4.4 Molecular bands modelling

Molecular lines provide evidence of cool spots on the surfaces of active stars. If the effective temperature of the stellar photosphere is high enough, molecular lines can only be formed in cool starspots. The first detection of molecular bands from starspots was reported by Vogt (1979 ) for a star whose spectral type K2 was not compatible with the presence of TiO and VO bands. From the relative strengths and overall appearance of the molecular features, an equivalent spectral type of the spot spectrum was estimated as late as M6. A phase-dependent variation in the strength of the TiO band was detected by Huenemoerder et al. (1989 ), with TiO being strongest at the photometric minimum. This confirmed that the photometric modulation is indeed caused by cool spots. Moreover, a comparison of photometric variations with TiO band strengths provided reliable estimates of unspotted stellar magnitudes (Berdyugina et al., 1998b , 1999b ).

A technique for determining spot filling factors and temperatures from molecular band modelling (MBM) was suggested by Huenemoerder and Ramsey (1987 ) and further developed by Neff et al. (1995 ) and O’Neal et al. (1996 ). They modelled the observed spectrum by combining spectra of suitable standard stars of different effective temperatures weighted by spot filling factor and continuum surface flux ratio. For instance, observations in two TiO bands of different temperature sensitivity, at $7055 ºA$ and $8860 ºA$ , were combined to estimate the area and the temperature of spots.

Since TiO lines are only formed in starspots on the surfaces of G-K giants and subgiants, polarisation observations in these lines can provide measurements of magnetic fields directly in spatially unresolved spots. As shown in Figure 5 , the TiO lines at $7055 ºA$ are rather strongly magnetically sensitive, having effective Landé factors up to 1 (Berdyugina and Solanki, 2002 ; Berdyugina et al., 2003 ). The wavelength separation between rotational lines in the band is small and lines of low rotational numbers (larger splitting) almost coincide with those of high numbers (smaller splitting) in the band head. Nonetheless, a clear Stokes $V$ signal should be measured from starspots Berdyugina (2002 ).

Figure 5:

Calculated (solid line) and observed (dashed line) Stokes $V$ profile for the TiO $g$ (0,0)R $3$ band head in a sunspot. The field strength is $3 kG$ and the filling factor is 0.75 for an angle between the magnetic vector and the line of sight of $o 0$ . Vertical dashes indicate positions of lines included in the spectral synthesis. From Berdyugina (2002

An excess of the absorption in the infrared OH lines at $1.5mm$ due to starspots has been detected by O’Neal and Neff (1997 ) and O’Neal et al. (2001

). Since OH lines can be observed at higher temperature than TiO, starting from $5000 K$ and below, they can be used for studying starspots on hotter stars. Otherwise, they are contaminated by the photospheric contribution, which should be carefully taken into account. On the other hand, OH lines provide a greater temperature range over which starspots can be detected through molecular absorption features.