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C. Quintero Noda

Publications and source records attributed to C. Quintero Noda.

At least 19 recordsLinked to original sources

The Sunrise Chromospheric Infrared Spectro-Polarimeter SCIP: an instrument for SUNRISE III

The Sunrise balloon-borne solar observatory is equipped with a one-meter aperture optical telescope, offering a unique platform for uninterrupted seeing-free observations across ultraviolet, visible, and infrared wavelengths from altitudes higher than 33 km. For the third flight of the upgraded Sunrise observatory conducted in 2024, now called Sunrise III, a new spectro-polarimeter called the Sunrise Chromospheric Infrared spectroPolarimeter (SCIP) was developed for observing near-infrared wavelength ranges around 770 nm and 850 nm. These wavelength ranges contain many spectral lines, including two of the Ca II infrared triplet, K I D1 and D2 lines, and multiple Fe I lines, that are sensitive to solar magnetic fields and velocities in the photosphere and chromosphere. SCIP consists of a grating spectrograph in which polarimetric measurements are conducted using a rotating waveplate as a modulator and polarizing beam splitters placed in front of the cameras. The spatial and spectral resolutions are 0.21" and 1x10^5, respectively, and a polarimetric sensitivity of 0.03% (1sigma) of the continuum intensity is achieved with a 10 s integration time per a resolution element. To achieve high-precision detection of small polarization signals, we carefully designed the optical and mechanical systems, polarization components, control electronics, and onboard data processing. Together with the other post-focus instrumentation developed for Sunrise III, the Sunrise Ultraviolet Spectropolarimeter and Imager (SUSI) and the visible imaging spectro-polarimeter Tunable Magnetograph (TuMag), SCIP provides novel observations that help elucidate energy transfer and time-dependent phenomena across the solar photosphere and chromosphere.

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Infrared spectropolarimetry of a C-class solar flare footpoint plasma -- I. Spectral features and forward modelling

We performed high-spatial resolution spectropolarimetric observations of active region NOAA 13363 during a C-class flare with the Gregor Infrared Spectrograph (GRIS) on 16 July 2023. We examine the coupling between the photosphere and the chromosphere, studying the polarimetric signals during a period that encompasses the decaying phase of a C-class flare and the appearance of a new C-class flare at the same location. We focus on the analysis of various spectral lines. In particular, we study the Si I 10827 {\AA}, Ca I 10833.4 {\AA}, Na I 10834.9 {\AA}, and Ca I 10838.9 {\AA} photospheric lines, as well as the He I 10830 {\AA} triplet. GRIS data revealed the presence of flare-related red- and blueshifted spectral line components, reaching Doppler velocities up to 90 km/s, and complex Si I profiles where the He i spectral line contribution is blueshifted. In contrast, the photospheric Ca i and Na i transitions remained unchanged, indicating that the flare did not modify the physical conditions of the lower photosphere. We combined that information with simultaneous imaging in the Ca ii H line and TiO band with the improved High-resolution Fast Imager (HiFI+), finding that the flare emission did not affect the inverse granulation or nearby plage, in agreement with the results from GRIS. We also complement the previous studies with a forward modelling computation, concluding that the He I spectral line emission reflects a complex response of the flaring chromosphere. Radiative excitation from coronal EUV irradiation, energy deposition by flare-accelerated electrons, and dynamic field-aligned plasma flows likely act together to produce the observed supersonic downflows and upflows. We plan to expand these findings through inversions of the He I 10830 {\AA} triplet signals in the future.

