5 Conclusions

From the new light and colour curves obtained in 1998 and 1999, data sets given in Paper I and H$\alpha$spectroscopy made in 1999, the following conclusions for MM Her have been obtained:
(1) MM Her has at least two separate spots or spot groups in 1998 and 1999. The effect of the first spot that causes more light loss outside eclipses is seen at phase 0.10, while the effect of the other spot appears at phase 0.62 in 1998. Similar effects on the 1999 light curve are seen at phases 0.05 and 0.43, respectively. The amplitudes of the light variations outside eclipse are about  $0\hbox{$.\!\!^{\rm m}$ }04$ and  $0\hbox{$.\!\!^{\rm m}$ }05$ in 1998 and 1999, respectively, and are the smallest we have obtained so far.
(2) The displacements of the phases of the second spot obtained in 1998 and 1999 have improved the migration period of Spot 2, leading to a migration period of 5.9 years, very close to that of Spot 1. Both spot groups migrate toward smaller orbital phases, i.e. rotate faster than the co-rotation period. In the solar analogy, with rotational angular velocity increasing toward the equator, we suggest that the co-rotation occurs at intermediate latitudes and that spot groups are closer to the equator than the co-rotation latitudes. This is the case, for example, for RS CVn, as shown by the detailed mapping analysis which gives average spot latitudes moving from 25 $\hbox{$^\circ$ }$ in the period 1963-1984 to 10 $\hbox{$^\circ$ }$ in the period 1988-1993, with the spots always rotating faster than the orbital period (Rodonò et al. 1995).
(3) When the spots located on the cooler component are seen at phase $\approx$0.50, the amplitude of the light variation is larger than in other phases. This effect is attributed to a greater concentration of spots when the active longitude is on the hemisphere facing the companion. Similar results have been found for AR Lac (Lanza et al. 1998) and II Peg (Berdyugina et al. 1999). One can conclude that the tidal effect seems to enhance the magnetic flux tube emergence and therefore the spot formation.
(4) MM Her certainly shows H$\alpha$ emission associated only with the K0 IV component. No clear rotational modulation is seen, but the average EW emission values at the first quadrature are slightly smaller than those at the second quadrature. This small asymmetry is in the same sense as the light variation.

We have analyzed various causes which may be responsible for such an asymmetry, like faculae on the bright hemisphere or absorbing matter on the trailing hemisphere of the K0 IV component, but the effect is so marginal and close to the size of the observational errors that we are inclined to think that present MM Her data do not show a definite rotational modulation in the H$\alpha$chromospheric emission.

Since MM Her is rather an active star, the absence of H$\alpha$ modulation may be a temporary situation, as observed in other RS CVn systems, for example UX Ari (Catalano et al. 2000).
(5) New radial velocity measurements and orbital parameters have been obtained. A new solution for the system elements leads to a mass difference between the two components that is a little larger than that found by previous authors, but in better agreement with the spectral types of the two stars and their evolutionary stage. The barycentric velocity $\gamma$ of the system seems to remain constant in time, within the errors.

Acknowledgements

G. Tas would like to thank the Director Prof. M. Rodonò and the staff of Catania Astrophysical Observatory (Mount Etna) for allocation of telescope time and kind hospitality. This work was supported by Ege University Research Fund (Project No. 99/FEN/014). G. Tas is also grateful to the Scientific and Technical Resource Council of Turkey; without their financial support she could not gather the spectroscopic data. This work has been also supported by the Italian Ministero dell' Università e della Ricerca Scientifica e Tecnologica and by the Regione Sicilia who are gratefully acknowledged. The authors are indepted to the anonymous referee, who made valuable comments on the paper.