FREDHOLM AND PROPERNESS PROPERTIES OF QUASILINEAR ELLIPTIC SYSTEMS OF SECOND ORDER

For a large class of subsets $\varOmega\subset\mathbb{R}^{N}$ (including unbounded domains), we discuss the Fredholm and properness properties of second-order quasilinear elliptic operators viewed as mappings from $W^{2,p}(\varOmega;\mathbb{R}^{m})$ to $L^{p}(\varOmega;\mathbb{R}^{m})$ with N\ltp\lt\infty and $m\geq1$. These operators arise in the study of elliptic systems of $m$ equations on $\varOmega$. A study in the case of a single equation ($m=1$) on $\mathbb{R}^{N}$ was carried out by Rabier and Stuart. AMS 2000 Mathematics subject classification: Primary 35J45; 35J60. Secondary 47A53; 47F0

Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

AbstractWe consider second-order quasilinear elliptic systems on unbounded domains in the setting of Sobolev spaces. We complete our earlier work on the Fredholm and properness properties of the associated differential operators by giving verifiable conditions for the linearization to be Fredholm of index zero. This opens the way to using the degree for C1-Fredholm maps of index zero as a tool in the study of such quasilinear systems. Our work also enables us to check the Fredholm assumption which plays an important role in Rabier's approach to proving exponential decay to zero at infinity of solutions

Looking for pulsations in HgMn stars through CoRoT lightcurves

HgMn Chemically Peculiar stars are among the quietest stars of the main-sequence. However, according to theoretical predictions, these stars could have pulsations related to the very strong overabundances of iron peak elements, which are produced by atomic diffusion in upper layers. Such pulsations have never been detected from ground based observations. Our aim is to search for signatures of pulsations in HgMn stars using the high quality lightcurves provided by the CoRoT satellite. We identified three faint stars (V>12), from VLT-GIRAFFE multiobject spectrograph survey in a field which was planned for observation by CoRoT. They present the typical characteristics of HgMn stars. They were observed by the CoRoT satellite during the long run (131 days) which started from the 24th of October 2007, with the exoplanets CCD's (Additional Programme). In the present work, we present the analysis of the ground based spectra of these three stars and the analysis of the corresponding CoRoT lightcurves. Two of these three HgMn candidates show low amplitude (less than 1.6 mmag) periodic variations (4.3 and 2.53 days respectively, with harmonics) which are compatible with periods predicted by theoretical models.Comment: Accepted paper in A&A (7 May 2009

The Gaia spectrophotometric standard stars survey -II. Instrumental effects of six ground-based observing campaigns

The Gaia SpectroPhotometric Standard Stars (SPSS) survey started in 2006, it was awarded almost 450 observing nights, and accumulated almost 100,000 raw data frames, with both photometric and spectroscopic observations. Such large observational effort requires careful, homogeneous, and automated data reduction and quality control procedures. In this paper, we quantitatively evaluate instrumental effects that might have a significant (i.e.,$\geq$1%) impact on the Gaia SPSS flux calibration. The measurements involve six different instruments, monitored over the eight years of observations dedicated to the Gaia flux standards campaigns: DOLORES@TNG in La Palma, EFOSC2@NTT and ROSS@REM in La Silla, [email protected] in Calar Alto, BFOSC@Cassini in Loiano, and [email protected] in San Pedro Martir. We examine and quantitatively evaluate the following effects: CCD linearity and shutter times, calibration frames stability, lamp flexures, second order contamination, light polarization, and fringing. We present methods to correct for the relevant effects, which can be applied to a wide range of observational projects at similar instruments.Comment: 16 pages, 13 figures, accepted for publication in Astron. Nach

Gaia data release 1: Principles of the photometric calibration of the G band

Context. Gaia is an ESA cornerstone mission launched on 19 December 2013 aiming to obtain the most complete and precise 3D map of our Galaxy by observing more than one billion sources. This paper is part of a series of documents explaining the data processing and its results for Gaia Data Release 1, focussing on the G band photometry. Aims. This paper describes the calibration model of the Gaia photometric passband for Gaia Data Release 1. Methods. The overall principle of splitting the process into internal and external calibrations is outlined. In the internal calibration, a self-consistent photometric system is generated. Then, the external calibration provides the link to the absolute photometric flux scales. Results. The Gaia photometric calibration pipeline explained here was applied to the first data release with good results. Details are given of the various calibration elements including the mathematical formulation of the models used and of the extraction and preparation of the required input parameters (e.g. colour terms). The external calibration in this first release provides the absolute zero point and photometric transformations from the Gaia G passband to other common photometric systems. Conclusions. This paper describes the photometric calibration implemented for the first Gaia data release and the instrumental effects taken into account. For this first release no aperture losses, radiation damage, and other second-order effects have not yet been implemented in the calibration.Comment: 15 pages, 16 figures, Gaia data release 1 documentation special volum

Spectroscopic survey of Kepler stars. I. HERMES/Mercator observations of A- and F-type stars

