Astronomy & Astrophysics

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Issue		A&A Volume 405, Number 3, July III 2003
Page(s)		1095 - 1105
Section		Formation and evolution of planetary systems
DOI		10.1051/0004-6361:20030619

A&A 405, 1095-1105 (2003)
DOI: 10.1051/0004-6361:20030619

New grids of ATLAS9 atmospheres

II. Limb-darkening coefficients for the Strömgren photometric system for A-F stars

C. Barban^{1, 2}, M. J. Goupil², C. Van't Veer-Menneret², R. Garrido³, F. Kupka^{4, 5} and U. Heiter⁶

¹ National Solar Observatory, 950 N. Cherry Ave., Tucson, AZ 85719, USA
    e-mail: barban@noao.edu
² Observatoire de Paris-Meudon, 5 place Jules Janssen, 92195 Meudon Cedex, France
    e-mail: Caroline.Barban@obspm.fr; MarieJo.Goupil@obspm.fr; Claude.VantVeer@obspm.fr
³ Instituto de Astrofisica de Andalucia, CSIC, Apdo. 3004, 18080 Granada, Spain
    e-mail: garrido@iaa.es
⁴ Astronomy Unit, School of Mathematical Sciences, Queen Mary, University of London Mile End Road, London E1 4NS, UK
    e-mail: f.kupka@qmul.ac.uk
⁵ Institut für Astronomie, Universität Wien, Türkenschanzstraße 17, 1180 Vienna, Austria
⁶ Department of Astronomy, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH 44106-7215, USA
    e-mail: ulrike@fafnir.astr.cwru.edu

(Received 6 March 2003 / Accepted 16 April 2003)

Abstract
Using up-to-date model atmospheres (Heiter et al. 2002) with the turbulent convection approach developed by Canuto et al. (1996, CGM), quadratic, cubic and square root limb darkening coefficients (LDC) are calculated with a least square fit method for the Strömgren photometric system. This is done for a sample of solar metallicity models with effective temperatures between 6000 and 8500 K and with $\log g$ between 2.5 and 4.5. A comparison is made between these LDC and the ones computed from model atmospheres using the classical mixing length prescription with a mixing length parameter $\alpha=1.25$ and $\alpha=0.5$ . For CGM model atmospheres, the law which reproduces better the model intensity is found to be the square root one for the u band and the cubic law for the v band. The results are more complex for the b and y bands depending on the temperature and gravity of the model. Similar conclusions are reached for MLT $\alpha=0.5$ models. As expected much larger differences are found between CGM and MLT with $\alpha=1.25$ . In a second part, the weighted limb-darkening integrals, $b_{\ell}$ , and their derivatives with respect to temperature and gravity, are then computed using the best limb-darkening law. These integrals are known to be very important in the context of photometric mode identification of non-radial pulsating stars. The effect of convection treatment on these quantities is discussed and as expected differences in the $b_{\ell}$ coefficients and derivatives computed with CGM and MLT $\alpha=0.5$ are much smaller than differences obtained between computations with CGM and MLT $\alpha=1.25$ .

Key words: stars: atmospheres -- stars: oscillations -- convection

Offprint request: C. Barban, Caroline.Barban@obspm.fr

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