kiliankr

• Krikova, Kilian & Pereira, Tiago (2025). Small-scale energetic phenomena in Hϵ: Ellerman bombs, UV bursts, and small flares. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 695. doi: 10.1051/0004-6361/202453118. Full text in Research Archive Show summary

  Aims. We investigated the potential of using Hε to diagnose small-scale energetic phenomena such as Ellerman bombs, UV bursts, and small-scale flares. Our focus is to understand the formation of the line and how to use its properties to get insight into the dynamics of small-scale energetic phenomena. Methods. We carried out a forward modeling study, combining simulations and detailed radiative transfer calculations. The 3D radiative magnetohydrodynamic simulations were run with the Bifrost code and included energetic phenomena. We employed a Markovian framework to study the Hε multilevel source function, used relative contribution functions to identify its formation regions, and correlated the properties of synthetic spectra with atmospheric parameters. Results. Ellerman bombs are predominantly optically thick in Hε, appearing as well-defined structures. UV bursts and small flares are partially optically thin and give rise to diffuse structures. The Hε line serves as a good velocity diagnostic for small-scale heating events in the lower chromosphere. However, its emission strength is a poor indicator of temperature, and its line width offers limited utility due to the interplay of various broadening mechanisms. Compared to Hα, Hε exhibits greater sensitivity to phenomena such as Ellerman bombs, as its line core experiences higher extinction than the Hα wing. Conclusions. Hε is a valuable tool for studying small-scale energetic phenomena in the lower chromosphere. It provides more reliable estimates of velocities than those extracted from wing emission in Hα or Hβ. Maps of Hε emission show more abundant energetic events than the Hα counterpart. Our findings highlight Hε’s potential to advance our understanding of dynamic processes in the solar atmosphere.

• Voort, Luc Rouppe van der; Joshi, Jayant & Krikova, Kilian (2024). Observations of magnetic reconnection in the deep solar atmosphere in the Hε line. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 683. doi: 10.1051/0004-6361/202348976. Full text in Research Archive Show summary

  Context. Magnetic reconnection in the deep solar atmosphere can give rise to enhanced emission in the Balmer hydrogen lines, a phenomenon known as Ellerman bombs (EBs). It is most common to observe EBs in the H α and H β spectral lines. High-quality shorter-wavelength Balmer line observations of EBs are rare, but have the potential to provide the most highly resolved view on magnetic reconnection. Aims. We aim to evaluate the H ε 3970 Å line as an EB diagnostic by analyzing high-quality observations in different Balmer lines. Methods. Observations of different targets and viewing angles were acquired with the Swedish 1-m Solar Telescope. These observations sample EBs in different environments: active regions, the quiet Sun, and the penumbra and moat of a sunspot. We employed an automated detection method for quiet-Sun EBs based on k -means clustering. Results. Ellerman bombs in the H ε line show similar characteristics as in the longer-wavelength Balmer lines: a higher intensity than in the surroundings, rapid variability, and a flame-like morphology. In a 24 min quiet-Sun time series, we detected 1674 EBs in the H ε line. This is 1.7 times more EBs than in H β . The quiet-Sun EBs measured in H ε are very similar to those in H β : They have similar lifetimes and a similar area, brightness, and spatial distribution. Most of the EBs detected in H ε are closer to the limb than their H β counterparts because the H ε line core EB emission is formed higher in the atmosphere than the H β EB wing emission. Conclusions. We conclude that the H ε line is well suited for studying EBs, and consequently, for measuring the dynamics of magnetic reconnection in the solar atmosphere at the smallest scales. Our findings suggests that the deep atmosphere in the quiet Sun may host more than 750 000 reconnection events with an EB signature at any time. This is significantly more than what was found in earlier H β observations.

