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Charged particles are constantly accelerated to non-thermal energies by the reconnecting magnetic field in the solar atmosphere. Our understanding of the interactions between the particles and their environment can benefit from three-dimensional atmospheric simulations accounting for non-thermal particle beams. In a previous publication, we presented the first results from such a simulation. However, the original treatment of beam propagation ignores potentially important phenomena. Here, we present a more general beam propagation model incorporating magnetic gradient forces, the return current, acceleration by the ambient electric field, and temperature-dependent collision rates. Neglecting collisional velocity randomisation makes the model sufficiently lightweight to simulate millions of beams. We investigate how each new physical effect changes beam energy transport in a three-dimensional atmosphere. We applied the method of characteristics to the steady-state continuity equation for electron flux to derive ordinary differential equations for the mean evolution of energy, pitch angle, and flux with distance. For each beam, we solved these numerically for a range of initial energies to obtain the evolving flux spectrum, from which we computed the energy deposited into the ambient plasma. Magnetic gradient forces significantly influence the deposition of beam energy. The strong magnetic field convergence leads to a small coronal deposition peak followed by a heavy dip caused by the onset of magnetic mirroring. Mirrored electrons carry away 5 to 10% of the injected beam energy on average. The transition region peak produced by the remaining energetic electrons occurs slightly deeper than in a uniform magnetic field. An initial diverging magnetic field enhances the subsequent impact of mirroring. The other new physical effects are less significant for the studied atmospheric conditions., Comment: Accepted for publication in Astronomy & Astrophysics

Nanoflare heating through small-scale magnetic reconnection events is one of the prime candidates to explain heating of the solar corona. However, direct signatures of nanoflares are difficult to determine, and unambiguous observational evidence is still lacking. Numerical models that include accelerated electrons and can reproduce flaring conditions are essential in understanding how low-energetic events act as a heating mechanism of the corona, and how such events are able to produce signatures in the spectral lines that can be detected through observations. We investigate the effects of accelerated electrons in synthetic spectra from a 3D radiative magnetohydrodynamics simulation to better understand small-scale heating events and their impact on the solar atmosphere. We synthesised the chromospheric Ca II and Mg II lines and the transition region Si IV resonance lines from a quiet Sun numerical simulation that includes accelerated electrons. We calculated the contribution function to the intensity to better understand how the lines are formed, and what factors are contributing to the detailed shape of the spectral profiles. The synthetic spectra are highly affected by variations in temperature and vertical velocity. Beam heating exceeds conductive heating at the heights where the spectral lines form, indicating that the electrons should contribute to the heating of the lower atmosphere and hence affect the line profiles. However, we find that it is difficult to determine specific signatures from the non-thermal electrons due to the complexity of the atmospheric response to the heating in combination with the relatively low energy output (~1e21 erg/s). Even so, our results contribute to understanding small-scale heating events in the solar atmosphere, and give further guidance to future observations.

Context. The magnetic field in the solar atmosphere continually reconnects and accelerates charged particles to high energies. Simulations of the atmosphere in three dimensions that include the effects of accelerated particles can aid our understanding of the interplay between energetic particle beams and the environment where they emerge and propagate. We presented the first attempt at such a simulation in a previous paper, emphasising the physical model of particle beams. However, the numerical implementation of this model is not straightforward due to the diverse conditions in the atmosphere and the way we must distribute computation between multiple CPU cores. Aims. Here, we describe and verify our numerical implementation of energy transport by electron beams in a 3D magnetohydrodynamics code parallelised by domain decomposition. Methods. We trace beam trajectories using a Runge-Kutta scheme with adaptive step length control and integrate deposited beam energy along the trajectories with a hybrid analytical and numerical approach. To parallelise this, we coordinate beam transport across subdomains owned by separate processes using a buffering system designed to optimise data flow. Results. Using an ad hoc magnetic field with analytical field lines as a test scenario, we show that our parallel implementation of adaptive tracing efficiently follows a challenging trajectory with high precision. By timing executions of electron beam transport with different numbers of processes, we found that the processes communicate with minimal overhead but that the parallel scalability is still sublinear due to workload imbalance caused by the uneven spatial distribution of beams., Comment: Submitted to Astronomy & Astrophysics