The Kepler space mission provided near-continuous and high-precision photometry of about 207 000 stars, which can be used for asteroseismology. However, for successful seismic modeling it is equally important to have accurate stellar physical parameters. Therefore, supplementary ground-based data are needed. We report the results of the analysis of high-resolution spectroscopic data of A- and F-type stars from the Kepler field, which were obtained with the HERMES spectrograph on the Mercator telescope. We determined spectral types, atmospheric parameters and chemical abundances for a sample of 117 stars. Hydrogen Balmer, Fe i, and Fe ii lines were used to derive effective temperatures, surface gravities, and microturbulent velocities. We determined chemical abundances and projected rotational velocities using a spectrum synthesis technique. The atmospheric parameters obtained were compared with those from the Kepler Input Catalogue (KIC), confirming that the KIC effective temperatures are underestimated for A stars. Effective temperatures calculated by spectral energy distribution fitting are in good agreement with those determined from the spectral line analysis. The analysed sample comprises stars with approximately solar chemical abundances, as well as chemically peculiar stars of the Am, Ap, and λ Boo types. The distribution of the projected rotational velocity, vsin i, is typical for A and F stars and ranges from 8 to about 280 km s−1, with a mean of 134 km s−1

The effect of rotation on the abundances of the chemical elements of the A-type stars in the Praesepe cluster

We study how chemical abundances of late B-, A- and early F-type stars evolve with time, and we search for correlations between the abundance of chemical elements and other stellar parameters, such as effective temperature and Vsini. We have observed a large number of B-, A- and F-type stars belonging to open clusters of different ages. In this paper we concentrate on the Praesepe cluster (log t = 8.85), for which we have obtained high resolution, high signal-to-noise ratio spectra of sixteen normal A- and F-type stars and one Am star, using the SOPHIE spectrograph of the Observatoire de Haute-Provence. For all the observed stars, we have derived fundamental parameters and chemical abundances. In addition, we discuss another eight Am stars belonging to the same cluster, for which the abundance analysis had been presented in a previous paper. We find a strong correlation between peculiarity of Am stars and Vsini. The abundance of the elements underabundant in Am stars increases with Vsini, while it decreases for the overabundant elements. Chemical abundances of various elements appear correlated with the iron abundance.Comment: Accepted for publication on A&

AmFm and lithium gap stars: Stellar evolution models with mass loss

A thorough study of the effects of mass loss on internal and surface abundances of A and F stars is carried out in order to constrain mass loss rates for these stars, as well as further elucidate some of the processes which compete with atomic diffusion. Self-consistent stellar evolution models of 1.3 to 2.5 M_sun stars including atomic diffusion and radiative accelerations for all species within the OPAL opacity database were computed with mass loss and compared to observations as well as previous calculations with turbulent mixing. Models with unseparated mass loss rates between 5 x 10^-14 and 10^-13 M_sun/yr reproduce observations for many cluster AmFm stars as well as Sirius A and o Leonis. These models also explain cool Fm stars, but not the Hyades lithium gap. Like turbulent mixing, these mass loss rates reduce surface abundance anomalies; however, their effects are very different with respect to internal abundances. For most of the main sequence lifetime of an A or F star, surface abundances in the presence of such mass loss depend on separation which takes place between log(Delta M/M_star)= -6 and -5. The current observational constraints do not allow us to conclude that mass loss is to be preferred over turbulent mixing (induced by rotation or otherwise) in order to explain the AmFm phenomenon. Internal concentration variations which could be detectable through asteroseismic tests should provide further information. If atomic diffusion coupled with mass loss are to explain the Hyades Li gap, the wind would need to be separated.Comment: 27 pages, 25 figures, accepted for publication in A&

The Gaia spectrophotometric standard stars survey - IV. Results of the absolute photometry campaign

We present Johnson-Kron-Cousins BVRI photometry of 228 candidate spectrophotometric standard stars for the external (absolute) flux calibration of Gaia data. The data were gathered as part of a 10-yr observing campaign with the goal of building the external grid of flux standards for Gaia and we obtained absolute photometry, relative photometry for constancy monitoring, and spectrophotometry. Preliminary releases of the flux tables were used to calibrate the first two Gaia releases. This paper focuses on the imaging frames observed in good sky conditions (about 9100). The photometry will be used to validate the ground-based flux tables of the Gaia spectrophotometric standard stars and to correct the spectra obtained in non-perfectly photometric observing conditions for small zero-point variations. The absolute photometry presented here is tied to the Landolt standard stars system to ≃1 per cent or better, depending on the photometric band. Extensive comparisons with various literature sources show an overall ≃1 per cent agreement, which appears to be the current limit in the accuracy of flux calibrations across various samples and techniques in the literature. The Gaia photometric precision is presently of the order of 0.1 per cent or better, thus various ideas for the improvement of photometric calibration accuracy are discussed.This work was supported by the MINECO (Spanish Ministry of Economy and Competitiveness) through grant RTI2018-095076-B-C21 (MINECO/FEDER- Fondo Europeo de Desarrollo Regional, UE). APV acknowledges FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for the postdoctoral fellowship No. 2017/15893-1 and the DGAPA (Dirección General de Asuntos del Personal Académico) PAPIIT grant IG100319