Context. Rapid blue- and redshifted excursions (RBEs and RREs) may play an important role in mass-loading and heating the solar corona, but their nature and origin are still debatable.

Aims. We aim to model these features to learn more about their properties, formation, and origin.

Methods. We created a realistic three-dimensional (3D) magnetohydrodynamic model of a solar plage region. Synthetic Hα spectra were generated and the spectral signatures of these features identified. The magnetic field lines associated with these events were traced, and the underlying dynamic was studied.

Results. The model reproduces many properties of RBEs and RREs well, such as spatial distribution, lateral movement, length, and lifetimes. Synthetic Hα line profiles, similarly to observed ones, show a strong blue- or redshift as well as asymmetries. These line profiles are caused by the vertical component of velocities higher than 30 − 40 km s⁻¹, which mostly appear in the height range 2 − 4 Mm. By tracing magnetic field lines, we show that the vertical velocity that causes the appearance of RBEs or RREs is always associated with the component of velocity perpendicular to the magnetic field lines.

Conclusions. The study confirms the hypothesis that RBEs and RREs are signs of Alfvénic waves with, in some cases, a significant contribution from slow magneto-acoustic modes.

Context. Ellerman bombs (EBs) and UV bursts are small-scale reconnection events that occur in the region of the upper photosphere to the chromosphere. It has recently been discovered that these events can have emission signatures in the He I D₃ and He I 10 830 Å lines, suggesting that their temperatures are higher than previously expected.

Aims. We aim to explain the line formation of He I D₃ and He I 10 830 Å in small-scale reconnection events.

Methods. We used a simulated EB in a Bifrost-generated radiative magnetohydrodynamics snapshot. The resulting He I D₃ and He I 10 830 Å line intensities were synthesized in 3D using the non-local thermal equilibrium (non-LTE) Multi3D code. The presence of coronal extreme UV (EUV) radiation was included self-consistently. We compared the synthetic helium spectra with observed raster scans of EBs in He I 10 830 Å and He I D₃ obtained at the Swedish Solar Telescope with the TRI-Port Polarimetric Echelle-Littrow Spectrograph.

Results. Emission in He I D₃ and He I 10 830 Å is formed in a thin shell around the EB at a height of ∼0.8 Mm, while the He I D₃ absorption is formed above the EB at ∼4 Mm. The height at which the emission is formed corresponds to the lower boundary of the EB, where the temperature increases rapidly from 6 × 10³ K to 10⁶ K. The synthetic line profiles at a heliocentric angle of μ = 0.27 are qualitatively similar to the observed profiles at the same μ-angle in dynamics, broadening, and line shape: emission in the wing and absorption in the line core. The opacity in He I D₃ and He I 10 830 Å is generated through photoionization-recombination driven by EUV radiation that is locally generated in the EB at temperatures in the range of 2 × 10⁴ − 2 × 10⁶ K and electron densities between 10¹¹ and 10¹³ cm⁻³. The synthetic emission signals are a result of coupling to local conditions in a thin shell around the EB, with temperatures between 7 × 10³ and 10⁴ K and electron densities ranging from ∼10¹² to 10¹³ cm⁻³. This shows that both strong non-LTE and thermal processes play a role in the formation of He I D₃ and He I 10 830 Å in the synthetic EB/UV burst that we studied.

Conclusions. In conclusion, the synthetic He I D₃ and He I 10 830 Å emission signatures are an indicator of temperatures of at least 2 × 10⁴ K; in this case, as high as ∼10⁶ K.

Context. Ellerman bombs (EBs), observed in the photospheric wings of the H alpha line, and UV bursts, observed in the transition region Si IV line, are both brightenings related to flux emergence regions and specifically to magnetic flux of opposite polarity that meet in the photosphere. These two reconnection-related phenomena, nominally formed far apart, occasionally occur in the same location and at the same time, thus challenging our understanding of reconnection and heating of the lower solar atmosphere.

Aims. We consider the formation of an active region, including long fibrils and hot and dense coronal plasma. The emergence of a untwisted magnetic flux sheet, injected 2.5 Mm below the photosphere, is studied as it pierces the photosphere and interacts with the preexisting ambient field. Specifically, we aim to study whether EBs and UV bursts are generated as a result of such flux emergence and examine their physical relationship.

Methods. The Bifrost radiative magnetohydrodynamics code was used to model flux emerging into a model atmosphere that contained a fairly strong ambient field, constraining the emerging field to a limited volume wherein multiple reconnection events occur as the field breaks through the photosphere and expands into the outer atmosphere. Synthetic spectra of the different reconnection events were computed using the 1.5D RH code and the fully 3D MULTI3D code.

Results. The formation of UV bursts and EBs at intensities and with line profiles that are highly reminiscent of observed spectra are understood to be a result of the reconnection of emerging flux with itself in a long-lasting current sheet that extends over several scale heights through the chromosphere. Synthetic spectra in the H alpha and Si iv 139.376 nm lines both show characteristics that are typical of the observations. These synthetic diagnostics suggest that there are no compelling reasons to assume that UV bursts occur in the photosphere. Instead, EBs and UV bursts are occasionally formed at opposite ends of a long current sheet that resides in an extended bubble of cool gas.

