A method for unambiguous determination of starspot temperatures and areas - Application to II Pegasi, BY Draconis, and HD 209813

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A method is presented for the unique derivation of both starspot temperatures and effective areas from the range of standardized V and R light curves obtained through the rotation periods, and the method is applied to spots observed on II Pegasi, BY Draconis, and HD 209813. The method involves the determination of the temperature difference between the spot and the surrounding photosphere from V and V-R photometry and the Barnes-Evans visual surface brightness relation, and area determination by the derivation of a parameterized effective area representing the fractional area of disk covered by spots under the assumption that the spot or spot group is adequately described by a single circular spot. By this method, an effective temperature of 3400 K and an area representing 37% of the facing hemisphere are derived for the large, cool spot observed on II Pegasi during 1977, an effective temperature of 3500 K and area of 34% are derived for BY Dra and an effective temperature of less than 3840 K is obtained for HD 209813. The derived starspot temperatures, which are believed to correspond to the starspot penumbrae, imply umbral temperatures of 2600-2900 K, in excellent agreement with the 3 kilogauss umbral spot models of Mullan (1974). The geometric modelling of the formation and migration of the spot on BY Dra also indicates a differential rotation amounting to -9.7 x 10 to the -9th rad/sec per deg, in agreement with the solar value.