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Chromospheric velocities in an M3.2 flare using He I 1083.0 nm and Ca II 854.2 nm

We study the chromospheric LOS velocities during the GOES M3.2 flare (SOL2013-05-17T08:43) using simultaneous spectroscopic data of the He I 1083.0 nm triplet and Ca II 854.2 nm line. A filament was present in the flaring area. The observational data were acquired with the VTT (Tenerife, Spain) and covered the pre-flare, flare, and post-flare phases. Spectroscopic inversion techniques (HAZEL and STiC) were applied individually to He I and Ca II lines to recover the atmospheric parameters. Different inversion configurations were tested for Ca II and two families of solutions were found to explain the red asymmetry of the profiles: a redshifted emission feature or a blueshifted absorption feature. These solutions could explain two different flare scenarios (condensation vs. evaporation). The ambiguity was solved by comparing these results to the He I inferred velocities. At the front of the flare ribbon, we observed a thin, short-lived blueshifted layer. This is seen in both spectral regions but is much more pronounced in He I, with velocities of up to -10 km/s. In addition, at the front we found the coexistence of multiple He I profiles within one pixel. The central part of the ribbon is dominated by He I and Ca II redshifted emission profiles. A flare-loop system, visible only in He I absorption and not in Ca II, becomes visible in the post-flare phase and shows strong downflows at the footpoints of up to 39 km/s. In the flare, the Ca II line represents lower heights compared to the quiet Sun, with peak sensitivity shifting from $\log τ\simeq -5.2$ to $\log τ\simeq -3.5$. The inferred LOS velocities support a cool-upflow scenario at the leading edge of the flare. The solar filament in the region remained stable. The inclusion of the He I triplet in the analysis helped resolve the ambiguity between two possible solutions for the plasma velocities detected in the Ca II line.

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Multi-wavelength spectropolarimetric observations of AR13724 performed by GRIS

Multi-line spectropolarimetric observations allow for the simultaneous inference of the magnetic field at different layers of the solar atmosphere and provide insight into how these layers are magnetically coupled. The new upgrade of the Gregor Infrared Spectrograph (GRIS) instrument offers such a possibility, allowing for the simultaneous observation of the Ca II line at 8542 A, the Si I line at 10827 A, and the He I triplet at 10830 A in addition to some additional weaker spectral lines that can probe deeper in the photosphere. Because these spectral lines are sensitive to the plasma properties at different regions of the solar atmosphere, their combined analysis can help understand the stratification of its thermal and magnetic properties from the photosphere to the chromosphere. This work showcases recent observations of the upgraded GRIS at the active region AR13724, which shows the instrument's potential for unravelling the most minute details of solar phenomena. In particular, we analyse the spatial distribution of the polarisation signals as well as the distribution of Stokes profiles for different regimes of the magnetic field strength. We also conduct a preliminary data analysis using relatively simple and approximate methods.

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Observations of umbral flashes in the resonant sunspot chromosphere

In sunspot umbrae, the core of some chromospheric lines exhibits periodic brightness enhancements known as umbral flashes. The consensus is that they are produced by the upward propagation of shock waves. This view has recently been challenged by the detection of downflowing umbral flashes and the confirmation of the existence of a resonant cavity above sunspots. We aim to determine waves' propagating or standing nature in the low umbral chromosphere and confirm or refute the existence of downflowing umbral flashes. Spectroscopic temporal series of Ca II 8542 Å, Ca II H, and Halpha in a sunspot were acquired with the Swedish Solar Telescope. The Halpha velocity was inferred using bisectors. Simultaneous inversions of the Ca II 8542 Å line and the Ca II H core were performed using the NICOLE code. The nature of the oscillations and insights into the resonant oscillatory pattern were determined by analyzing the phase shift between the velocity signals and examining the temporal evolution. Propagating waves in the low chromosphere are more common in regions with frequent umbral flashes, where the transition region is shifted upward, making resonant cavity signatures less noticeable. In contrast, areas with fewer umbral flashes show velocity fluctuations that align with standing oscillations. Evidence suggests dynamic changes in the location of velocity resonant nodes due to variations in transition region height. Downflowing profiles appear at the onset of some umbral flashes, but upflowing motion dominates during most of the flash. These downflowing flashes are more common in standing umbral flashes. We confirm the existence of a chromospheric resonant cavity above sunspot umbrae produced by wave reflections at the transition region. The oscillatory pattern depends on the transition region height, which exhibits spatial and temporal variations due to the impact of the waves.

