Measurement of the limb darkening coefficient of stars

This paper introduces a new method of describing the limb darkening phenome non of stellar atmospheres in the 1st and 2nd order approximations. The lim b darkening coefficients are given by direct measurements of relevant physi cal quantities or measurements of flux and a supplementary quantity, namely , the star's surface temperature. The comparison either with solar observat ions or with the method of numerical simulation of the atmosphere shows tha t the new method can very accurately describe the star's limb darkening and determine its relevant coefficients. The accuracy of the new direct method is assessed using 176 observational data points of the Sun, and the mean f ractional differences is found to be 0.38% for the 1st-, and 0.26% for the 2nd-order approximations. The mean differences of the indirect method are c lose to, and slightly larger than these values. When compared with numerica l models of the atmosphere, the differences are in the range from under 1% to under 3%.