5.1 Temperature and filling factor

Observed amplitudes of the optical brightness modulation imply that a large fraction of the stellar photosphere is covered by cool starspots. The largest ever observed light-curve amplitude $DV = 0.65 mag$ of a spotted star was reported for the weak-line T Tauri type star V410 Tau (Strassmeier et al., 1997 ). Two RS CVn-type stars HD 12545 and II Peg have been observed at the largest $DV = 0.63 mag$ by Strassmeier (1999

) and Tas and Evren (2000 ), respectively. Such big amplitudes in brightness variations are accompanied by large in-phase variations of a colour, suggesting the presence of cool spotted areas covering up to 20% of the entire stellar surface or about 40% of the stellar disk (Figure 6

Figure 6:

Doppler image of the RS CVn type star HD 12545 at the time of its largest amplitude of brightness variations. From Strassmeier (1999

Our current knowledge on starspot temperatures is based on measurements obtained from simultaneous modelling of brightness and colour variations, Doppler imaging results, modelling of molecular bands and atomic line-depth ratios, the latter being the most accurate method. A representative sample of starspot temperatures for active dwarfs, giants and subgiants is collected in Table 5 and plotted in Figure 7

. As seen from the plot, there is a clear tendency for spots to be more contrasting with respect to the photosphere in hotter stars: the temperature difference between spots and the photosphere decreases from about $2000 K$ in G0 stars to $200 K$ in M4 stars. There seems to be no difference in this property between active dwarfs and giants, at least for G-K stars, that implies the nature of starspots to be the same in all active stars. Also a weak-line T Tauri star V410 Tau seems to follow the relation. The only exception found is a young solar analogue EK Dra whose starspot temperature, estimated from light-curve modelling and Doppler imaging, significantly deviates from the relation. However, the value obtained from molecular band modelling fits the sequence quite well (O’Neal et al., 2004

Figure 7:

Spot temperature contrast with respect to the photospheric temperature in active giants (squares) and dwarfs (circles). Thin lines connect symbols referring to the same star. The thick solid line is a second order polynomial fit to the data excluding EK Dra. Dots in circles indicate solar umbra ( $DT = 1700 K$ ) and penumbra ( $DT = 750 K$ ) (based on data in Table 5).

High filling factors, up to 50% of the stellar disk, have been determined by O’Neal et al. (1996

, 1998

) from modelling molecular bands observed in the spectra of spotted stars (see Section 4.4). For instance, for the very active RS CVn-type star II Peg they derived a spot temperature of about $3500 K$ and a filling factor varying between 43% and 55%. Such large spot filling factors were found also for other active stars (O’Neal et al., 1996 , 2004

). They apparently contradict to Doppler imaging results. This suggests that Doppler images may not easily reveal the absolute spot coverage and, perhaps, leave unnoticed non-modulating and unresolved spots. An excess of the absorption in molecular bands implies that even at the maximum brightness stellar photospheres have a substantial spot occupancy. Note, however, that molecular band modelling is rather sensitive to the assumed photosphere temperature and chemical composition as well as to Doppler shifts accross the spots which may affect the spot filling factor (Berdyugina, 2002

; O’Neal et al., 2004

Large spot areas and spot temperature contrasts recovered on active stars suggest that photometric and spectroscopic variability of these stars is dominated by the starspot umbra. Low temperature contrast of spots and small spot filling factors in M dwarfs, as well as contradictory results for EK Dra obtained by different methods, can be due to a decreasing of individual spot sizes and, thus, increasing relative contribution from the spot penumbra. For instance, the spot contrast obtained from Doppler imaging and light-curve modelling for EK Dra corresponds to the temperature contrast of the sunspot penumbra. Accordingly, we should expect that active late F-type stars possess spots with dominating penumbra and, thus, show lower contrast spots. As in the case of EK Dra, observations in molecular bands are more reliable for detection of starspot umbra.