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.

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 thin radiation escape, from gas-pressure domination to magnetic-pressure domination, from a neutral to an ionised state, from MHD to plasma physics, and from near-equilibrium (LTE) to non-equilibrium conditions. Aims. Our aim is to provide the community with realistic simulations of the magnetic solar outer atmosphere. This will enable detailed comparison of existing and upcoming observations with synthetic observables from the simulations, thereby elucidating the complex interactions of magnetic fields and plasma that are crucial for our understanding of the dynamic outer atmosphere. Methods. We used the radiation magnetohydrodynamics code Bifrost to perform simulations of a computational volume with a magnetic field topology similar to an enhanced network area on the Sun. Results. The full simulation cubes are made available from the Hinode Science Data Centre Europe. The general properties of the simulation are discussed, and limitations are discussed.

Sunspot umbrae--the dark central regions of the spots--are surrounded by brighter filamentary penumbrae, the existence of which remains largely inexplicable. The penumbral filaments contain magnetic fields with varying inclinations and are associated with flowing gas, but discriminating between theoretical models has been difficult because the structure of the filaments has not hitherto been resolved. Here we report observations of penumbral filaments that reveal dark cores inside them. We cannot determine the nature of these dark cores, but their very existence provides a crucial test for any model of penumbrae. Our images also reveal other very small structures, in line with the view that many of the fundamental physical processes in the solar photosphere occur on scales smaller than 100 km.

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