Simulations of stellar convection, pulsation and semiconvection

We report on modelling in stellar astrophysics with the ANTARES code. First, we describe properties of turbulence in solar granulation as seen in high-resolution calculations. Then, we turn to the first 2D model of pulsation-convection interaction in a cepheid. We discuss properties of the outer and the HEII ionization zone. Thirdly, we report on our work regarding models of semiconvection in the context of stellar physics.Comment: Astrophysical Dynamics: From Stars to Galaxies. IAU Symposium 27

Multidimensional realistic modelling of Cepheid-like variables. I: Extensions of the ANTARES code

We have extended the ANTARES code to simulate the coupling of pulsation with convection in Cepheid-like variables in an increasingly realistic way, in particular in multidimensions, 2D at this stage. Present days models of radially pulsating stars assume radial symmetry and have the pulsation-convection interaction included via model equations containing ad hoc closures and moreover parameters whose values are barely known. We intend to construct ever more realistic multidimensional models of Cepheids. In the present paper, the first of a series, we describe the basic numerical approach and how it is motivated by physical properties of these objects which are sometimes more, sometimes less obvious. - For the construction of appropriate models a polar grid co-moving with the mean radial velocity has been introduced to optimize radial resolution throughout the different pulsation phases. The grid is radially stretched to account for the change of spatial scales due to vertical stratification and a new grid refinement scheme is introduced to resolve the upper, hydrogen ionisation zone where the gradient of temperature is steepest. We demonstrate that the simulations are not conservative when the original weighted essentially non-oscillatory method implemented in ANTARES is used and derive a new scheme which allows a conservative time evolution. The numerical approximation of diffusion follows the same principles. Moreover, the radiative transfer solver has been modified to improve the efficiency of calculations on parallel computers. We show that with these improvements the ANTARES code can be used for realistic simulations of the convection-pulsation interaction in Cepheids. We discuss the properties of several models which include the upper 42% of a Cepheid along its radial coordinate, assume different opening angles, and are suitable for an in-depth study of convection and pulsation.Comment: 15 pages, 10 figures, 9 tables, to be submitted to Monthly Notices of the RA

Dynamics of small-scale convective motions

Previous studies have discovered a population of small granules with diameters less than 800 km showing differing physical properties. High resolution simulations and observations of the solar granulation, in combination with automated segmentation and tracking algorithms, allow us to study the evolution of the structural and physical properties of these granules and surrounding vortex motions with high temporal and spatial accuracy. We focus on the dynamics of granules (lifetime, fragmentation, size, position, intensity, vertical velocity) over time and the influence of strong vortex motions. Of special interest are the dynamics of small granules compared to regular-sized granules. We developed a temporal tracking algorithm based on our developed segmentation algorithm for solar granulation. This was applied to radiation hydrodynamics simulations and high resolution observations of the quiet Sun by SUNRISE/IMaX. The dynamics of small granules differ in regard to their diameter, intensity and depth evolution compared to regular granules. The tracked granules in the simulation and observations reveal similar dynamics (lifetime, evolution of size, vertical velocity and intensity). The fragmentation analysis shows that the majority of granules in simulations do not fragment, while the opposite was found in observations. Strong vortex motions were detected at the location of small granules. Regions of strong vertical vorticity show high intensities and downflow velocities, and live up to several minutes. The analysis of granules separated according to their diameter in different groups reveals strongly differing behaviors. The largest discrepancies can be found within the groups of small, medium-sized and large granules and have to be analyzed independently. The predominant location of vortex motions on and close to small granules indicates a strong influence on the dynamics of granules

Structure of the solar photosphere studied from the radiation hydrodynamics code ANTARES

