Measuring starspot temperature from line depth ratios - I. The method

Gray and collaborators have recently demonstrated that line-depth ratios are a powerful tool for temperature discrimination, able to resolve differences less than or equal to 10 K. The method has been applied to detect temperature variations in the 5-15 K range due to activity cycles (e.g. Gray et al. 1996a, 1996b) or to rotation modulation produced by large surface features, called star-patches, like that detected in xi Boo A by Toner & Gray (1988). Cool starspots of a few tenths of the stellar surface produce bumps in a line profile, which migrate through the line profile allowing Doppler-imaging in fast rotating stars. In the hypothesis that in slowly-rotating stars the passage of dark spots produces modulation of the center line depth of different amount in lines of different sensitivity to temperature, we have made test observations on three active binaries of the RS CVn type. Based on observations made at the Catania Astrophysical Observatory at a resolution R = 14 000, we show that line-depth ratios can be effectively used to determine spot temperatures of active binary systems. Using, on average, ten line pairs, selected in the 6100-6300 Angstrom wavelength range, with the help of observations of 30 main sequence and giant stars, we have derived a calibration relation of line-depth ratios (LDR) in an absolute temperature scale, taking into account the gravity effect in the calibration relation. Single LDRs converted to temperature through the calibration relations have led to clear rotational modulation of the average surface temperature with amplitudes of 177 K, 119 K, and 127 K for VY Ari, IM Peg and HK Lac, with average estimated errors of about 10 K. We show that the observed temperature variation amplitude allows us to define a minimum fractional spotted area coverage as a function of spot-photosphere temperature ratio. Adopting the maximum value of average temperature, determined from the LDRs, as that of the unspotted photosphere, we computed the average spot temperature corresponding to the minimum spot coverage. Although not univocally constrained, the temperature difference (DeltaT = T-ph - T-sp) obtained for the three systems, DeltaT = 890 K for VY Ari, DeltaT = 750 K for IM Peg, and DeltaT = 810 K for HK Lac, are in good agreement with values derived with other methods.