Temperature and size of starspots from line depth ratios

It has been recently proved that line-depth ratios (LDR) are a powerful tool for temperature discrimination, able to resolve differences ≤10 K.With the help of such diagnostics it has been possible to detect long-term variations with time scales of several years, ascribed to activity cycles (e.g. Gray et al. 1996a, 1996b). In very few cases, rotational modulation due to surface inhomogeneities has been observed (Toner & Gray 1988). In this work, we have made a test of this method on three slowly-rotating active binaries of RS CVn type by means of observations accomplished at Catania Astrophysical Observatory at a resolution R = 14 000 with the aim to search for and analyze rotational modulation of photospheric temperature.We suppose that in these stars the passage of dark spots produces modulation of the center-line depth of different amount in lines of different sensitivity to temperature, that cannot be analyzed by means of the Doppler-imaging technique. It is instead useful for fast-rotating active stars where cool spots of a few tenths of the stellar surface give rise to bumps in the line profiles. In order to determine spot temperatures of active binary systems, we have converted single LDRs to temperature through calibration relations. A sharp rotational modulation of the average surface temperature with amplitudes of 177 K, 119 K, and 127K for VY Ari, IM Peg and HK Lac, respectively, has been detected with errors of about 10K. Such variations are almost perfectly correlated to the simultaneous V light curves, lower temperature corresponding to lower luminosity. We show that, on the basis of the amplitudes and maximum observed values of temperature and brightness, it is possible to define, in an univocal way, the temperature and the fractional spotted area by means of an analytical approach.