Hans-Günter Ludwig

Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere

Numerical simulation of the three-dimensional structure and dynamics of the non-magnetic solar chromosphere

Numerical simulations of surface convection in a late M-dwarf

Based on detailed 2D and 3D numerical radiation-hydrodynamics (RHD) simulations of time-dependent compress- ible convection, we have studied the dynamics and thermal structure of the convective surface layers of a prototypical late-type M-dwarf (Teff ≈ 2800K, log g = 5.0, solar chemical composition). The RHD models predict stellar granulation qualitatively similar to the familiar solar pattern. Quantitatively, the granular cells show a convective turn-over time scale of ≈100s, and a horizontal scale of 80km; the relative intensity contrast of the granular pattern amounts to 1.1%, and root-mean-square verti- cal velocities reach 240ms −1 at maximum. Deviations from radiative equilibrium in the higher, formally convectively stable atmospheric layers are found to be insignificant allowing a reliable modeling of the atmosphere with 1D standard model atmo- spheres. A mixing-length parameter of αMLT = 2.1 provides the best representation of the average thermal structure of the RHD model atmosphere while alternative values are found when fitting the asymptotic entropy encountered in deeper layers of the stellar envelope (αMLT = 1.5), or when matching the vertical velocity (αMLT = 3.5). The close correspondence between RHD and standard model atmospheres implies that presently existing discrepancies between observed and predicted stellar colors in the M-dwarf regime cannot be traced back to an inadequate treatment of convection in the 1D standard models. The RHD models predict a modest extension of the convectively mixed region beyond the formal Schwarzschild stability boundary which provides hints for the distribution of dust grains in cooler (brown dwarf) atmospheres.

On the Limb Darkening, Spectral Energy Distribution, and Temperature Structure of Procyon

We have fit synthetic visibilities from three-dimensional ((COBOLD)-B-5+PHOENIX) and one-dimensional (PHOENIX, ATLAS 12) model stellar atmospheres of Procyon (F5 IV) to high-precision interferometric data from the VLT Interferometer (K band) and from the Mark III interferometer (500 and 800 nm). These data sets provide a test of theoretical wavelength-dependent limb-darkening predictions. The work of Allende Prieto et al. has shown that the temperature structure from a spatially and temporally averaged three-dimensional hydrodynamic model produces significantly less limb darkening at 500 nm relative to the temperature structure of a one-dimensional MARCS model atmosphere with a standard mixing-length approximation for convection. Our direct fits to the interferometric data confirm this prediction. A one-dimensional ATLAS 12 model with approximate overshooting provides the required temperature gradient. We show, however, that one-dimensional models cannot reproduce the ultraviolet spectrophotometry below 160 nm with effective temperatures in the range constrained by the measured bolometric flux and angular diameter. We find that a good match to the full spectral energy distribution can be obtained with a composite model consisting of a weighted average of 12 one-dimensional model atmospheres based on the surface intensity distribution of a three-dimensional granulation simulation. We emphasize that one-dimensional models with overshooting may realistically represent the mean temperature structure of F-type stars such as Procyon, but the same models will predict redder colors than observed because they lack the multicomponent temperature distribution expected for the surfaces of these stars. (Less)

Broad-band photometric colors and effective temperature calibrations for late-type giants - I. Z = 0.02

