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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., Comment: 12 pages, 7 figures, Appendix, Submitted to A&A

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 \r{A} and Ca II 8542 \r{A} 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., Comment: accepted for publication in ApJ

The strongly coupled hydrodynamic, magnetic, and radiation properties of the plasma in the solar chromosphere makes it a region of the Sun's atmosphere that is poorly understood. We use data obtained with the high-resolution Visible Broadband Imager (VBI) equipped with an H$\beta$ filter and the Visible Spectro-Polarimeter (ViSP) at the Daniel K. Inouye Solar Telescope to investigate the fine-scale structure of the plage chromosphere. To aid the interpretation of the VBI imaging data, we also analyze spectra from the CHROMospheric Imaging Spectrometer on the Swedish Solar Telescope. The analysis of spectral properties, such as enhanced line widths and line depths explains the high contrast of the fibrils relative to the background atmosphere demonstrating that H$\beta$ is an excellent diagnostic for the enigmatic fine-scale structure of the chromosphere. A correlation between the parameters of the H$\beta$ line indicates that opacity broadening created by overdense fibrils could be the main reason for the spectral line broadening observed frequently in chromospheric fine-scale structures. Spectropolarimetric inversions of the ViSP data in the Ca II 8542 {\AA} and Fe I 6301/6302 {\AA} lines are used to construct semiempirical models of the plage atmosphere. Inversion outputs indicate the existence of dense fibrils in the Ca II 8542 {\AA} line. The analyses of the ViSP data show that the morphological characteristics, such as orientation, inclination and length of fibrils are defined by the topology of the magnetic field in the photosphere. Chromospheric maps reveal a prominent magnetic canopy in the area where fibrils are directed towards the observer., Comment: 17 pages, 11 figures, accepted in ApJ

Plage regions are patches of concentrated magnetic field in the Sun's atmosphere where hot coronal loops are rooted. While previous studies have shed light on the properties of plage magnetic fields in the photosphere, there are still challenges in measuring the overlying chromospheric magnetic fields, which are crucial to understanding the overall heating and dynamics. Here, we utilize high-sensitivity, spectropolarimetric data obtained by the four-meter Daniel K. Inouye Solar Telescope (DKIST) to investigate the dynamic environment and magnetic field stratification of an extended, decaying plage region. The data show strong circular polarization signals in both plage cores and surrounding fibrils. Notably, weak linear polarization signals clearly differentiate between plage patches and the fibril canopy, where they are relatively stronger. Inversions of the Ca II 8542 $\mathring{A}$ spectra show an imprint of the fibrils in the chromospheric magnetic field, with typical field strength values ranging from $\sim$ 200-300 G in fibrils. We confirm the weak correlation between field strength and cooling rates in the lower chromosphere. Additionally, we observe supersonic downflows and strong velocity gradients in the plage periphery, indicating dynamical processes occurring in the chromosphere. These findings contribute to our understanding of the magnetic field and dynamics within plages, emphasizing the need for further research to explore the expansion of magnetic fields with height and the three-dimensional distribution of heating rates in the lower chromosphere., Comment: 17 pages, 8 figures, accepted for publication in ApJL

Quiescent filaments appear as absorption features on the solar disk when observed in chromospheric lines and at continuum wavelengths in the millimeter (mm) range. Active region (AR) filaments are their small-scale, low-altitude analogues, but they could not be resolved in previous mm observations. This spectral diagnostic can provide insight into the details of the formation and physical properties of their fine threads, which are still not fully understood. Here, we shed light on the thermal structure of an AR filament using high-resolution brightness temperature ($T_{\rm b}$) maps taken with ALMA Band 6 complemented by simultaneous IRIS near-UV spectra, Hinode/SOT photospheric magnetograms, and SDO/AIA extreme-UV images. Some of the dark threads visible in the AIA 304 {\AA} passband and in the core of Mg II resonance lines have dark ($T_{\rm b}<5000$K) counterparts in the 1.25 mm maps, but their visibility significantly varies across the filament spine and in time. These opacity changes are possibly related to variations in temperature and electron density in filament fine structures. The coolest $T_{\rm b}$ values ($<$5000 K) coincide with regions of low integrated intensity in the Mg II h and k lines. ALMA Band 3 maps taken after the Band 6 ones do not clearly show the filament structure, contrary to the expectation that the contrast should increase at longer wavelengths based on previous observations of quiescent filaments. The ALMA maps are not consistent with isothermal conditions, but the temporal evolution of the filament may partly account for this., Comment: 15 pages, 4 figures. Accepted for publication in Front. Astron. Space Sci.; research topic: "The Sun Seen with the Atacama Large mm and sub-mm Array (ALMA) - First Results"

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., Comment: 18 pages, 13 figures. Accepted for publication in A&A. Typos and bibtex corrected

Context. A proper estimate of the chromospheric magnetic fields is believed to improve modelling of both active region and coronal mass ejection evolution. Aims. We investigate the similarity between the chromospheric magnetic field inferred from observations and the field obtained from a magnetohydrostatic (MHS) extrapolation. Methods. Based Fe i 6173 {\AA} and Ca ii 8542 {\AA} observations of NOAA active region 12723, we employed the spatially-regularised weak-field approximation (WFA) to derive the vector magnetic field in the chromosphere from Ca ii, as well as non-LTE inversions of Fe i and Ca ii to infer a model atmosphere for selected regions. Milne-Eddington inversions of Fe i serve as photospheric boundary for the MHS model that delivers the three-dimensional field, gas pressure and density. Results. For the line-of-sight component, the MHS chromospheric field generally agrees with the non-LTE inversions and WFA, but tends to be weaker than those when larger in magnitude than 300 G. The observationally inferred transverse component is stronger, especially in magnetically weaker regions, yet the qualitative distribution with height is similar to the MHS results. For either field component the MHS chromospheric field lacks the fine structure derived from the inversions. Furthermore, the MHS model does not recover the magnetic imprint from a set of high fibrils connecting the main polarities. Conclusions. The MHS extrapolation and WFA provide a qualitatively similar chromospheric field, where the azimuth of the former is better aligned with Ca ii 8542 {\AA} fibrils than that of the WFA, especially outside strong-field concentrations. The amount of structure as well as the transverse field strengths are underestimated by the MHS extrapolation. This underscores the importance of considering a chromospheric magnetic field constraint in data-driven modelling of active regions., Comment: under review at A&A, abstract has been abridged