Heating signatures from small-scale magnetic reconnection events in the solar atmosphere have proven to be difficult to detect through observations. Numerical models that reproduce flaring conditions are essential in the understanding of how nanoflares may act as a heating mechanism of the corona. We study the effects of non-thermal electrons in synthetic spectra from 1D hydrodynamic RADYN simulations of nanoflare heated loops to investigate the diagnostic potential of chromospheric emission from small-scale events. The Mg II h and k, Ca II H and K, Ca II 854.2 nm, H-alpha and H-beta chromospheric lines were synthesised from various RADYN models of coronal loops subject to electron beams of nanoflare energies. The contribution function to the line intensity was computed to better understand how the atmospheric response to the non-thermal electrons affects the formation of spectral lines and the detailed shape of their spectral profiles. The spectral line signatures arising from the electron beams highly depend on the density of the loop and the lower cutoff energy of the electrons. Low-energy (5 keV) electrons deposit their energy in the corona and transition region, producing strong plasma flows that cause both redshifts and blueshifts of the chromospheric spectra. Higher-energy (10 and 15 keV) electrons deposit their energy in the lower transition region and chromosphere, resulting in increased emission from local heating. Our results indicate that effects from small-scale events can be observed with ground-based telescopes, expanding the list of possible diagnostics for the presence and properties of nanoflares.

Observational and theoretical evidence suggest that beams of accelerated particles are produced in flaring events of all sizes in the solar atmosphere, from X-class flares to nanoflares. Current models of these types of particles in flaring loops assume an isolated 1D atmosphere. A more realistic environment for modelling accelerated particles can be provided by 3D radiative magnetohydrodynamics codes. Here, we present a simple model for particle acceleration and propagation in the context of a 3D simulation of the quiet solar atmosphere, spanning from the convection zone to the corona. We then examine the additional transport of energy introduced by the particle beams. The locations of particle acceleration associated with magnetic reconnection were identified by detecting changes in magnetic topology. At each location, the parameters of the accelerated particle distribution were estimated from local conditions. The particle distributions were then propagated along the magnetic field, and the energy deposition due to Coulomb collisions with the ambient plasma was computed. We find that particle beams originate in extended acceleration regions that are distributed across the corona. Upon reaching the transition region, they converge and produce strands of intense heating that penetrate the chromosphere. Within these strands, beam heating consistently dominates conductive heating below the bottom of the transition region. This indicates that particle beams qualitatively alter the energy transport even outside of active regions., Comment: Accepted for publication in A&A

The measured average velocities in solar and stellar spectral lines formed at transition region temperatures have been difficult to interpret. However, realistic three-dimensional radiation magnetohydrodynamics (3D rMHD) models of the solar atmosphere are able to reproduce the observed dominant line shifts and may thus hold the key to resolve these issues. Our new 3D rMHD simulations aim to shed light on how mass flows between the chromosphere and corona and on how the coronal mass is maintained. Passive tracer particles, so-called corks, allow the tracking of parcels of plasma over time and thus the study of changes in plasma temperature and velocity not only locally, but also in a co-moving frame. By following the trajectories of the corks, we can investigate mass and energy flows and understand the composition of the observed velocities. Our findings show that most of the transition region mass is cooling. The preponderance of transition region redshifts in the model can be explained by the higher percentage of downflowing mass in the lower and middle transition region. The average upflows in the upper transition region can be explained by a combination of both stronger upflows than downflows and a higher percentage of upflowing mass. The most common combination at lower and middle transition region temperatures are corks that are cooling and traveling downward. For these corks, a strong correlation between the pressure gradient along the magnetic field line and the velocity along the magnetic field line has been observed, indicating a formation mechanism that is related to downward propagating pressure disturbances. Corks at upper transition region temperatures are subject to a rather slow and highly variable but continuous heating process., Comment: 13 pages, 10 figures, online movie