We investigate the effects of metallicity on the broad-band photometric colors of late-type giants, and make a comparison of synthetic colors with observed photometric properties of late-type giants over a wide range of effective temperatures (T-eff = 3500- 4800K) and gravities (log g = 0.0-2.5), at [M/H] = -1.0 and -2.0. The influence of metallicity on the synthetic photometric colors is small at effective temperatures above similar to 3800K, but the effects grow larger at lower T-eff,T- due to the changing effciency of molecule formation which reduces molecular opacities at lower [M/H]. To make a detailed comparison of the synthetic and observed photometric colors of late type giants in the T-eff-color and color-color planes (which is done at two metallicities, [M/H] = -1.0 and -2.0), we derive a set of new T-eff-log g-color relations based on synthetic photometric colors, at [M/H] = -0.5, -1.0, -1.5, and -2.0. These relations are based on the T-eff- log g scales that we derive employing literature data for 178 late-type giants in 10 Galactic globular clusters (with metallicities of the individual stars between [M/H] = -0.7 and -2.5), and synthetic colors produced with the PHOENIX, MARCS and ATLAS stellar atmosphere codes. Combined with the T-eff- log g-color relations at [M/H] = 0.0 (Kucinskas et al. 2005), the set of new relations covers metallicities [M/H] = 0.0... -2.0 ([M/H] = 0.5), effective temperatures T-eff = 3500... 4800 K (T-eff = 100K), and gravities log g = - 0.5... 3.0. The new T-eff- log g-color relations are in good agreement with published T-eff-color relations based on observed properties of late-type giants, both at [M/H] = -1.0 and -2.0. The differences in all T-eff- color planes are typically well within similar to 100K. We find, however, that effective temperatures predicted by the scales based on synthetic colors tend to be slightly higher than those resulting from the T-eff- color relations based on observations, with the offsets up to similar to 100 K. This is clearly seen both at [M/H] = -1.0 and -2.0, especially in the T-eff-(B - V) and T-eff-(V - K) planes. The consistency between T-eff- log g-color scales based on synthetic colors calculated with different stellar atmosphere codes is very good, with typical differences being well within. Delta T-eff similar to 70 K at [M/H] = - 1.0 and. T-eff similar to 40 K at [M/H] = -2.0. (Less)

Are granules good tracers of solar surface velocity fields

Using a numerical simulation of compressible convection with radiative transfer mimicking the solar photosphere, we compare the velocity eld derived from granule motions to the actual velocity eld of the plasma. We thus test the idea that granules may be used to trace large-scale velocity elds at the suns surface. Our results show that this is indeed the case provided the scale separation is sucient. We thus estimate that neither velocity elds at scales less than 2500 km nor time evolution at scales shorter than 0.5 hr can be faithfully described by granules. At larger scales the granular motions correlate linearly with the underlying fluid motions with a slope of 2 reaching correlation coecients up to0.9.

Excitation of Radial P-Modes in the Sun and Stars

P-mode oscillations in the Sun and stars are excited stochastically by Reynolds stress and entropy fluctuations produced by convection in their outer envelopes. The excitation rate of radial oscillations of stars near the main sequence from K to F and a subgiant K IV star have been calculated from numerical simulations of their surface convection zones. P-mode excitation increases with increasing effective temperature (until envelope convection ceases in the F stars) and also increases with decreasing gravity. The frequency of the maximum excitation decreases with decreasing surface gravity.

The Atmospheric Dynamics in 2D and 3D Simulations of Stellar Surface Convection

A pressing problem in our understanding of the structure and evolution of late-type stars is the lack of a reliable theory of convection. Convective flows transport mass, momentum, and energy, thus influencing the internal distribution of energy, chemical species, and angular momentum. They drive the stellar magnetic and oscillatory activity. Although the underlying physical principles are well known, the nonlinear and nonlocal character of the equations describing a radiating, partially ionized fluid has prevented the development of a closed analytical theory.

Excitation of P-modes in the sun and stars

P-mode oscillations in the Sun and stars are excited stochasticly by Reynolds stress and entropy fluctuations produced by convection in their outer envelopes. The excitation increases with increasing effective temperature (until envelope convection ceases in the F stars) and also increases with decreasing gravity.

Energy Transport, Overshoot, and Mixing in the Atmospheres of Very Cool Stars

We constructed hydrodynamical model atmospheres for mid M-type main-, as well as pre-main-sequence objects. Despite the complex chemistry encountered in such cool atmospheres a reasonably accurate representation of the radiative transfer is possible. The detailed treatment of the interplay between radiation and convection in the hydrodynamical models allows to study processes usually not accessible within the framework conventional model atmospheres. In particular, we determined the efficiency of the convective energy transport, and the efficiency of mixing by convective overshoot. The convective transport efficiency expressed in terms of an equivalent mixing-length parameter amounts to values around 2 in the optically thick, and 2.8 in the optically thin regime. The thermal structure of the formally convectively stable layers is little affected by convective overshoot and wave heating, i.e. stays close to radiative equilibrium. Mixing by convective overshoot shows an exponential decline with geometrical distance from the Schwarzschild stability boundary. The scale height of the decline varies with gravitational acceleration roughly as g(-1/2), with 0.5 pressure scale heights at log(g)=5.0. (Less)