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Non-Local Thermodynamic Equilibrium inversions of the Si I 10827 A spectral line

Inferring the coupling of different atmospheric layers requires observing spectral lines sensitive to the atmospheric parameters, particularly the magnetic field vector, at various heights. The best way to tackle this goal is to perform multi-line observations simultaneously. For instance, the new version of the Gregor Infrared Spectrograph instrument offers the possibility to observe the spectral lines at 8542 and 10830 A simultaneously for the first time. The first spectral window contains the Ca II 8542 A spectral line, while the Si I 10827 A transition and He I 10830 A triplet infrared lines can be found in the second spectral window. As the sensitivity to the atmospheric parameters and the height of formation of those transitions is different, combining them can help understand the properties of the solar photosphere and chromosphere and how they are magnetically coupled. Traditionally, the analysis of the Si I 10827 A transition assumes local thermodynamic equilibrium (LTE), which is not the best approximation to model this transition. Hence, in this work, we examine the potential of performing non-LTE (NLTE) inversions of the full Stokes vector of the Si I 10827 A spectral line. The results indicate that we properly infer the atmospheric parameters through an extended range of atmospheric layers in comparison with the LTE case (only valid for the spectral line wings, i.e., the low photosphere), with no impact on the robustness of the solution and just a minor increase in computational time. Thus, the NLTE assumption will help to accurately constrain the photospheric physical parameters when performing combined inversions with, e.g., the Ca II 8542 A spectral line.

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Understanding the thermal and magnetic properties of a X-class flare in the low solar atmosphere

We analyse the spatial distribution and vertical stratification of the physical parameters of the solar atmosphere when an X-class flare occurs. We made use of observations acquired by the Interferometric Bidimensional Spectropolarimeter instrument when observing the full Stokes parameters for the Fe I 6173 A and Ca II 8542 A transitions. We analysed the observed spectra using the newly developed DeSIRe code to infer the atmospheric parameters at photospheric and chromospheric layers over the entire observed field of view. Our findings reveal that the chromosphere is characterised by temperature enhancements and strong upflows in the flare ribbon area, which indicates that the flaring event is producing hot material that is moving outwards from the Sun. We did not detect any trace of temperature enhancements or strong velocities (of any sign) at photospheric layers, signalling that the impact of the flaring event mainly happens at the middle and upper layers. The information about the magnetic field vector revealed relatively smooth stratifications with height for both magnetic field strength and inclination. Still, when examining the spatial distribution of the magnetic field inclination, we observed the presence of large-scale mixed polarities in the regions where the flare ribbon is located. These results suggest that the interaction between those mixed polarities could be the flare's triggering mechanism.

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Synthesis of infrared Stokes spectra in an evolving solar chromospheric jet

Chromospheric jets are plausible agents of energy and mass transport in the solar chromosphere, although their driving mechanisms have not yet been elucidated. Magnetic field measurements are key for distinguishing the driving mechanisms of chromospheric jets. We performed a full Stokes synthesis in the infrared range with a realistic radiative magnetohydrodynamics simulation that generated a chromospheric jet to predict spectro-polarimetric observations from the Sunrise Chromospheric Infrared spectro-Polarimeter (SCIP) onboard the SUNRISE III balloon telescope. The jet was launched by the collision between the transition region and an upflow driven by the ascending motion of the twisted magnetic field at the envelope of the flux tube. This motion is consistent with upwardly propagating non-linear Alfvenic waves. The upflow could be detected as continuous Doppler signals in the CaII 849.8 nm line at the envelope where the dark line core intensity and strong linear polarisation coexist. The axis of the flux tube was bright in both FeI 846.8 nm and CaII 849.8 nm lines with down-flowing plasma inside it. The structure, time evolution, and Stokes signals predicted in our study will improve the physical interpretation of future spectro-polarimetric observations with SUNRISE III/SCIP.

