Tobias Felipe

Context. Numerical simulations are essential for studying the complex structure of the solar atmosphere, especially in the context of the coronal heating problem. Understanding how numerical factors and boundary conditions (BCs) influence the energetic structure of these models is crucial for unraveling the mechanisms behind the heating of the solar corona. Aims. We investigate how the spatial dimensions of the computational domain, the upper BCs, and the vertical grid resolution influence the relaxed thermal structure, energetics, and long-term stability of simulations of the solar atmosphere in 2D with a vertical magnetic field. Methods. Using the MAGEC code, we conducted several 2D parametric studies, varying the domain width and height, vertical grid stretching, and top BCs (including the hot-plate, closed, unrestricted temperature, background heating configurations, and nonreflecting characteristics). We evaluated the resulting average temperature profiles to determine their parameter dependence and temporal stability. Additionally, we analyzed the accumulated energetic budget as a function of height, isolating the contributions from radiative losses, thermal conduction, pressure work, and internal energy flux; this allowed us to evaluate how the balance of these distinct energetic contributions shifts depending on the chosen top BCs and explain the relaxed thermal profiles of the models. Results. The temperature structure of the models behaves significantly differently as a function of the domain height and top BC. We identified clear dependencies of these factors on the average temperature profile and the gradient of the horizontally averaged transition region (TR). In general, models with larger vertical domains yield higher average temperatures in the intermediate corona and steeper gradients across the average TR. Comparative analysis reveals that, among the less artificial BCs, the nonreflecting characteristics are the most effective at delaying coronal cooling. Furthermore, we determined the threshold height at which simulations that employ a dynamic top BC can effectively mimic the temporal behavior of fixed-temperature setups. We also established the maximum allowable degree of grid stretching in the corona that preserves physical accuracy while substantially reducing computational costs. Finally, the accumulated effects of the energetic terms change significantly according to the chosen BC, with specific mechanisms acting as cooling agents in different layers of the atmosphere. Conclusions. Our results demonstrate that in 2D the domain height, vertical grid design, and BC critically dictate the relaxed thermal structure and energetic balance of the simulated solar atmosphere.

Context . Active region atmospheres host many oscillatory phenomena. The chromosphere is delimited by steep temperature gradients at the photosphere and transition region, where magnetoacoustic waves are trapped and can form standing oscillations within this resonant cavity. Aims . We aim to detect the signature of the resonant nodes of standing waves, which are expected to produce sudden jumps in the oscillatory phase and power dips. Methods . Spectroscopic temporal series of H α in a pore were acquired with the Swedish Solar Telescope. The velocity and temperature fluctuations at multiple atmospheric heights were inferred from the analysis of the intensity at many spectral positions along the line wings. Wavelet analysis was employed to characterize the phase differences and the power at different heights. Results . The phase shift between velocity and temperature shows a ±90° value, which is consistent with standing oscillations. Robust evidence of the presence of a nodal layer in the temperature at around the height probed by the intensity at H α ± 0.30 Å is found, such as the detection of 180° jumps in the phase of the temperature oscillations and remarkable power dips at the same atmospheric layer. The exact height of the resonant nodes depends on the spatial location and time. We generally find a mixture of standing and propagating waves. This is consistent with a leaky resonator where waves are partially reflected at the transition region, while some of them are able to propagate into the corona. Conclusions . For the first time, we report the detection and characterization of resonant nodes in the solar chromosphere. This result provides strong observational support for the chromospheric resonant cavity model and paves the way for the development of new seismological techniques to investigate the structure of active-region chromospheres.

Mapping the subsurface structure and flow field of sunspots has been a challenging task for helioseismology. In this work, we investigate the propagation of acoustic waves in a sunspot in NOAA active region 11312 using time–distance helioseismology. Travel-times of waves traveling into and out of the sunspot are measured as functions of travel distance and azimuthal angle relative to the local radial direction. The same time–distance analysis is also applied to simulated data based on a magnetohydrostatic (MHS) model of the sunspot, and forward modeling of travel-times is performed using ray tracing based on both the MHS sunspot model and a magnetohydrodynamic (MHD) simulation. We find that both ingoing (traveling from the quiet area into the sunspot) and outgoing waves (traveling from the sunspot into the quiet area) have shorter travel-times than in the quiet Sun, with travel-time reductions of up to ∼40 s. The magnitude of the mean time shift is largest for waves traveling along the radial direction at small travel distances. A clear asymmetry is detected between ingoing and outgoing waves: outgoing waves generally exhibit shorter travel-times. This asymmetry is strongest for the radial direction and small travel distances, with differences exceeding 1 minute for 3.5 and 4.5 mHz waves. From the results of both observations and models, our analysis indicates that the overall reduction in travel-time could be primarily caused by the combined effects of Wilson depression, magnetic field, and wave-speed perturbations, while the ingoing–outgoing asymmetry could be partly attributable to subsurface flows. Although the forward-modeling results reproduce several qualitative features of the observations, quantitative discrepancies remain, highlighting limitations of current sunspot models and ray-theoretical approximations.

