Context. A proper estimate of the chromospheric magnetic fields is thought to improve modelling of both active region and coronal mass ejection evolution. However, because the chromospheric field is not regularly obtained for sufficiently large fields of view, estimates thereof are commonly obtained through data-driven models or field extrapolations, based on photospheric boundary conditions alone and involving pre-processing that may reduce details and dynamic range in the magnetograms.

Aims. We investigate the similarity between the chromospheric magnetic field that is directly inferred from observations and the field obtained from a magnetohydrostatic (MHS) extrapolation based on a high-resolution photospheric magnetogram.

Methods. Based on Swedish 1-m Solar Telescope Fe I 6173 Å and Ca II 8542 Å 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-local thermodynamic equilibrium (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 conditions for the MHS model that delivers the three-dimensional field, gas pressure, and density self-consistently.

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 by 16% on average than these when larger in magnitude than 300 G. The observationally inferred transverse component is systematically stronger, up to an order of magnitude in magnetically weaker regions, but 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 Å fibrils than that of the WFA, especially outside strong-field concentrations. The amount of structure as well as the transverse field strengths are, however, underestimated by the MHS extrapolation. This underscores the importance of considering a chromospheric magnetic field constraint in data-driven modelling of active regions, particularly in the context of space weather predictions.

Context. 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.

Aims. 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).

Methods. We used Milne–Eddington inversions, nonlocal thermodynamic equilibrium (non-LTE) inversions, and a magnetohydrostatic extrapolation to obtain constraints on the three-dimensional (3D) 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.

Results. We find enhanced heating rates in the upper chromosphere of up to ∼5 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 (∼1.2″). Band 3 brightness temperatures reach about ∼10⁴ K in the region, and the transverse magnetic field strength inferred from the non-LTE inversions is on the order of ∼500 G in the chromosphere.

Conclusions. 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.

The chromosphere is an intermediate layer of the Sun's atmosphere where radiative equilibrium breaks down. The standard chromospheric diagnostics such as the Mg II h and k and Ca II H and K spectral lines are formed under nonlocal thermodynamic equilibrium (NLTE) and they are only partially sensitive to the local conditions. Consequently, the interpretation of their profiles is not straightforward. In contrast, millimeter (mm) continuum radiation is produced by thermal free-free collisional interactions in the chromosphere under most solar conditions, and the observed brightness temperatures are better proxies for plasma temperatures. Observations at these long wavelengths have been recently enabled thanks to the Atacama Large Millimeter/submillimeter Array (ALMA), but the Sun remains largely unexplored in this spectral range.

In this thesis I explore the diagnostic potential of the mm continuum to study the solar chromosphere using inversions and radiation-magnetohydrodynamics (r-MHD) simulations. In particular, this work takes an unprecedented look at solar active-regions in the mm using some of the first solar ALMA observations.

In Paper I, we investigated whether the mm continuum helps to constrain temperatures in NLTE inversions of the MgII and CaII resonance lines using synthetic data from a 3D r-MHD simulation. In Paper II, we applied the same inversion technique to observational data in order to constrain temperature and microturbulence in plage, and we detected signatures of wave heating in coordinated observations with the IRIS satellite. In Paper III, we reported the first results of a comprehensive effort to characterize the visibility of small-scale heating events in an active-region using multiwavelength observations from the mm to the extreme-ultraviolet. We detected multiple, dynamic, transient brightenings -- we called them "millimeter bursts", and we investigated magnetic reconnection using a simulation.

This thesis shows that ALMA offers a complementary spectral diagnostic to the existing ones at visible and ultraviolet wavelengths and it underscores the importance of mm continuum observations for constraining models of the solar atmosphere.

Aims. We aim to investigate the temperature enhancements and formation heights of solar active-region brightenings 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).

Methods. We examined 3 mm signatures of heating events identified in Solar Dynamics Observatory 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.

Results. We report the null detection of EBs in the 3 mm continuum at ∼1.2″ 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 ∼14 200 K in some events have a contribution (up to ∼7%) from the corona. We also detect FAF-like events in the 3 mm continuum. These events show rapid motions of > 10 kK plasma launched with high plane-of-sky velocities (37 − 340 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.

