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

Concentration of the first eigenfunction for a second order elliptic operator

We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold when the diffusion constant $\epsilon$ goes to zero. We assume that the first order term is given by a vector field $b$, whose recurrent components are either hyperbolic points or cycles or two dimensional torii. The limits of the normalized eigenfunctions concentrate on the recurrent sets of maximal dimension where the topological pressure \cite{Kifer90} is attained. On the cycles and torii, the limit measures are absolutely continuous with respect to the invariant probability measure on these sets. We have determined these limit measures, using a blow-up analysis.Comment: Note to appear in C.R.A.

Stellar model atmospheres with magnetic line blanketing

Model atmospheres of A and B stars are computed taking into account magnetic line blanketing. These calculations are based on the new stellar model atmosphere code LLModels which implements direct treatment of the opacities due to the bound-bound transitions and ensures an accurate and detailed description of the line absorption. The anomalous Zeeman effect was calculated for the field strengths between 1 and 40 kG and a field vector perpendicular to the line of sight. The model structure, high-resolution energy distribution, photometric colors, metallic line spectra and the hydrogen Balmer line profiles are computed for magnetic stars with different metallicities and are discussed with respect to those of non-magnetic reference models. The magnetically enhanced line blanketing changes the atmospheric structure and leads to a redistribution of energy in the stellar spectrum. The most noticeable feature in the optical region is the appearance of the 5200 A depression. However, this effect is prominent only in cool A stars and disappears for higher effective temperatures. The presence of a magnetic field produces opposite variation of the flux distribution in the optical and UV region. A deficiency of the UV flux is found for the whole range of considered effective temperatures, whereas the ``null wavelength'' where flux remains unchanged shifts towards the shorter wavelengths for higher temperatures.Comment: accepted by Astronomy & Astrophysic

Fast Recognition of Partial Star Products and Quasi Cartesian Products

This paper is concerned with the fast computation of a relation $\R$ on the edge set of connected graphs that plays a decisive role in the recognition of approximate Cartesian products, the weak reconstruction of Cartesian products, and the recognition of Cartesian graph bundles with a triangle free basis. A special case of $\R$ is the relation $\delta^\ast$, whose convex closure yields the product relation $\sigma$ that induces the prime factor decomposition of connected graphs with respect to the Cartesian product. For the construction of $\R$ so-called Partial Star Products are of particular interest. Several special data structures are used that allow to compute Partial Star Products in constant time. These computations are tuned to the recognition of approximate graph products, but also lead to a linear time algorithm for the computation of $\delta^\ast$ for graphs with maximum bounded degree. Furthermore, we define \emph{quasi Cartesian products} as graphs with non-trivial $\delta^\ast$. We provide several examples, and show that quasi Cartesian products can be recognized in linear time for graphs with bounded maximum degree. Finally, we note that quasi products can be recognized in sublinear time with a parallelized algorithm