Magnetohydrodynamic waves redistribute energy in magnetic structures of the lower solar atmosphere, yet constraints on how wave power and dominant frequencies are organized above sunspots remain limited, because most studies use only a few well-separated diagnostics. Here, we present multiline wave signatures in a sunspot from near-ultraviolet (near-UV) spectroscopy with the S unrise-iii UV Spectropolarimeter and Imager (SUSI). We analyse a 2 hr time series of repeated raster scans of a sunspot near disc center in the 327–329 nm spectral window (>100 lines). From these, we select 44 lines that radiative-transfer calculations suggest sample effective formation heights within the umbral core, from the deep photosphere toward the low chromosphere. For each line, we extract line-core intensity and line-of-sight velocity time series using a dedicated multiline fitting routine and compute Morlet wavelet power spectra. The refined global wavelet spectra show that most lines (in both intensity and velocity) are genuinely multifrequency, with a dominant peak and substantial statistically significant power up to 12 mHz. Unsupervised clustering of the normalized spectra groups lines into families with similar spectral shapes and reveals a progression of dominant frequencies from ∼2 to ∼10 mHz across the ensemble, for both intensity and velocity (not necessarily in the same lines). This behavior is not reproduced by a simple formation-height ranking, suggesting that uncertainties in the formation-height estimates and line-dependent diagnostic response together shape the ordering. These S unrise-iii /SUSI observations open a new regime for near-UV multiline wave studies and provide the first systematic characterization of frequency-structured sunspot wave behaviour in this spectral region.

Small-scale vortices are ubiquitous structures that exist over a wide range of spatial extents in the solar atmosphere. They are considered to play an important role in the energy transport and local heating. However, numerical simulations frequently assess the effect of vortices without simultaneously considering the effects of spatial resolution and differences in magnetic configuration. We investigate the influence of different magnetic field configurations and spatial resolutions on vortex structures. We evaluate two detection methods to determine their impact on the morphology, statistical properties, and temperature profiles of vortices. We analyzed a set of six 3D realistic simulations of the solar atmosphere under three different magnetic field configurations: a small-scale dynamo and two initially vertical implanted magnetic fields of 50 G and 200 G. Three different spatial resolutions were employed: 20 20 14, 10 10 7, and 5 5 3.5 km3. We applied two vortex detection methods based on the velocity gradient tensor to all of the models: swirling strength and the SWIRL code. We performed a comparison of vortex locations obtained with the two methods, and a statistical analyses of the vortex generation mechanisms, the area covered by vortices, their number and characteristic sizes, and temperature profiles as a function of height. We have confirmed that different magnetic field configurations and spatial resolutions impact the area coverage, number, and sizes of vortices. Likewise, the detection methods impact the statistics obtained. Swirling strength detects vortices with any orientation, but a height-dependent threshold is needed. SWIRL only detects vertically oriented vortices, but shows a better agreement with the rotating horizontal velocity field. Simulations with a vertical magnetic field of 50 G support the formation of chromospheric vortices without a photospheric counterpart, while most of the vortices in the 200 G model directly connect the photosphere with the chromosphere. Small-scale dynamo simulations are characterized by a large number of horizontal vortices; vertical vortices are nearly absent at chromospheric layers. The temperature profiles of the vortices confirm that they are hotter than their surroundings, regardless the simulation setup. Vortices are ubiquitous throughout the solar atmosphere. Their detection is affected by the methodology employed; SWIRL is a more robust method. The strength of the magnetic field and the numerical resolution considerably affect the number and size of the structures detected. Despite this, they all show temperatures higher than those of their surroundings.

Umbral flashes are manifestations of magnetoacoustic shocks in the solar chromosphere. These phenomena are thought to influence the evolution of chromospheric umbral magnetic fields. However, the impact of these shocks on inferred chromospheric magnetic field oscillations remains unclear. We examined five different sunspots located near the solar disk center, observed with the GRIS instrument installed at the GREGOR telescope. The HAZEL2 Spectropolarimetric inversion code is used to obtain the photospheric and chromospheric line-of-sight velocities and magnetic fields in Si 10827 Å and He 10830 Å spectral lines, respectively, using various inversion strategies. In the inversions with one chromospheric component, three of the sunspots exhibit remarkably stronger magnetic fields accompanying the shocks, while the other two sunspots show striking reductions in the magnetic field. Alternatively, the Stokes profiles can be reproduced by models with two chromospheric slabs, one on top of the other, through two-component inversions. These inversions provide excellent fits even when magnetic field fluctuations are discarded by imposing a constant magnetic field during the whole temporal series. In this scenario, the observed Stokes profiles are interpreted as the result of strong velocity gradients, where the He 10830 Å line is sensitive to both sides of the shock front. Both competing models explaining the spectral profiles during the shocks, either large magnetic field fluctuations or velocity gradients, are critically discussed.

