Photometric modelling of starspots - I. A Barnes-Evans-like surface brightness-colour relation using (I-c-K)

In the first part of this work, the empirical correlation of stellar surface brightness F-V with (I-c-K) broad-band colour is investigated by using a sample of stars cooler than the Sun. A bilinear correlation is found to represent well the brightness of G, K and M giant stars. The change in slope occurs at (I-c - K) similar to 2.1 or at about the transition from K to M spectral types. The same relationship is also investigated for dwarf stars and found to be distinctly different from that of the giants. The dwarf star correlation differs by an average of -0.4 in (I-c - K) or by a maximum in F-V of similar to-0.1, positioning it below that of the giants, with both trends tending towards convergence for the hotter stars in our sample. The flux distribution derived from the F-V - (I-c - K) relationship for the giant stars, together with that derived from an F-V - (V - K) relationship and the blackbody flux distribution, is then utilized to compute synthetic light V and colour (V - R)(c), (V - I)(c) and (V - K) curves of cool spotted stars. We investigate the effects on the amplitudes of the curves by using these F-V-colour relations and by assuming the effective gravity of the spots to be lower than the gravity of the unspotted photosphere. We find that the amplitudes produced by using the F-V-(I-c - K) relationship are larger than those produced by the other two brightness correlations, meaning smaller and/or warmer spots.