atmosphere.

We investigate the diagnostic potential of the spectral lines at 850 nm for understanding the magnetism of the lower atmosphere. For that purpose, we use a newly developed 3D simulation of a chromospheric jet to check the sensitivity of the spectral lines to this phenomenon as well as our ability to infer the atmospheric information through spectropolarimetric inversions of noisy synthetic data. We start comparing the benefits of inverting the entire spectrum at 850 nm versus only the Ca ii 8542 Å spectral line. We found a better match of the input atmosphere for the former case, mainly at lower heights. However, the results at higher layers were not accurate. After several tests, we determined that we need to weight more the chromospheric lines than the photospheric ones in the computation of the goodness of the fit. The new inversion configuration allows us to obtain better fits and consequently more accurate physical parameters. Therefore, to extract the most from multiline inversions, a proper set of weights needs to be estimated. Besides that, we conclude again that the lines at 850 nm, or a similar arrangement with Ca ii 8542 Å plus Zeeman-sensitive photospheric lines, pose the best-observing configuration for examining the thermal and magnetic properties of the lower solar atmosphere. © 2019 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.

Context. Determining empirical atmospheric models for the solar chromosphere is difficult since it requires the observation and analysis of spectral lines that are affected by non-local thermodynamic equilibrium (NLTE) effects. This task is especially difficult in sunspot umbrae because of lower continuum intensity values in these regions with respect to the surrounding brighter granulation. Umbral data is therefore more strongly affected by the noise and by the so-called scattered light, among other effects. Aims. The purpose of this study is to analyze spectropolarimetric sunspot umbra observations taken in the near-infrared Si I 1082.7 nm line taking NLTE effects into account. Interestingly, we detected emission features at the line core of the Si I 1082.7 nm line in the sunspot umbra. Here we analyze the data in detail and offer a possible explanation for the Si I 1082.7 nm line emission. Methods. Full Stokes measurements of a sunspot near disk center in the near-infrared spectral range were obtained with the GRIS instrument installed at the German GREGOR telescope. A point spread function (PSF) including the effects of the telescope, the Earth's atmospheric seeing, and the scattered light was constructed using prior Mercury observations with GRIS and the information provided by the adaptive optics system of the GREGOR telescope during the observations. The data were then deconvolved from the PSF using a principal component analysis deconvolution method and were analyzed via the NICOLE inversion code, which accounts for NLTE effects in the Si I 1082.7 nm line. The information of the vector magnetic field was included in the inversion process. Results. The Si I 1082.7 nm line seems to be in emission in the umbra of the observed sunspot after the effects of scattered light (stray light coming from wide angles) are removed. We show how the spectral line shape of umbral profiles changes dramatically with the amount of scattered light. Indeed, the continuum levels ra