Solar pores are strongly magnetized regions without a photospheric penumbra, with predominantly vertical magnetic fields. We present a multiline investigation of flashes in a pore using high-resolution Swedish Solar Telescope observations in Fe I 6302, Ca II ( λ 8542 and K), and H β , complemented with (extreme-)UV observations from the Interface Region Imaging Spectrograph and Solar Dynamics Observatory. Complementary to bisector analysis, spectral inversions with the Stokes Inversion based on Response functions (SIR) code and Non-LTE Inversion Code using the Lorien Engine (NICOLE) provided temperature, line-of-sight velocity, and magnetic field stratifications. Flashes, confined to the left half of the pore, exhibited cooler temperatures (Δ T ≈ 400 K), stronger magnetic fields (Δ B ≈ 250 G), greater inclination (∼25° vs. ∼18°), and persistent upflows (∼0.5 km s ⁻¹ ) relative to the quiescent pore in the photosphere. Flashes were cospatial with enhanced 3- and 5-minute power in the photosphere, with only 3-minute power persisting in the chromosphere. Flashes were seen up to 50% line depth in Ca II λ 8542 intensity, but not below, and showed central upflows (∼1 km s ⁻¹ , 1″–2″) flanked by strong downflows (∼8 km s ⁻¹ ) in the chromosphere. Associated temperature enhancements reached ∼500 K at log τ ≈ −5 and ∼2500 K at log τ ≈ −6. Flash spectra displayed a bimodal velocity distribution, with ∼52% showing downflows at log τ ≈ −5. Flashes corresponded one to one with radially outward-propagating running waves (5–15 km s ⁻¹ , amplitude ∼1 km s ⁻¹ ) near the pore boundary. Spectral diagnostics revealed strong Ca II ( λ 8542 and K) core emission, occasional Stokes V reversals, and broadband H β enhancements. The results suggest that pore flashes are confined to the lower and mid-chromosphere, with little influence on the transition region or corona.

Context . Modeling the solar atmosphere is challenging due to its layered structure and dynamic multi-scale processes. Aims . We aim to validate the new radiative magnetohydrodynamic (MHD) code MAGEC—built by integrating the M ANCHA 3D and MAGNUS codes into a finite-volume, shock-capturing framework—and to explore its capabilities through 2D simulations of magnetoconvection in the solar atmosphere. Methods . The MAGEC code is parallelized with Message Passing Interface (MPI), enabling efficient scalability for large-scale simulations. We have enhanced it with advanced numerical techniques to address the specific complexities of the solar corona, including a module for local thermodynamic equilibrium (LTE) radiative coronal losses. To address the small time steps due to large heat flux values, we adopted the hyperbolic treatment for the thermal conduction of M ANCHA 3D, which significantly improves the computational times. In addition, we estimated the effective numerical resistivity and viscosity through a dedicated set of experiments. To evaluate the robustness and accuracy of MAGEC, we performed a series of 2D simulations covering a domain extending from 2 Mm below the solar surface to 18.16 Mm into the corona. Simulations were conducted with both open and closed magnetic field configurations. For each case, we analyzed the resulting steady-state temperature profiles and examined the energy contributions at different heights. In addition, we investigated the influence of the perpendicular component of thermal conduction in a dedicated simulation. Results . The MAGEC code effectively reproduced expected temperature profiles based on the boundary conditions applied and the imposed magnetic field configuration. All simulations reached a thermally stable state. When using an open vertical magnetic field, the temperature in the middle corona was higher than in the case with a closed, arcade-like magnetic field structure. We quantified the contributions to the internal energy from all explicit and implicit terms in the steady state, both in terms of temporal averages and as functions of height, as well as their relative contributions to total heating and cooling. In a second phase of the study, we investigated the role of the perpendicular component of thermal conduction, which is often neglected in coronal models, and found that it can influence plasma dynamics around reconnection events. Although local effects are modest, their cumulative impact can lead to measurable changes in the average temperature profile. Conclusions . Through detailed validation, MAGEC is a reliable and efficient code for radiative MHD simulations of the solar atmosphere. The integration of shock-capturing methods is particularly well suited to modeling the plasma environment, effectively handling the shocks and discontinuities characteristic of the solar atmosphere. MAGEC is a robust tool for high-fidelity magneto-convection simulations of the solar atmospheric dynamics.

Aims. Our aim was to study the chromospheric line-of-sight (LOS) velocities during the GOES M3.2 flare (SOL2013-05-17T08:43) using simultaneous high-resolution ground-based spectroscopic data of the He I 10830 Å triplet and Ca II 8542 Å line. A filament was present in the flaring area. Methods. The observational data were acquired with the Vacuum Tower Telescope (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 of the emitting plasma. 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. Results. 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⁻¹. 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⁻¹. In the flare the Ca II line represents lower heights compared to the quiet Sun, with peak sensitivity shifting from log τ≃−5.2 to log τ≃−3.5. The loop system's downflows persist for over an hour in the post-flare phase. Conclusions. The inferred LOS velocities support a cool-upflow scenario at the leading edge of the flare, with rapid transition from blueshifts to redshifts likely to occur within seconds to tens of seconds. Although the flare had a significant impact on the surrounding atmosphere, the solar filament in the region remained stable throughout all flare phases. 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. This highlights the importance of combining multiple chromospheric spectral lines to achieve a more comprehensive understanding of flare dynamics.