Boris Vilhelm Gudiksen

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 ergscm 2 s 1 in a highly intermittent corona, maintaining an average temperature of ∼ 10 6 K, at coronal density values for which emulated images of the Transition Region And Coronal Explorer(TRACE) 171 and 195 u pass bands reproduce observed photon count rates. Subject headings: Sun: corona – Sun: magnetic fields – MHD

FORWARD MODELING OF THE CORONA OF THE SUN AND SOLAR-LIKE STARS: FROM A THREE-DIMENSIONAL MAGNETOHYDRODYNAMIC MODEL TO SYNTHETIC EXTREME-ULTRAVIOLET SPECTRA

A forward model is described in which we synthesize spectra from an ab initio three-dimensional 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 spectroscopic observations, 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.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. Subject headings: MHD — stars: coronae — Sun: corona — Sun: UV radiation

Bulk Heating and Slender Magnetic Loops in the Solar Corona

The heating of the solar corona and the puzzle of the slender high reaching magnetic loops seen in observations from the Transition Region and Coronal Explorer (TRACE) has been investigated through three-dimensional numerical simulations and found to be caused by the well-observed plasma flows in the photosphere displacing the footpoints of magnetic loops in a nearly potential configuration. It is found that even the small convective displacements cause magnetic dissipation sufficient to heat the corona to temperatures of the order of a million K. The heating is intermittent in both space and time—at any one height and time it spans several orders of magnitude, and localized heating causes transonic flows along field lines, which explains the observed nonhydrostatic stratification of loops that are bright in emission measure.

An Ab Initio Approach to Solar Coronal Loops

Data from recent numerical simulations of the solar corona and transition region are analyzed, and the magnetic field connections between the low corona and the photosphere are found to be close to ...

Radiative transfer with scattering for domain-decomposed 3D MHD simulations of cool stellar atmospheres - numerical methods and application to the quiet, non-magnetic, surface of a solar-type star

Aims. 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. Methods. 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. Results. 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 log10 τ5000 < −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.

Coronal Heating through Braiding of Magnetic Field Lines

Cool stars such as our Sun are surrounded by a million degree hot outer atmosphere, the corona. For more than 60 years, the physical nature of the processes heating the corona to temperatures well in excess of those on the stellar surface have remained 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 that are finally dissipated. These forward models enable us to synthesize observed properties such as (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.

A publicly available simulation of an enhanced network region of the Sun

Context. The solar chromosphere is the interface between the solar surface and the solar corona. Modelling of this region is difficult because it represents the transition from optically thick to t ...

On the minimum temperature of the quiet solar chromosphere

Aims. We aim to provide an estimate of the minimum temperature of the quiet solar chromosphere. Methods. We perform a 2D radiation-MHD simulation spanning the upper convection zone to the lower corona. The simulation includes non-LTE radiative transfer and an equation-of-state that includes non-equilibrium ionization of hydrogen and non-equilibrium H2 molecule formation. We analyze the reliability of the various assumptions made in our model in order to assess the realism of the simulation. Results. Our simulation contains pockets of cool gas with down to 1660 K from 1 Mm up to 3.2 Mm height. It overestimates the radiative heating, and contains non-physical heating below 1660 K. Therefore we conclude that cool pockets in the quiet solar chromosphere might have even lower temperatures than in the simulation, provided that there exist areas in the chromosphere without significant magnetic heating. We suggest off-limb molecular spectroscopy to look for such cool pockets and 3D simulations including a local dynamo and a magnetic carpet to investigate Joule heating in the quiet chromosphere.

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 app roach, we solve iteratively the radiative transfer equatio n for the general case of a source function with a coherent scattering term, tr eating 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 la yers; 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 sc attering as pure absorption everywhere, which is the standard case in the 3D modelling by the CO 5 BOLD collaboration. Results. For all simulations, we find that the second approach produce s temperature structures with cool upper photospheric layers very similar to the case in which scattering is treated corre ctly. In contrast, treating scattering as pure absorption l eads instead to significantly hotter and shallower temperature stratificat ions. The main differences in temperature structure between our published models computed with the Stagger- and Bifrost codes and those generated with the CO 5 BOLD 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 eq uation in metal-poor stellar surface convection simulatio ns, and at a much lower computational cost. Our results also demonstrate that the cool temperature stratifications predicted for metal-poor l ate-type stars by previous models by our collaboration are not an artifact of the approximated treatment of scattering.

The stellar atmosphere simulation code Bifrost. Code description and validation

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.