New grids of ATLAS9 atmospheres - II. Limb-darkening coefficients for the Stromgren photometric system for A-F stars

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 Str?mgren 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(l), 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(l) 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.