• Krikova, Kilian & Pereira, Tiago (2024). A Markovian description of the multi-level source function and its application to the Lyman series in the Sun. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 689. doi: 10.1051/0004-6361/202450506. Full text in Research Archive Show summary

  Aims. We introduce a new method to calculate and interpret indirect transition rates populating atomic levels using Markov chain theory. Indirect transition rates are essential to evaluate interlocking in a multi-level source function, which quantifies all the processes that add and remove photons from a spectral line. A better understanding of the multi-level source function is central to interpret optically thick spectral line formation in stellar atmospheres, especially outside local thermodynamical equilibrium (LTE). Methods. We compute the level populations from a hydrogen model atom in statistical equilibrium, using the solar FALC model, a 1D static atmosphere. From the transition rates, we reconstruct the multi-level source function using our new method and compare it with existing methods to build the source function. We focus on the Lyman series lines and analyze the different contributions to the source functions and synthetic spectra. Results. Absorbing Markov chains can represent the level-ratio solution of the statistical equilibrium equation and can therefore be used to calculate the indirect transition rates between the upper and lower levels of an atomic transition. Our description of the multi-level source function allows a more physical interpretation of its individual terms, particularly a quantitative view of interlocking. For the Lyman lines in the FALC atmosphere, we find that interlocking becomes increasingly important with order in the series, with Ly-α showing very little, but Ly-β nearly 50% and Ly-γ about 60% contribution coming from interlocking. In some cases, this view seems opposed to the conventional wisdom that these lines are mostly scattering, and we discuss the reasons why. Conclusions. Our formalism to describe the multi-level source function is general and can provide more physical insight into the processes that set the line source function in a multi-level atom. The effects of interlocking for lines formed in the solar chromosphere can be more important than previously thought, and our method provides the basis for further exploration.

• Krikova, Kilian; Pereira, Tiago & Voort, Luc Rouppe van der (2023). Formation of Hϵ in the solar atmosphere. Astronomy and Astrophysics (A & A). ISSN 0004-6361. 677. doi: 10.1051/0004-6361/202346796. Full text in Research Archive Show summary

  Context. In the solar spectrum, the Balmer series line H ε is a weak blend on the wing of Ca  II H. Recent high-resolution H ε spectroheliograms reveal a reversed granulation pattern and in some cases, even unique structures. It is apparent that H ε could potentially be a useful diagnostic tool for the lower solar atmosphere. Aims. Our aim is to understand how H ε is formed in the quiet Sun. In particular, we consider the particular physical mechanism that sets its source function and extinction, how it is formed in different solar structures, and why it is sometimes observed in emission. Methods. We used a 3D radiative magnetohydrodynamic (MHD) simulation that accounts for non-equilibrium hydrogen ionization, run with the Bifrost code. To synthesize H ε and Ca  II H spectra, we made use of the RH code, which was modified to take into account the non-equilibrium hydrogen ionization. To determine the dominant terms in the H ε source function, we adopted a multi-level description of the source function. Making use of the synthetic spectra and simulation, we studied the contribution function to the relative line absorption or emission and compared it with atmospheric quantities at different locations. Results. Our multi-level source function description suggests that the H ε source function is dominated by interlocking, with the dominant interlocking transition being through the ground level, populating the upper level of H ε via the Lyman series. This makes the H ε source function partly sensitive to temperature. The H ε extinction is set by Lyman- α . In some cases, this temperature dependence gives rise to H ε emission, indicating heating. The typical absorption profiles show reversed granulation and the H ε line core reflects mostly the Ca  II H background radiation. Conclusions. Synthetic H ε spectra can reproduce quiet Sun observations quite well. High-resolution observations reveal that H ε is not just a weak absorption line. Regions with H ε in emission are especially interesting to detect small-scale heating events in the lower solar atmosphere, such as Ellerman bombs. Thus, H ε can be an important new diagnostic tool for studies of heating in the solar atmosphere, augmenting the diagnostic potential of Ca  II H when observed simultaneously.

• Siverio, Daniel Elias Nóbrega; Moreno-Insertis, F.; Galsgaard, K.; Krikova, Kilian; Voort, Luc Rouppe van der & Joshi, Reetika [Show all 7 contributors for this article] (2023). Deciphering Solar Coronal Heating: Energizing Small-scale Loops through Surface Convection. Astrophysical Journal Letters. ISSN 2041-8205. 958(2). doi: 10.3847/2041-8213/ad0df0. Full text in Research Archive Show summary