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A study of the capabilities for inferring atmospheric information from high-spatial-resolution simulations

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$\times10^{-3}$ 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$\times10^{-4}$of $I_c$. We, therefore, advise aiming for noise values on the order of or lower than 5$\times10^{-4}$ 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.

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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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DeSIRe: Departure coefficient aided Stokes Inversion based on Response functions

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.

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A modified Milne-Eddington approximation for a qualitative interpretation of chromospheric spectral lines

The Milne-Eddington approximation provides an analytic and simple solution to the radiative transfer equation. It can be easily implemented in inversion codes that are used to fit spectro-polarimetric observations to infer average values of the magnetic field vector and the line-of-sight velocity of the solar plasma. However, it is in principle restricted to spectral lines formed under local thermodynamic conditions. We show that a simple modification in the linear source function of the Milne-Eddington approximation is sufficient to infer relevant physical parameters from spectral lines that deviate from local thermodynamic equilibrium. This is not a new modification for the solar community but it has been forgotten for quite some time To check the validity of such approximation we make use of the Mg I b2 and the Ca II lines. We first study the influence of these new terms on the profile shape by means of the response functions. Then, we test the performance of an inversion code including such modification against the presence of noise. The approximation is also tested with realistic spectral lines generated with the RH numerical radiative transfer code. Finally, we confront the code with synthetic profiles generated from magneto-hydrodynamic simulations.

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Inference of electric currents in the solar photosphere

We aim at demonstrating the capabilities of a newly developed method for determining electric currents in the solar photosphere. 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 (DKIST) 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, $\mathbf{B}(x,y,z),$ from the synthetic Stokes profiles. We then apply Ampere's law to determine the electric currents, ${\bf j}$, from the inferred magnetic field, $\mathbf{B}(x,y,z),$ and compare the results with the electric currents present in the original MHD simulation. 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 $B\ge300$ G) in the inference of electric currents for low atmospheric heights (optical depths at 500 nm $τ_{5}\in$[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. We present a method that allows the inference of the three components of the electric current vector at deep atmospheric layers (photospheric layers) from spectropolarimetric observations.

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Multiple Stokes I inversions to infer magnetic fields in the spectral range around Cr I 5782 Å

The spectral window, containing Fraunhofer lines formed in the solar photosphere, around the magnetically sensitive Cr I lines at 5780.9, 5781.1, 5781.7, 5783.0, and 5783.8 Å, with Landé g-factors between 1.6 and 2.5, is explored. The goal is to analyze simultaneously 15 spectral lines, which comprise Cr I, Cu I, Fe I, Mn I, and Si I lines, without polarimetry to infer the thermodynamic and magnetic properties in strongly magnetized plasmas using an inversion code. The study is based on a new setup at the Vacuum Tower Telescope (VTT, Tenerife) which includes fast spectroscopic scans in the wavelength range around the Cr I 5781.75 Å line. The snapshot 385 of the Enhanced Network simulation from the Bifrost code serves to synthesize all the lines, which are in turn inverted simultaneously with SIR to establish the best inversion strategy. This strategy is then applied to VTT observations of a sunspot belonging to NOAA 12723 on 2018 September 30 and the results are compared to full-disk vector-field data obtained with the Helioseismic and Magnetic Imager (HMI). The 15 simultaneously inverted intensity profiles (Stokes I) delivered accurate temperatures and Doppler velocities when compared against the simulations. The derived magnetic fields and inclinations are most accurate when the fields are oriented along the line-of-sight (LOS) and less accurate when the fields are transverse to the LOS. In general, the results appear similar to the HMI vector-field data, although some discrepancies exist. The analyzed spectral range has the potential to deliver thermal, dynamic, and magnetic information in strongly magnetized features on the Sun, such as pores and sunspots, even without polarimetry. The highest sensitivity of the lines is found in the lower photosphere, on average around $\log τ= -1$. The multiple-line inversions provide smooth results across the whole field-of-view.

