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

Stellar model atmospheres with magnetic line blanketing. III. The role of magnetic field inclination

Context. See abstract in the paper. Aims. In the last paper of this series we study the effects of the magnetic field, varying its strength and orientation, on the model atmosphere structure, the energy distribution, photometric colors and the hydrogen Balmer line profiles. We compare with the previous results for an isotropic case in order to understand whether there is a clear relation between the value of the magnetic field angle and model changes, and to study how important the additional orientational information is. Also, we examine the probable explanation of the visual flux depressions of the magnetic chemically peculiar stars in the context of this work. Methods. We calculated one more grid of the model atmospheres of magnetic A and B stars for different effective temperatures (Teff=8000K, 11000K, 15000K), magnetic field strengths (B=0, 5, 10, 40 kG) and various angles of the magnetic field (Omega=0-90 degr) with respect to the atmosphere plane. We used the LLmodels code which implements a direct method for line opacity calculation, anomalous Zeeman splitting of spectral lines, and polarized radiation transfer. Results. We have not found significant changes in model atmosphere structure, photometric and spectroscopic observables or profiles of hydrogen Balmer lines as we vary the magnetic field inclination angle Omega. The strength of the magnetic field plays the main role in magnetic line blanketing. We show that the magnetic field has a clear relation to the visual flux depressions of the magnetic CP stars. Conclusions. See abstract in the paper.Comment: 10 pages, 5 figure

Electronic States in Diffused Quantum Wells

In the present study we calculate the energy values and the spatial distributions of the bound electronic states in some diffused quantum wells. The calculations are performed within the virtual crystal approximation, $sp^3 s^*$ spin dependent empirical tight-binding model and the surface Green function matching method. A good agreement is found between our results and experimental data obtained for AlGaAs/GaAs quantum wells with thermally induced changes in the profile at the interfaces. Our calculations show that for diffusion lengths $L_{D}=20\div100$ {\AA} the transition (C3-HH3) is not sensitive to the diffusion length, but the transitions (C1-HH1), (C1-LH1), (C2-HH2) and (C2-LH2) display large "blue shifts" as L_{D} increases. For diffusion lengths $L_{D}=0\div20$ {\AA} the transitions (C1-HH1) and (C1-LH1) are less sensitive to the L_{D} changes than the (C3-HH3) transition. The observed dependence is explained in terms of the bound states spatial distributions.Comment: ReVTeX file, 7pp., no macros, 4 figures available on the reques

MOST discovers a multimode delta Scuti star in a triple system: HD 61199

A field star, HD 61199 (V ~ 8), simultaneously observed with Procyon by the MOST (Microvariability & Oscillations of STars) satellite in continuous runs of 34, 17, and 34 days in 2004, 2005, and 2007, was found to pulsate in 11 frequencies in the delta Scuti range with amplitudes from 1.7 down to 0.09 mmag. The photometry also showed variations with a period of about four days. To investigate the nature of the longer period, 45 days of time-resolved spectroscopy was obtained at the Thueringer Landessternwarte Tautenburg in 2004. The radial velocity measurements indicate that HD 61199 is a triple system. A delta Scuti pulsator with a rich eigenspectrum in a multiple system is promising for asteroseismology. Our objectives were to identify which of the stars in the system is the delta Scuti variable and to obtain the orbital elements of the system and the fundamental parameters of the individual components, which are constrained by the pulsation frequencies of the delta Scuti star. Classical Fourier techniques and least-squares multi-sinusoidal fits were applied to the MOST photometry to identify the pulsation frequencies. The groundbased spectroscopy was analysed with least-squares-deconvolution (LSD) techniques, and the orbital elements derived with the KOREL and ORBITX routines. Asteroseismic models were also generated. The photometric and spectroscopic data are compatible with a triple system consisting of a close binary with an orbital period of 3.57 days and a delta Scuti companion (HD 61199,A) as the most luminous component. The delta Scuti star is a rapid rotator with about vsin i = 130 km/s and an upper mass limit of about 2.1 Msun. For the close binary components, we find they are of nearly equal mass, with lower mass limits of about 0.7 Msun.Comment: 11 pages, 14 figures, accepted by A&