  Abstract The solar atmosphere is filled with clusters of hot small-scale loops commonly known as coronal bright points (CBPs). These ubiquitous structures stand out in the Sun by their strong X-ray and/or extreme-ultraviolet (EUV) emission for hours to days, which makes them a crucial piece when solving the solar coronal heating puzzle. In addition, they can be the source of coronal jets and small-scale filament eruptions. Here we present a novel 3D numerical model using the Bifrost code that explains the sustained CBP heating for several hours. We find that stochastic photospheric convective motions alone significantly stress the CBP magnetic field topology, leading to important Joule and viscous heating concentrated around the CBP’s inner spine at a few megameters above the solar surface. We also detect continuous upflows with faint EUV signals resembling observational dark coronal jets and small-scale eruptions when H α fibrils interact with the reconnection site. We validate our model by comparing simultaneous CBP observations from the Solar Dynamics Observatory (SDO) and the Swedish 1‐m Solar Telescope (SST) with observable diagnostics calculated from the numerical results for EUV wavelengths as well as for the H α line using the Multi3D synthesis code. Additionally, we provide synthetic observables to be compared with Hinode, Solar Orbiter, and the Interface Region Imaging Spectrograph (IRIS). Our results constitute a step forward in the understanding of the many different facets of the solar coronal heating problem.

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• Krikova, Kilian (2023). Hε a new spectral line to detect small-scale reconnection phenomena in the solar photosphere. Full text in Research Archive
• Krikova, Kilian; Pereira, Tiago Assis & Voort, Luc H. M. Rouppe Van Der (2022). Diagnostic potential of Hε for small-scale energetic phenomena. Full text in Research Archive
• Krikova, Kilian; Pereira, Tiago; Voort, Luc Rouppe van der & Carlsson, Mats (2022). Diagnostic potential of Hε for small-scale energetic phenomena. Full text in Research Archive
• Krikova, Kilian; Pereira, Tiago & Voort, Luc Rouppe van der (2025). Small-scale energetic phenomena in Hε: line formation and diagnostic potential. Universitetet i Oslo. Full text in Research Archive Show summary

  This dissertation focuses on forward modeling, using state-of-theart 3D radiative magnetohydrodynamic simulations combined with modern non-LTE radiative transfer codes to synthesize spectral lines and analyze their formation. The focus lies on investigating the formation and diagnostic potential of the hydrogen Balmer line Hε in the solar atmosphere, particularly in the context of small-scale energetic phenomena such as Ellerman bombs, UV bursts, and smallscale flares. A deeper understanding of the formation of Hε will help to understand a newly identified phenomenon called quiet Sun Ellerman bombs. Additionally, a modern, in-depth study of the formation of Hε has not yet been performed. By combining state-of-the-art Bifrost 3D radiative magnetohydrodynamic simulations, representing quiet Sun conditions and reproducing small-scale energetic phenomena in combination with the RH1.5D and MULTI3D radiative transfer codes, synthetic spectra were generated to investigate the response of Hε under various solar conditions. We address three core research questions, explored in three papers: 1. How is the Hε spectral line formed under quiet Sun conditions and for different solar features? 2. How can the multi-level source function be calculated, and what role does interlocking play in the line source function? 3. How does Hε respond to small-scale energetic events, such as Ellerman bombs, UV bursts, and small-scale flares? Answering these questions will assist the solar physics community to interpret Hε observations, and also clarify line formation in multi-level atoms, particularly through a deeper understanding of the multi-level source function. Our findings demonstrate that Hε, despite being an unobtrusive spectral line in the solar spectrum, can serve as a valuable diagnostic tool for analyzing and, more importantly, detecting small-scale energetic phenomena. In particular, Hε’s pronounced sensitivity to temperature enhancements in the lower solar atmosphere makes it exceptionally wellsuited for detecting weak heating events in quiet Sun regions, such as quiet Sun Ellerman bombs. This work also underscores the advantages of Hε over other Balmer series lines, such as Hα, in identifying weak energetic events. Unlike Hα or Hβ the line core of Hε is largely unaffected by the solar chromosphere, making it a promising candidate for measuring velocities in the lower chromosphere near the temperature minimum. This dissertation contributes to the field of solar physics by improving the understanding of hydrogen line formation in the solar atmosphere and validating the potential of Hε for upcoming solar missions, such as the Daniel K. Inouye Solar Telescope or the planned European Solar Telescope. Additionally, it provides a detailed investigation of the multi-level source function, a subject rarely addressed in the literature, which will support the interpretation of non-LTE line formation in both solar and stellar atmospheres. The findings especially contribute to the interpretation of high-resolution Hε observations, advancing the exploration of the Sun’s dynamic magnetic processes, and enabling further investigations of a new phenomenon called quiet Sun Ellerman bombs.

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