Herbert J. Muthsam

ANTARES - A Numerical Tool for Astrophysical RESearch with applications to solar granulation

Abstract We discuss the general design of the ANTARES code which is intended for simulations in stellar hydrodynamics with radiative transfer and realistic microphysics in 1D, 2D and 3D. We then compare the quality of various numerical methods. We have applied ANTARES in order to obtain high resolution simulations of solar granulation which we describe and analyze. In order to obtain high resolution, we apply grid refinement to a region predominantly occupied by an exploding granule. Strong, rapidly rotating vortex tubes of small diameter ( ∼ 100 km ) generated by the downdrafts and ascending into the photosphere near the granule boundaries evolve, often entering the photosphere from below in an arclike fashion. They essentially contribute to the turbulent velocity field near the granule boundaries.

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.

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 rst 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 dierent pulsation phases. The grid is radially stretched to account for the change of spatial scales due to vertical stratication and a new grid renement 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 diusion follows the same principles. Moreover, the radiative transfer solver has been modied to improve the efciency 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 numerical models of this kind which include the upper 42% of a Cepheid along its radial coordinate and assume dierent opening angles. The models are suitable for an in-depth study of convection and pulsation in these objects.

Dynamics of isolated magnetic bright points derived from Hinode/SOT G-band observations

Context. Small-scale magnetic fields in the solar photosphere can be identified in high-resolution magnetograms or in the G-band as magnetic bright points (MBPs). Rapid motions of these fields can cause magneto-hydrodynamical waves and can also lead to nanoflares by magnetic field braiding and twisting. The MBP velocity distribution is a crucial parameter for estimating the amplitudes of those waves and the amount of energy they can contribute to coronal heating. Aims. The velocity and lifetime distributions of MBPs are derived from solar G-band images of a quiet sun region acquired by the Hinode/SOT instrument with different temporal and spatial sampling rates. Methods. We developed an automatic segmentation, identification and tracking algorithm to analyse G-Band image sequences to obtain the lifetime and velocity distributions of MBPs. The influence of temporal/spatial sampling rates on these distributions is studied and used to correct the obtained lifetimes and velocity distributions for these digitalisation effects. Results. After the correction of algorithm effects, we obtained a mean MBP lifetime of (2.50 ± 0.05) min and mean MBP velocities, depending on smoothing processes, in the range of (1-2) km s -1 . Corrected for temporal sampling effects, we obtained for the effective velocity distribution a Rayleigh function with a coefficient of (1.62 ± 0.05) km s -1 . The x- and y-components of the velocity distributions are Gaussians. The lifetime distribution can be fitted by an exponential function.

Interacting convection zones

Abstract 3D Numerical simulations of convection zones separated by a stable layer (according to the Schwarzschild criterion) are presented. The compressible case is considered. We make use of idealized microphysics closely related to polytropes. Decreasing the importance of the separating stable layer by diminishing its vertical extent in a series of models we investigate how the two convection zones merge into one. In our parameter range it is the upper zone which increases in size and ultimately squeezes the lower convection zone more or less out of existence. Properties of various fluxes and other physical quantities are discussed.

A low Mach number solver: Enhancing applicability

In astrophysics and meteorology there exist numerous situations where flows exhibit small velocities compared to the sound speed. To overcome the stringent timestep restrictions posed by the predominantly used explicit methods for integration in time the Euler (or Navier-Stokes) equations are usually replaced by modified versions. In astrophysics this is nearly exclusively the anelastic approximation. Kwatra et al. (2009) [19] have proposed a method with favorable time-step properties integrating the original equations (and thus allowing, for example, also the treatment of shocks). We describe the extension of the method to the Navier-Stokes and two-component equations. However, when applying the extended method to problems in convection and double diffusive convection (semiconvection) we ran into numerical difficulties. We describe our procedure for stabilizing the method. We also investigate the behavior of Kwatra et al.s method for very low Mach numbers (down to Ma=0.001) and point out its very favorable properties in this realm for situations where the explicit counterpart of this method returns absolutely unusable results. Furthermore, we show that the method strongly scales over three orders of magnitude of processor cores and is limited only by the specific network structure of the high performance computer we use.

High-resolution models of solar granulation: the two-dimensional case

Using advanced numerical schemes and grid refinement, we present 2D high-resolution models of solar granulation with particular emphasis on downflowing plumes. In the high-resolution portion of our simulation, a box measuring 1.97 x 2.58 Mm 2 (vertical x horizontal), the grid size is 1.82 x 2.84 km 2 . Calculations at the resolution usually applied in this type of simulations amount to only a few horizontal gridpoints for a downflowing plume. Due to the increased number of gridpoints in our high-resolution domain, the simulations show the development of vigorous secondary instabilities of both the plumes head and stem. The plumes head produces counterrotating vortex patches, a topology due to the 2D nature of the simulations. Below a depth of about 1 Mm, the plumes head and stem instabilities produce, in these 2D models, patches of low density, temperature, pressure and high vorticity which may last for all of our simulation time, ∼10 min, and probably considerably longer. Centrifugal forces acting in these patches counteract the strong inward pressure. Probably most importantly, the plumes instabilities give rise to acoustic pulses created predominantly down to ∼1.5 Mm. The pulses proceed laterally as well as upwards and are ubiquitous. Ultimately, most of them emerge into the photosphere. A considerable part of the photospheric turbulence in these models is due to those pulses rather than to some sort of eddies. The upflows in granules are smooth where they reach the photosphere from below even in the present calculations; however, the pulses may enter in the photosphere also in granular upflows.

Multidimensional realistic modelling of Cepheid-like variables – II. Analysis of a Cepheid model

Non-local, time-dependent convection models have been used to explain the location of double-mode pulsations in Cepheids in the HR diagram as well as the existence and location of the red edge of the instability strip. These properties are highly sensitive to model parameters. We use 2D radiation hydrodynamical simulations with realistic microphysics and grey radiative-transfer to model a short period Cepheid. The simulations show that the strength of the convection zone varies significantly over the pulsation period and exhibits a phase shift relative to the variations in radius. We evaluate the convective flux and the work integral as predicted by the most common convection models. It turns out that over one pulsation cycle the model parameter

Curvilinear Grids for WENO Methods in Astrophysical Simulations

alpha_{rm c}

Modelling of stellar convection

, has to be varied by up to a factor of beyond 2 to match the convective flux obtained from the simulations. To bring convective fluxes integrated over the He II convection zone and the overshoot zone below into agreement, this parameter has to be varied by a factor of up to