Three-dimensional (3D) radiative hydrodynamic model atmospheres of metal-poor late-type stars are characterized by cooler upper photospheric layers than their 1D counterparts. This property of 3D models can dramatically affect elemental abundances derived from temperature-sensitive spectral lines. We investigate whether the cool surface temperatures predicted by metal-poor 3D models can be ascribed to the approximated treatment of scattering in the radiative transfer. We use the Bifrost code to test three different ways to handle scattering in 3D model atmospheres of metal-poor stars. First, we solve self-consistently the radiative transfer equation for a source function with a coherent scattering term. Second, we solve the radiative transfer equation for a Planckian source function, neglecting the contribution of continuum scattering to extinction in the optically thin layers; this has been the default mode in previous models of ours. Third, we treat scattering as pure absorption everywhere, which is the standard case in CO5BOLD models. We find that the second approach produces temperature structures with cool upper photospheric layers very similar to the correct coherent scattering solution. In contrast, treating scattering as pure absorption leads to significantly hotter and shallower temperature stratifications. The main differences in temperature structure between our published models and those generated with the CO5BOLD code can be traced to the different treatments of scattering. Neglecting the contribution of continuum scattering to extinction in optically thin layers provides a good approximation to the full radiative transfer solution for metal-poor stars. Our results demonstrate that the cool temperature stratifications predicted for metal-poor late-type stellar atmospheres by previous models of ours are not an artifact of the approximated treatment of scattering., Comment: 12 pages, accepted for publication on A&A

We present the implementation of a radiative transfer solver with coherent scattering in the new BIFROST code for radiative magneto-hydrodynamical (MHD) simulations of stellar surface convection. The code is fully parallelized using MPI domain decomposition, which allows for large grid sizes and improved resolution of hydrodynamical structures. We apply the code to simulate the surface granulation in a solar-type star, ignoring magnetic fields, and investigate the importance of coherent scattering for the atmospheric structure. A scattering term is added to the radiative transfer equation, requiring an iterative computation of the radiation field. We use a short-characteristics-based Gauss-Seidel acceleration scheme to compute radiative flux divergences for the energy equation. The effects of coherent scattering are tested by comparing the temperature stratification of three 3D time-dependent hydrodynamical atmosphere models of a solar-type star: without scattering, with continuum scattering only, and with both continuum and line scattering. We show that continuum scattering does not have a significant impact on the photospheric temperature structure for a star like the Sun. Including scattering in line-blanketing, however, leads to a decrease of temperatures by about 350\,K below log tau < -4. The effect is opposite to that of 1D hydrostatic models in radiative equilibrium, where scattering reduces the cooling effect of strong LTE lines in the higher layers of the photosphere. Coherent line scattering also changes the temperature distribution in the high atmosphere, where we observe stronger fluctuations compared to a treatment of lines as true absorbers., Comment: A&A, in press

A forward model is described in which we synthesize spectra from an ab-initio 3D MHD simulation of an outer stellar atmosphere, where the coronal heating is based on braiding of magnetic flux due to photospheric footpoint motions. We discuss the validity of assumptions such as ionization equilibrium and investigate the applicability of diagnostics like the differential emission measure inversion. We find that the general appearance of the synthesized corona is similar to the solar corona and that, on a statistical basis, integral quantities such as average Doppler shifts or differential emission measures are reproduced remarkably well. The persistent redshifts in the transition region, which have puzzled theorists since their discovery, are explained by this model as caused by the flows induced by the heating through braiding of magnetic flux. While the model corona is only slowly evolving in intensity, as is observed, the amount of structure and variability in Doppler shift is very large. This emphasizes the need for fast coronal spectroscopy, as the dynamical response of the corona to the heating process manifests itself in a comparably slow evolving coronal intensity but rapid changes in Doppler shift., Comment: 13 pages, 10 figures, submitted to ApJ