Context. Numerical simulations of the solar chromosphere predict a diverse thermal structure with both hot and cool regions. Observations of plage regions in particular typically feature broader and brighter chromospheric lines, which suggests that they are formed in hotter and denser conditions than in the quiet Sun, but also implies a nonthermal component whose source is unclear. Aims. We revisit the problem of the stratification of temperature and microturbulence in plage and the quiet Sun, now adding millimeter (mm) continuum observations provided by the Atacama Large Millimiter Array (ALMA) to inversions of near-ultraviolet Interface Region Imaging Spectrograph (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. Methods. We use the STiC nonlocal thermodynamic equilibrium (NLTE) inversion code to simultaneously fit real ultraviolet and mm spectra in order to infer the thermodynamic parameters of the plasma. Results. We confirm the anticipated constraining potential of ALMA in NLTE 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 (similar to 3-6 km s(-1) in plage compared to similar to 4-7 km s(-1) from IRIS alone) in the chromosphere. The average brightness temperature of the plage region at 1.25 mm is 8500 K, but the ALMA maps also show much cooler (similar to 3000 K) and hotter (similar to 11000 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.

Context. 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 warm regions of their circumstellar envelopes (CSEs). Aims. We analyse the CO emission spectra, including a large number of high-J CO lines (from J = 14-13 to J = 45-44, nu = 0), 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 to the young planetary nebulae phase. Methods. We used the rotational diagram (RD) technique to derive rotational temperatures (T-rot) and masses (M-H2) of the envelope layers where the CO transitions observed with PACS arise. Additionally, we obtained a first order estimate of the mass-loss rates and assessed the impact of the opacity correction for a range of envelope characteristic radii. We used 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-rot and M-H2. Results. The sensitivity of PACS allowed for the study of higher rotational numbers than before indicating the presence of a significant amount of warmer gas (similar to 200-900 K) that is not traceable with lower J CO observations at submillimetre/millimetre wavelengths. The masses are in the range M-H2 similar to 10(-2)-10(-5)M(Theta), anticorrelated with temperature. For some strong CO emitters we infer a double temperature (warm T-rot similar to 400 K and hot T-rot similar to 820 K) component. From the analysis of IRC+10216, we corroborate that the effect of line variability is perceptible on the T-rot of the hot component only, and certainly insignificant on M-H2 and, hence, the mass-loss rate. The agreement between our mass-loss rates and the literature across the sample is good. Therefore, the parameters derived from the RD are robust even when strong line flux variability occurs, and the major source of uncertainty in the estimate of the mass-loss rate is the size of the CO-emitting volume.

In this Licentiate thesis I review the properties of the solar atmosphere and the diagnostic value ofdifferent spectral lines in the visible and ultraviolet (UV) along with the millimeter (mm) continua in theelectromagnetic spectrum of the Sun.While the solar atmosphere has been routinely observed in high-resolution from ground-based opti-cal telescopes such as the Swedish Solar Telescope (SST), and more recently in the UV from space tele-scopes such as the Interface Region Imaging Spectrograph (IRIS), radio observations lag behind despitetheir great usefulness. This is likely to change thanks to the Atacama Large Millimeter Array (ALMA)that only started observing the Sun in 2016 with a few limitations, but the first results are promising.ALMA observations probe the solar chromosphere at different heights by tuning into slightly differentfrequencies at potentially milliarcsecond scales if the full array is able to operate with the longest base-lines. This new spectral window onto the Sun is expected to advance various fields of research suchas wave propagation and oscillations in the chromosphere, thermal structure of filaments/prominences,triggering of flares and microflares, and more generally chromospheric and coronal heating, because themm-intensities can be modelled by simply assuming local-thermodynamic equilibrium.In da Silva Santos et al. (2018) we find that coordinated observations from SST, IRIS and ALMA willpermit us to estimate with greater accuracy the full thermodynamical state of the plasma as a functionof optical depth based on experiments with a snapshot of a three-dimensional magnetohydrodynamicsimulation of the Sun’s atmosphere. Particularly, the mm-continuum improves the accuracy of inferredtemperatures in the chromosphere. Here we expand on the Why and How this can be done. The goal isto better constrain the temperature stratification in the solar atmosphere in order to understand chromo-spheric heating.