Realistic numerical simulations of the solar atmosphere can be used to interpret different phenomena observed on the solar surface. To gain insight into the atmospheric physical conditions, we compare the observations with 3D radiative magnetohydrodynamic models combined with forward modeling (radiative transfer). This thesis focuses particularly on the less understood chromospheric layer between the photosphere and the transition region. Only a few and complex spectral lines can probe the chromosphere making its observations a real challenge.The chromospheric environment is strongly influenced by departures from local thermodynamic equilibrium (non-LTE), horizontal radiative transfer (3D effects), and partially-coherent scattering of photons (partial redistribution effects). All these effects make the detailed 3D non-LTE radiative transfer very computationally demanding.In paper I, we focus on increasing the efficiency of non-LTE modeling of spectral lines in realistic solar models. We implemented a non-linear multigrid solver into the Multi3D code and showed that the method can handle realistic model atmospheres produced by radiative-MHD simulations. We obtained a speed-up of a factor 4.5-6 compared to multilevel accelerated lambda iteration.In paper II, we studied the chromospheric resonance lines Ca \textsc{ii} H\&K. Understanding their formation is crucial to interpreting the observations from the new imaging spectrometer CHROMIS, recently installed at the Swedish 1-m Solar Telescope. We investigated how the synthetic observables of Ca \textsc{ii} H\&K lines are related to atmospheric parameters.In paper III, we investigated a simulated active region including flux emergence that produced a flare. We modeled strong chromospheric lines, such as Ca \textsc{ii} H\&K, 8542 \AA, Mg \textsc{ii} h\&k, and H-$\alpha$, to investigate how it appears in synthetic images and spectra.

Context. Because of the complex physics that governs the formation of chromospheric lines, interpretation of solar chromospheric observations is difficult. The origin and characteristics of many chromospheric features are, because of this, unresolved.

Aims. We focus on studying two prominent features: long fibrils and flare ribbons. To model these features, we use a 3D magnetohydrodynamic simulation of an active region, which self-consistently reproduces both of these features.

Methods. We modeled the Ha, Mg it k, Call K, and Call 8542 A lines using the 3D non-LTE radiative transfer code Multi3D. To obtain non-LTE electron densities, we solved the statistical equilibrium equations for hydrogen simultaneously with the charge conservation equation. We treated the Call K and Mg It k lines with partially coherent scattering.

Results. This simulation reproduces long fibrils that span between the opposite -polarity sunspots and go up to 4 Mm in height. They can be traced in all lines owing to density corrugation. In contrast to previous studies, Ha, Mg II h&k, and Call H&K are formed at similar height in this model. Although some of the high fibrils are also visible in the Call 8542 A line, this line tends to sample loops and shocks lower in the chromosphere. Magnetic field lines are aligned with the Ha fibrils, but the latter holds to a lesser extent for the Call 8542 A line. The simulation shows structures in the Ha line core that look like flare ribbons. The emission in the ribbons is caused by a dense chromosphere and a transition region at high column mass. The ribbons are visible in all chromospheric lines, but least prominent in Call 8542 A line. In some pixels, broad asymmetric profiles with a single emission peak are produced similar to the profiles observed in flare ribbons. They are caused by a deep onset of the chromospheric temperature rise and large velocity gradients.

Conclusions. The simulation produces long fibrils similar to what is seen in observations. It also produces structures similar to flare ribbons despite the lack of nonthermal electrons in the simulation. The latter suggests that thermal conduction might be a significant agent in transporting flare energy to the chromosphere in addition to nonthermal electrons.

Context. CHROMIS, a new imaging spectrometer at the Swedish 1-m Solar Telescope (SST), can observe the chromosphere in the H and K lines of Ca II at high spatial and spectral resolution. Accurate modeling as well as an understanding of the formation of these lines are needed to interpret the SST/CHROMIS observations. Such modeling is computationally challenging because these lines are influenced by strong departures from local thermodynamic equilibrium, three-dimensional radiative transfer, and partially coherent resonance scattering of photons. Aims. We aim to model the Ca II H and K lines in 3D model atmospheres to understand their formation and to investigate their diagnostic potential for probing the chromosphere. Methods. We model the synthetic spectrum of Ca II using the radiative transfer code Multi3D in three different radiation-magnetohydrodynamic model atmospheres computed with the Bifrost code. We classify synthetic intensity profiles according to their shapes and study how their features are related to the physical properties in the model atmospheres. We investigate whether the synthetic data reproduce the observed spatially-averaged line shapes, center-to-limb variation and compare this data with SST/CHROMIS images. Results. The spatially-averaged synthetic line profiles show too low central emission peaks, and too small separation between the peaks. The trends of the observed center-to-limb variation of the profiles properties are reproduced by the models. The Ca II H and K line profiles provide a temperature diagnostic of the temperature minimum and the temperature at the formation height of the emission peaks. The Doppler shift of the central depression is an excellent probe of the velocity in the upper chromosphere.

Context. 3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far, multilevel accelerated lambda iteration (MALI) has been the method of choice to perform high-resolution computations in multidimensional problems. The disadvantage of MALI is that its computing time scales as O(n(2)), with n the number of grid points. When the grid becomes finer, the computational cost increases quadratically. Aims. We aim to develop a 3D non-LTE radiative transfer code that is more efficient than MALI. Methods. We implement a non-linear multigrid, fast approximation storage scheme, into the existing Multi3D radiative transfer code. We verify our multigrid implementation by comparing with MALI computations. We show that multigrid can be employed in realistic problems with snapshots from 3D radiative magnetohydrodynamics (MHD) simulations as input atmospheres. Results. With multigrid, we obtain a factor 3.3-4.5 speed-up compared to MALI. With full-multigrid, the speed-up increases to a factor 6. The speed-up is expected to increase for input atmospheres with more grid points and finer grid spacing. Conclusions. Solving 3D non-LTE radiative transfer problems using non-linear multigrid methods can be applied to realistic atmospheres with a substantial increase in speed.