Accelerated particle beams in a 3D simulation of the quiet Sun

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&

Implementing accelerated particle beams in a 3D simulation of the quiet Sun

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 & Astrophysic

Disentangling flows in the solar transition region

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 movi

Chromospheric emission from nanoflare heating in RADYN simulations

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

Accelerated particle beams in a 3D simulation of the quiet Sun. Lower atmospheric spectral diagnostics

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

Coronal heating through braiding of magnetic field lines

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 Ap

On red shifs in the transition region and corona

We present evidence that transition region red-shifts are naturally produced in episodically heated models where the average volumetric heating scale height lies between that of the chromospheric pressure scale height of 200 km and the coronal scale height of 50 Mm. In order to do so we present results from 3d MHD models spanning the upper convection zone up to the corona, 15 Mm above the photosphere. Transition region and coronal heating in these models is due both the stressing of the magnetic field by photospheric and convection `zone dynamics, but also in some models by the injection of emerging magnetic flux.Comment: 8 pages, 9 figures, NSO Workshop #25 Chromospheric Structure and Dynamic

The stellar atmosphere simulation code Bifrost

Context: Numerical simulations of stellar convection and photospheres have been developed to the point where detailed shapes of observed spectral lines can be explained. Stellar atmospheres are very complex, and very different physical regimes are present in the convection zone, photosphere, chromosphere, transition region and corona. To understand the details of the atmosphere it is necessary to simulate the whole atmosphere since the different layers interact strongly. These physical regimes are very diverse and it takes a highly efficient massively parallel numerical code to solve the associated equations. Aims: The design, implementation and validation of the massively parallel numerical code Bifrost for simulating stellar atmospheres from the convection zone to the corona. Methods: The code is subjected to a number of validation tests, among them the Sod shock tube test, the Orzag-Tang colliding shock test, boundary condition tests and tests of how the code treats magnetic field advection, chromospheric radiation, radiative transfer in an isothermal scattering atmosphere, hydrogen ionization and thermal conduction. Results: Bifrost completes the tests with good results and shows near linear efficiency scaling to thousands of computing cores

Flux-loss of buoyant ropes interacting with convective flows

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 & Astrophysic

Effects of fieldline topology on energy propagation in the corona

We study the effect of photospheric footpoint motions on magnetic field structures containing magnetic nulls. The footpoint motions are prescribed on the photospheric boundary as a velocity field which entangles the magnetic field. We investigate the propagation of the injected energy, the conversion of energy, emergence of current layers and other consequences of the non-trivial magnetic field topology in this situation. These boundary motions lead initially to an increase in magnetic and kinetic energy. Following this, the energy input from the photosphere is partially dissipated and partially transported out of the domain through the Poynting flux. The presence of separatrix layers and magnetic null-points fundamentally alters the propagation behavior of disturbances from the photosphere into the corona. Depending on the field line topology close to the photosphere, the energy is either trapped or free to propagate into the corona.Comment: 14 pages, 15 figure