Cool stars like our Sun are surrounded by a million degree hot outer atmosphere, the corona. Since more than 60 years the physical nature of the processes heating the corona to temperatures well in excess of those on the stellar surface remain puzzling. Recent progress in observational techniques and numerical modeling now opens a new window to approach this problem. We present the first coronal emission line spectra synthesized from three-dimensional numerical models describing the evolution of the dynamics and energetics as well as of the magnetic field in the corona. In these models the corona is heated through motions on the stellar surface that lead to a braiding of magnetic field lines inducing currents which are finally dissipated. These forward models enable us to synthesize observed properties like (average) emission line Doppler shifts or emission measures in the outer atmosphere, which until now have not been understood theoretically, even though many suggestions have been made in the past. As our model passes these observational tests, we conclude that the flux braiding mechanism is a prime candidate for being the dominant heating process of the magnetically closed corona of the Sun and solar-like stars., Comment: 4 pages, 3 figures, submitted to ApJ

Magnetic activity in M-dwarfs present enigmatic questions: On the one hand they have higher field strengths and larger filling factors than the magnetic field on the Sun, on the other hand, they are fully convective and their atmospheres are more neutral, hence they do not have an undershoot layer for magnetic flux storage and as we show here, cannot have small-scale dynamo action in their photospheres either. We present a discussion of these facts and propose a new numerical model to investigate M-dwarf magnetism., Comment: 3 pages, 4 figures, submitted to the proceedings of Cool Stars 13, to appear in an ESA-SP volume

We present an ab initio approach to the solar coronal heating problem by modelling a small part of the solar corona in a computational box using a 3D MHD code including realistic physics. The observed solar granular velocity pattern and its amplitude and vorticity power spectra, as reproduced by a weighted Voronoi tessellation method, are used as a boundary condition that generates a Poynting flux in the presence of a magnetic field. The initial magnetic field is a potential extrapolation of a SOHO/MDI high resolution magnetogram, and a standard stratified atmosphere is used as a thermal initial condition. Except for the chromospheric temperature structure, which is kept fixed, the initial conditions are quickly forgotten because the included Spitzer conductivity and radiative cooling function have typical timescales much shorter than the time span of the simulation. After a short initial start up period, the magnetic field is able to dissipate 3-4 10^6 ergs cm^{-2} s^{-1} in a highly intermittent corona, maintaining an average temperature of $\sim 10^6$ K, at coronal density values for which emulated images of the Transition Region And Coronal Explorer(TRACE) 171 and 195 pass bands reproduce observed photon count rates., Comment: 12 pages, 14 figures. Submitted to ApJ

Data from recent numerical simulations of the solar corona and transition region are analysed and the magnetic field connection between the low corona and the photosphere is found to be close to that of a potential field. The fieldline to fieldline displacements follow a power law distribution with typical displacements of just a few Mm. Three loops visible in emulated Transition Region And Coronal Explorer (TRACE) filters are analysed in detail and found to have significantly different heating rates and distributions thereof, one of them showing a small scale heating event. The dynamical structure is complicated even though all the loops are visible in a single filter along most of their lengths. None of the loops are static, but are in the process of evolving into loops with very different characteristics. Differential Emission Measure (DEM) curves along one of the loops illustrate that DEM curves have to be treated carefully if physical characteristics are to be extracted., Comment: 9 pages, 13 figures. Submitted to ApJ

We present 3-d numerical magneto-hydrodynamic simulations of a buoyant, twisted magnetic flux rope embedded in a stratified, solar-like model convection zone. The flux rope is given an initial twist such that it neither kinks nor fragments during its ascent. Moreover, its magnetic energy content with respect to convection is chosen so that the flux rope retains its basic geometry while being deflected from a purely vertical ascent by convective flows. The simulations show that magnetic flux is advected away from the core of the flux rope as it interacts with the convection. The results thus support the idea that the amount of toroidal flux stored at or near the bottom of the solar convection zone may currently be underestimated., Comment: 5 pages, 3 figures. Accepted for publication in Astronomy & Astrophysics