Context. High-resolution observations of the solar chromosphere at millimeter wavelengths are now possible with the Atacama Large Millimeter Array (ALMA), bringing with them the promise of tackling many open problems in solar physics. Observations from other ground and space-based telescopes will greatly benefit from coordinated endeavors with ALMA, yet the diagnostic potential of combined optical, ultraviolet and mm observations has remained mostly unassessed. Aims. In this paper we investigate whether mm-wavelengths could aid current inversion schemes to retrieve a more accurate representation of the temperature structure of the solar atmosphere. Methods. We performed several non-LTE inversion experiments of the emergent spectra from a snapshot of 3D radiation-MHD simulation. We included common line diagnostics such as Ca II K, 8542 angstrom and Mg II h and k, taking into account partial frequency redistribution effects, along with the continuum around 1.2 mm and 3 mm. Results. We find that including the mm-continuum in inversions allows a more accurate inference of temperature as function of optical depth. The addition of ALMA bands to other diagnostics should improve the accuracy of the inferred chromospheric temperatures between log tau similar to [-6, -4.5] where the Ca II and Mg II lines are weakly coupled to the local conditions. However, we find that simultaneous multiatom, non-LTE inversions of optical and UV lines present equally strong constraints in the lower chromosphere and thus are not greatly improved by the 1.2 mm band. Nonetheless, the 3 mm band is still needed to better constrain the mid-upper chromosphere.

In this work (Paper I), we analyse Herschel-PACS spectroscopy for a subsample of 23 O-rich and 3 S-type evolved stars, in different evolutionary stages from the asymptotic giant branch (AGB) to the planetary nebula (PN) phase, from the THROES catalogue. (C-rich targets are separately studied in Paper II). The broad spectral range covered by PACS (similar to 55-210 mu m) includes a large number of high-J CO lines, from J = 14-13 to J = 45-44 (v = 0), that allow us to study the warm inner layers of the circumstellar envelopes (CSEs) of these objects, at typical distances from the star of approximate to 10(14)-10(15) cm and approximate to 10(16) cm for AGBs and post-AGB-PNe, respectively. We have generated CO rotational diagrams for each object to derive the rotational temperature, total mass within the CO-emitting region and average mass-loss rate during the ejection of these layers. We present first order estimations of these basic physical parameters using a large number of high-J CO rotational lines, with upper-level energies from E-up similar to 580 to 5000 K, for a relatively big set of evolved low-to-intermediate mass stars in different AGB-to-PN evolutionary stages. We derive rotational temperatures ranging from T-rot similar to 200 to 700 K, with typical values around 500K for AGBs and systematically lower, similar to 200 K, for objects in more advanced evolutionary stages (post-AGBs and PNe). Our values of Trot are one order or magnitude higher than the temperatures of the outer CSE layers derived from low-J CO line studies. The total mass of the inner CSE regions where the PACS CO lines arise is found to range from M-H2 similar to 10(-6) to approximate to 10(-2) M-circle dot, which is expected to represent a small fraction of the total CSE mass. The mass-loss rates estimated are in the range M similar to 10(-7)-10(-4) M-circle dot yr(-1), in agreement (within uncertainties) with values found in the literature. We find a clear anticorrelation between M-H2 and. M vs. Trot that probably results from a combination of most e ffi cient line cooling and higher line opacities in high mass-loss rate objects. For some strong CO emitters in our sample, a double temperature (hot and warm) component is inferred. The temperatures of the warm and hot components are similar to 400-500K and similar to 600-900 K, respectively. The mass of the warm component (similar to 10(-5)-8 x 10(-2) M-circle dot) is always larger than that of the hot component, by a factor of between two and ten. The warm-to-hot MH2 and Trot ratios in our sample are correlated and are consistent with an average temperature radial profile of proportional to r(-0.5 perpendicular to 0.1), that is, slightly shallower than in the outer envelope layers, in agreement with recent studies.