We aim to investigate the temperature enhancements and formation heights of impulsive heating phenomena in solar active-regions such as Ellerman bombs (EBs), ultraviolet bursts (UVBs), and flaring active-region fibrils (FAFs) using interferometric observations in the millimeter (mm) continuum provided by the Atacama Large Millimeter/submillimeter Array (ALMA). We examined 3 mm signatures of heating events identified in Solar Dynamics Observatory (SDO) observations of an active region and compared the results with synthetic spectra from a 3D radiative magnetohydrodynamic simulation. We estimated the contribution from the corona to the mm brightness using differential emission measure analysis. We report the null detection of EBs in the 3 mm continuum at $\sim1.2$" spatial resolution, which is evidence that they are sub-canopy events that do not significantly contribute to heating the upper chromosphere. In contrast, we find the active region to be populated with multiple compact, bright, flickering mm bursts -- reminiscent of UVBs. The high brightness temperatures of up to $\sim14200$ K in some events have a significant contribution (up to $\sim$7%) from the corona. We also detect FAF-like events in the 3 mm continuum that show rapid motions of $>10000\,$K plasma launched with high plane-of-sky velocities ($37-340\rm\,km\,s^{-1}$) from bright kernels. The mm FAFs are the brightest class of warm canopy fibrils that connect magnetic regions of opposite polarities. The simulation confirms that ALMA should be able to detect the mm counterparts of UVBs and small flares and thus provide a complementary diagnostic for localized heating in the solar chromosphere., Comment: revised; accepted in Astronomy & Astrophysics

Numerical simulations of the solar chromosphere predict a diverse thermal structure with both hot and cool regions. Observations of plage regions in particular feature broader and brighter chromospheric lines, which suggest that they are formed in hotter and denser conditions than in the quiet-Sun, but also implies a non-thermal component whose source is unclear. We revisit the problem of the stratification of temperature and microturbulence in plage now adding millimeter continuum observations provided by ALMA to inversions of near-ultraviolet IRIS spectra as a powerful new diagnostic to disentangle the two parameters. We fit cool chromospheric holes and track the fast evolution of compact mm brightenings in the plage region. We use the STiC non-LTE inversion code to simultaneously fit real ultraviolet and millimeter spectra in order to infer the thermodynamic parameters of the plasma. We confirm the anticipated constraining potential of ALMA in non-LTE inversions of the solar chromosphere. We find significant differences between the inversion results of IRIS data alone compared to the results of a combination with the mm data: the IRIS+ALMA inversions have increased contrast and temperature range, and tend to favor lower values of microturbulence in the chromosphere of plage. The average brightness temperature of the plage region at 1.25 mm is 8500 K, but the ALMA maps also show much cooler ($\sim3000$ K) and hotter ($\sim11\,000$ K) evolving features partially seen in other diagnostics. To explain the former, the inversions require the existence of localized, low temperature regions in the chromosphere where molecules such as CO could form. The hot features could sustain such high temperatures due to non-equilibrium hydrogen ionization effects in a shocked chromosphere - a scenario that is supported by low-frequency shock wave patterns found in the MgII lines probed by IRIS., Comment: 17 pages, 12 figures; accepted in A&A (added references, corrected typos)

This is the second paper of a series making use of Herschel/PACS spectroscopy of evolved stars in the THROES catalogue to study the inner regions of their circumstellar envelopes (CSEs). We analyze the CO emission spectra, including a large number of high-$J$ CO lines (from $J$=14-13 to $J$=45-44), as a proxy for the warm molecular gas in the CSEs of a sample of bright carbon-rich stars spanning different evolutionary stages from the Asymptotic Giant Branch (AGB) to the young planetary nebulae (PNe) phase. We use the rotational diagram (RD) to derive rotational temperatures ($T_{\rm rot}$) and masses ($M_{\rm H_2}$) of the envelope layers where the CO transitions arise. We also obtain a first order estimate of the mass-loss rates and assess the impact of the opacity correction for a range of characteristic envelope radii. We use multi-epoch spectra for the well studied C-rich envelope IRC+10216 to investigate the impact of CO flux variability on the values of $T_{\rm rot}$ and $M_{\rm H_2}$. PACS sensitivity allowed the study of higher rotational numbers than before, indicating the presence of a significant amount of warmer gas ($\sim$200-900 K) not traceable with lower-$J$ CO observations at sub-mm/mm wavelengths. The masses are in the range $\sim10^{-2}-10^{-5}\,\rm M_{\odot}$, anti-correlated with temperature. For some strong CO emitters we infer a double temperature (warm $T_{\rm rot}\sim$400 K and hot $T_{\rm rot}\sim$820 K) component. From the analysis of IRC+10216, we corroborate that the effect of line variability is perceptible on the $T_{\rm rot}$ of the hot component only, and certainly insignificant on $M_{\rm H_2}$ and, hence, the mass-loss rate. Therefore, the parameters derived from the RD are robust even when strong line flux variability occurs, with the major source of uncertainty in the estimate of the mass-loss rate being the size of the CO-emitting volume., Comment: accepted in A&A