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Constraining the magnetic vector in the quiet solar photosphere and the impact of instrumental degradation

With the advent of next generation high resolution telescopes, our understanding of how the magnetic field is organized in the internetwork (IN) photosphere is likely to advance.We aim to evaluate the extent to which we can retrieve information about the magnetic vector in the IN photosphere using inversions. We use snapshots produced from high resolution 3D magnetohydrodynamic (MHD) simulations and employ the Stokes Inversions based on Response functions (SIR) code to produce synthetic observables in the near infrared spectral window observed by the GREGOR Infrared Spectrograph (GRIS), which contains the highly magnetically sensitive photospheric Fe I line pair at 15648.52 A and 15652.87 A. We perform nearly 14 million inversions to test how well the true MHD atmospheric parameters can be constrained. Finally, we degrade the synthetic Stokes vectors spectrally and spatially to GREGOR resolutions and examine how this influences observations, considering the impact of stray light, spatial resolution and signal-to-noise (S-to-N). We find the depth-averaged parameters can be recovered by the inversions of the undegraded profiles, and by adding gradients to magnetic field strength, inclination and line of sight velocity we show an improvement in the chi squared value is achieved. We evaluate the extent to which we can constrain these parameters at various optical depths, with the kinematic and thermodynamic parameters sensitive deeper in the atmosphere than the magnetic parameters. We find the S-to-N and spatial resolution play a significant role in determining how the atmosphere appears and the magnetic and kinematic parameters are invariant upon inclusion of unpolarized stray light. We studied a linear polarization feature which resembles those recently observed by GRIS, appearing as loop-like structures with similar magnetic flux density.

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Diagnostic capabilities of spectropolarimetric observations for understanding solar phenomena I. Zeeman-sensitive photospheric lines

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 15648 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 15648 A line to optimise our capabilities for inferring the thermal and magnetic properties of the lower atmosphere.

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Machine learning initialization to accelerate Stokes profile inversions

In this work, we discuss the application of convolutional neural networks (CNNs) as a tool to advantageously initialize Stokes profile inversions. 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 onboard the Hinode spacecraft as a test benchmark. First, we carefully analyze 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. 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. The CNNs allow us to significantly reduce the number of inversion cycles when used to compute initial guess model atmospheres, decreasing the computational time for LTE inversions by a factor of two to four. CNN's alone are much faster than assisted inversions, but the latter are more robust and accurate. The advantages and limitations of machine learning techniques for estimating optimum initial atmospheric models for spectral line inversions are discussed. Finally, we describe a python wrapper for the SIR and DeSIRe codes that allows for the easy setup of parallel inversions. The assisted inversions can speed up the inversion process, but the efficiency and accuracy of the inversion results depend strongly on the solar scene and the data used for the CNN training. This method (assisted inversions) will not obviate the need for analyzing individual events with the utmost care but will provide solar scientists with a much better opportunity to sample large amounts of inverted data, which will undoubtedly broaden the physical discovery space.

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High-resolution observations of the solar photosphere, chromosphere and transition region. A database of coordinated IRIS and SST observations

NASA's Interface Region Imaging Spectrograph (IRIS) provides high resolution observations of the solar atmosphere through UV spectroscopy and imaging. Since the launch of IRIS in June 2013, we have conducted systematic observation campaigns in coordination with the Swedish 1-m Solar Telescope (SST) on La Palma. The SST provides complementary high-resolution observations of the photosphere and chromosphere. The SST observations include spectro-polarimetric imaging in photospheric Fe I lines and spectrally-resolved imaging in the chromospheric Ca II 8542 A, H-alpha, and Ca II K lines. We present a database of co-aligned IRIS and SST datasets that is open for analysis to the scientific community. The database covers a variety of targets including active regions, sunspots, plage, quiet Sun, and coronal holes.

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