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

Magnetic field diagnostics and spatio-temporal variability of the solar transition region

Magnetic field diagnostics of the transition region from the chromosphere to the corona faces us with the problem that one has to apply extreme UV spectro-polarimetry. While for coronal diagnostic techniques already exist through infrared coronagraphy above the limb and radio observations on the disk, for the transition region one has to investigate extreme UV observations. However, so far the success of such observations has been limited, but there are various projects to get spectro-polarimetric data in the extreme UV in the near future. Therefore it is timely to study the polarimetric signals we can expect for such observations through realistic forward modeling. We employ a 3D MHD forward model of the solar corona and synthesize the Stokes I and Stokes V profiles of C IV 1548 A. A signal well above 0.001 in Stokes V can be expected, even when integrating for several minutes in order to reach the required signal-to-noise ratio, despite the fact that the intensity in the model is rapidly changing (just as in observations). Often this variability of the intensity is used as an argument against transition region magnetic diagnostics which requires exposure times of minutes. However, the magnetic field is evolving much slower than the intensity, and thus when integrating in time the degree of (circular) polarization remains rather constant. Our study shows the feasibility to measure the transition region magnetic field, if a polarimetric accuracy on the order of 0.001 can be reached, which we can expect from planned instrumentation.Comment: Accepted for publication in Solar Physics (4.Mar.2013), 19 pages, 9 figure

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

Three-dimensional surface convection simulations of metal-poor stars: The effect of scattering on the photospheric temperature stratification

Context: Three-dimensional (3D) radiative hydrodynamic model atmospheres of metal-poor late-type stars are characterized by cooler upper photospheric layers than their one-dimensional counterparts. This property of 3D model atmospheres can dramatically affect the determination of elemental abundances from temperature-sensitive spectral features, with profound consequences on galactic chemical evolution studies. Aims. We investigate whether the cool surface temperatures predicted by 3D model atmospheres of metal-poor stars can be ascribed to approximations in the treatment of scattering during the modelling phase. Methods. We use the Bifrost code to construct 3D model atmospheres of metal-poor stars and test three different ways to handle scattering in the radiative transfer equation. As a first approach, we solve iteratively the radiative transfer equation for the general case of a source function with a coherent scattering term, treating scattering in a correct and consistent way. As a second approach, we solve the radiative transfer equation in local thermodynamic equilibrium approximation, neglecting altogether the contribution of continuum scattering to extinction in the optically thin layers; this has been the default mode in our previous 3D modelling as well as in present Stagger-Code models. As our third and final approach, we treat continuum scattering as pure absorption everywhere, which is the standard case in the 3D modelling by the CO5BOLD collaboration. Results. For all simulations, we find that the second approach produces temperature structures with cool upper photospheric layers very similar to the case in which scattering is treated correctly. In contrast, treating scattering as pure absorption leads instead to significantly hotter and shallower temperature stratifications. The main differences in temperature structure between our published models computed with the Stagger- and Bifrost codes and those generated with the CO5BOLD code can be traced to the different treatments of scattering. Conclusions. Neglecting the contribution of continuum scattering to extinction in optically thin layers provides a good approximation to the full, iterative solution of the radiative transfer equation in metal-poor stellar surface convection simulations, and at a much lower computational cost. Our results also demonstrate that the cool temperature stratifications predicted for metal-poor late-type stars by previous models by our collaboration are not an artifact of the approximated treatment of scattering

Growth and Transport Properties of Complementary Germanium Nanowire Field Effect Transistors

n- and p-type Ge nanowires were synthesized by a multistep process in which axial elongation, via vapor–liquid–solid (VLS) growth, and doping were accomplished in separate chemical vapor deposition steps. Intrinsic, single-crystal, Ge nanowires prepared by Au nanocluster-mediated VLS growth were surface-doped in situ using diborane or phosphine, and then radial growth of an epitaxial Ge shell was used to cap the dopant layer. Field-effect transistors prepared from these Ge nanowires exhibited on currents and transconductances up to 850 µA/µm and 4.9 µA/V, respectively, with device yields of \u3e85%

Many-Body Effects on Tunneling of Electrons in Magnetic-Field-Induced Quasi One-Dimensional Electron Systems in Semiconductor Nanowhiskers

Effects of the electron-electron interaction on tunneling in a semiconductor nanowhisker are studied in a magnetic quantum limit. We consider the system with which bulk and edge states coexist. In bulk states, the temperature dependence of the transmission probability is qualitatively similar to that of a one-dimensional electron system. We investigate contributions of edge states on transmission probability in bulk states. Those contributions can be neglected within our approximation which takes into account only most divergent terms at low temperatures.Comment: 9 pages, 6 figure

An Ab Initio Approach to the Solar Coronal Heating Problem

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 Ap

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

Turbulent Coronal Heating Mechanisms: Coupling of Dynamics and Thermodynamics

Context. Photospheric motions shuffle the footpoints of the strong axial magnetic field that threads coronal loops giving rise to turbulent nonlinear dynamics characterized by the continuous formation and dissipation of field-aligned current sheets where energy is deposited at small-scales and the heating occurs. Previous studies show that current sheets thickness is orders of magnitude smaller than current state of the art observational resolution (~700 km). Aim. In order to understand coronal heating and interpret correctly observations it is crucial to study the thermodynamics of such a system where energy is deposited at unresolved small-scales. Methods. Fully compressible three-dimensional magnetohydrodynamic simulations are carried out to understand the thermodynamics of coronal heating in the magnetically confined solar corona. Results. We show that temperature is highly structured at scales below observational resolution and nonhomogeneously distributed so that only a fraction of the coronal mass and volume gets heated at each time. Conclusions. This is a multi-thermal system where hotter and cooler plasma strands are found one next to the other also at sub-resolution scales and exhibit a temporal dynamics.Comment: A&A Letter, in pres