Atmospheric velocity fields in tepid main sequence stars

The line profiles of the stars with v sin i below a few km/s can reveal direct signatures of local velocity fields (e.g. convection) in stellar atmospheres. This effect is well established in cool main sequence stars, and has been detected and studied in three A stars. This paper reports observations of main sequence B, A and F stars with two goals: (1) to identify additional stars having sufficiently low values of v sin i to search for spectral line profile signatures of local velocity fields, and (2) to explore how the signatures of the local velocity fields in the atmosphere depend on stellar parameters such as effective temperature T_eff and peculiarity type. For stars having T_eff below about 10000 K, we always detect local atmospheric velocity fields indirectly through a non-zero microturbulence parameter, but not for hotter stars. Among the A and F stars in our sample having the sharpest lines, direct tracers of atmospheric velocity fields are found in six new stars. The velocity field signatures identified include asymmetric excess line wing absorption, deeper in the blue line wing than in the red; line profiles of strong lines that are poorly fit by computed profiles; and strong lines that are broader than they should be for the v sin i values deduced from weak lines. These effects are found in both normal and Am stars, but seem stronger in Am stars. These data still have not been satisfactorily explained by models of atmospheric convection, including numerical simulations.Comment: Acepted for publication by Astronomy and Astrophysic

Critical evaluation of magnetic field detections reported for pulsating B-type stars in the light of ESPaDOnS, Narval and reanalyzed FORS1/2 observations

Recent spectropolarimetric studies of 7 SPB and $\beta$ Cep stars have suggested that photospheric magnetic fields are more common in B-type pulsators than in the general population of B stars, suggesting a significant connection between magnetic and pulsational phenomena. We present an analysis of new and previously published spectropolarimetric observations of these stars. New Stokes $V$ observations obtained with the high-resolution ESPaDOnS and Narval instruments confirm the presence of a magnetic field in one of the stars ($\epsilon$ Lup), but find no evidence of magnetism in 5 others. A re-analysis of the published longitudinal field measurements obtained with the low-resolution FORS1/2 spectropolarimeters finds that the measurements of all stars show more scatter from zero than can be attributed to Gaussian noise, suggesting the presence of a signal and/or systematic under-estimation of error bars. Re-reduction and re-measurement of the FORS1/2 spectra from the ESO archive demonstrates that small changes in reduction procedure lead to substantial changes in the inferred longitudinal field, and substantially reduces the number of field detections at the 3$\sigma$ level. Furthermore, we find that the published periods are not unique solutions to the time series of either the original or the revised FORS1/2 data. We conclude that the reported field detections, proposed periods and field geometry models for $\alpha$ Pyx, 15 CMa, 33 Eri and V1449 Aql are artefacts of the data analysis and reduction procedures, and that magnetic fields at the reported strength are no more common in SPB/$\beta$ Cep stars than in the general population of B stars.Comment: 10 pages, 5 figures, accepted for publication in ApJ, 2012, typo correcte

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

On the influence of Stark broadening on Si I lines in stellar atmospheres

We study the influence of Stark broadening and stratification effects on Si\i lines in the rapidly oscillating (roAp) star 10 Aql, where the Si\i 6142.48 \AA and 6155.13 \AA lines are asymmetrical and shifted. First we have calculated Stark broadening parameters using the semiclassical perturbation method for three Si\i lines: 5950.2 \AA, 6142.48 \AA and 6155.13 \AA. We revised the synthetic sp$ calculation code taking into account both Stark width and shift for these lines. From the comparison of our calculations with the observations we found that Stark broadening + the stratification effect can explain asymmetry of the Si\i 6142.48 \AA and 6155.13 \AA lines in the atmospere of roAp star 10 Aql.Comment: Accepted to A&

A self-consistent empirical model atmosphere, abundance and stratification analysis of the benchmark roAp star alpha Circini

Chemically peculiar (CP) stars are unique natural laboratories for investigation of the microscopic diffusion processes of chemical elements. The element segregation under the influence of gravity and radiation pressure leads to the appearance of strong abundance gradients in the atmospheres of CP stars. Consequently, the atmospheric temperature-pressure structure of these objects could deviate significantly from the atmospheres of normal stars with homogeneous abundances. In this study we performed a self-consistent, empirical model atmosphere study of the brightest rapidly oscillating Ap star alpha Cir. We account for chemical stratification in the model atmosphere calculations and assess the importance of non-uniformed vertical element distribution on the model structure, energy distribution and hydrogen line profiles. Based on an iterative procedure of the chemical abundance analysis of 52 ions of 35 elements, stratification modeling of 4 elements (Si, Ca, Cr and Fe) and subsequent re-calculations of the atmospheric structure, we derived a new model atmosphere of alpha Cir, which is consistent with the inferred atmospheric chemistry of the star. We find Teff=7500 K, logg=4.1, and demonstrate that chemical stratification has a noticeable impact on the model structure and modifies the formation of the hydrogen Balmer lines. Our spectroscopically determined Teff of alpha Cir agrees with the fundamental effective temperature of this star. This shows that temperatures inferred in detailed spectroscopic analyses of cool magnetic CP stars are not affected by a large systematic bias.Comment: 14 pages, 11 figures; accepted for publication in Astronomy & Astrophysic