The ANTARES radiation hydrodynamics code is capable of simulating the solar granulation in detail unequaled by direct observation. We introduce a state-of-the-art numerical tool to the solar physics community and demonstrate its applicability to model the solar granulation. The code is based on the weighted essentially non-oscillatory finite volume method and by its implementation of local mesh refinement is also capable of simulating turbulent fluids. While the ANTARES code already provides promising insights into small-scale dynamical processes occurring in the quiet-Sun photosphere, it will soon be capable of modeling the latter in the scope of radiation magnetohydrodynamics. In this first preliminary study we focus on the vertical photospheric stratification by examining a 3-D model photosphere with an evolution time much larger than the dynamical timescales of the solar granulation and of particular large horizontal extent corresponding to $25\!" \!\! \times \, 25\!"$ on the solar surface to smooth out horizontal spatial inhomogeneities separately for up- and downflows. The highly resolved Cartesian grid thereby covers $\sim 4~\mathrm{Mm}$ of the upper convection zone and the adjacent photosphere. Correlation analysis, both local and two-point, provides a suitable means to probe the photospheric structure and thereby to identify several layers of characteristic dynamics: The thermal convection zone is found to reach some ten kilometers above the solar surface, while convectively overshooting gas penetrates even higher into the low photosphere. An $\approx 145\,\mathrm{km}$ wide transition layer separates the convective from the oscillatory layers in the higher photosphere.Comment: Accepted for publication in Astrophysics and Space Science; 18 pages, 12 figures, 2 tables; typos correcte

Modelling convection in A star atmospheres. Bisectors and lineshapes of HD108642

We present a code, VeDyn, for modelling envelopes and atmospheres of A to F stars focusing on accurate treatment of convective processes. VeDyn implements the highly sophisticated convection model of Canuto and Dubovikov (1998) but is fast and handy enough to be used in practical astrophysical applications. We developed the HME envelope solver for this convection model furtheron to consistently model the envelope together with the stellar atmosphere. The synthesis code SynthV was extended to account for the resulting velocity structure. Finally, we tested our approach on atomic line bisectors. It is shown that our synthetic line bisectors of HD108642 bend towards the blue and are of a magnitude comparable to the observed ones. Even though this approach of modelling convection requires the solution of a coupled system of nonlinear differential equations, it is fast enough to be applicable to many of the investigation techniques relying on model atmospheres.Comment: 3 pages, 3 figure

The size distribution of magnetic bright points derived from Hinode/SOT observations

Context. Magnetic Bright Points (MBPs) are small-scale magnetic features in the solar photosphere. They may be a possible source of coronal heating by rapid footpoint motions that cause magnetohydrodynamical waves. The number and size distribution are of vital importance in estimating the small scale-magnetic-field energy. Aims. The size distribution of MBPs is derived for G-band images acquired by the Hinode/SOT instrument. Methods. For identification purposes, a new automated segmentation and identification algorithm was developed. Results. For a sampling of 0.108 arcsec/pixel, we derived a mean diameter of (218 +- 48) km for the MBPs. For the full resolved data set with a sampling of 0.054 arcsec/pixel, the size distribution shifted to a mean diameter of (166 +- 31) km. The determined diameters are consistent with earlier published values. The shift is most probably due to the different spatial sampling. Conclusions. We conclude that the smallest magnetic elements in the solar photosphere cannot yet be resolved by G-band observations. The influence of discretisation effects (sampling) has also not yet been investigated sufficiently.Comment: Astronomy and Astrophysics, Volume 498, Issue 1, 2009, pp.289-29

Plumes in stellar convection zones

All numerical simulations of compressible convection reveal the presence of strong downwards directed flows. Thanks to helioseismology, such plumes have now been detected also at the top of the solar convection zone, on super- granular scales. Their properties may be crudely described by adopting Taylor's turbulent entrainment hypothesis, whose validity is well established under various conditions. Using this model, one finds that the strong density stratification does not prevent the plumes from traversing the whole convection zone, and that they carry upwards a net energy flux (Rieutord & Zahn 1995). They penetrate to some extent in the adjacent stable region, where they establish a nearly adiabatic stratification. These plumes have a strong impact on the dynamics of stellar convection zones, and they play probably a key role in the dynamo mechanism.Comment: Proceedings of the 14th Florida Workshop in Nonlinear Astronomy and Physics, "Astrophysical Turbulence and Convection", Eds. J.R. Buchler and H. Kandrup, to appear in the Annals of the New York Academy of Sciences (15 pages, 3 figures

Turbulent convection: comparing the moment equations to numerical simulations

The non-local hydrodynamic moment equations for compressible convection are compared to numerical simulations. Convective and radiative flux typically deviate less than 20% from the 3D simulations, while mean thermodynamic quantities are accurate to at least 2% for the cases we have investigated. The moment equations are solved in minutes rather than days on standard workstations. We conclude that this convection model has the potential to considerably improve the modelling of convection zones in stellar envelopes and cores, in particular of A and F stars.Comment: 10 pages (6 pages of text including figure captions + 4 figures), Latex 2e with AAS Latex 5.0 macros, accepted for publication in ApJ