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4 Conclusions and discussions

FG Hya is an important and interesting binary, mostly because of its variable light curve and total eclipses. The totality of its eclipses allows it to have a photometrical determined mass ratio that is believable. In the present solutions, the obtained mass ratio of FG Hya is 0.1306 for the observations in 1962 (Binnendijk 1963), 0.1273 for the observations in 1882 (Yang et al. 1991) and 0.1289 for the present observations, respectively. The obtained values of the mass ratio of this binary are in agreement with each other and close to the derived one from the radial velocity curve (Lu et al. 1999). The shape of the light curves of FG Hya has displayed considerable changes. From Fig. 4 and Table 3 one can see that the difference of the eclipsing depth between the primary eclipse and the secondary one considerably changes. From 1955 to 1985 the difference of the eclipsing depth increased yearly, but the present light curve seems to be similar in shape to that obtained by Smith in 1955. The variability of the light curve is probably due to varying starspots on one or probably both of the components because of the late spectral type of this system. In our solutions, spot modeling was not tried because of some uncertainty of spot parameters derived by the present model. What this system really needs is more complete coverage throughout a season, i.e., several light curves in one season, each one obtained over a week or two, in order to study monthly changes in the light curves, and then model each light curve with spots. If enough light curves are accumulated with standardized methods and equipment, a fiducial "spotless" curve should emerge (the upper envelope of all of the phased light curves taken, say, over a decade). This system is important for evolutionary reasons as well. Its small mass ratio, over-contact nature and decreasing period would seem to indicate that it may be well on its way to coalescing. According to Maceroni & van't Veer (1996), the mass of the secondary component of the system is only $0.15~m_{\odot}$and the over-contact degree of the system is close to 80% which is in agreement with the present solution. Therefore, the secondary component could be unstable in both thermodynamics and dynamics and the instability of the secondary component could be responsible for the perplexing changes in both the light curve and the orbital period of the system. However, the light curve changes of FG Hya are more likely to be caused by varying starspots on one or probably both of the components because of their late-type spectra.

None the less, there are 9 W UMa type binaries with a smaller mass ratio than 0.2 (V677 Cen, FG Hya, XY Boo, AW UMa, TV Mus, RR Cen, MW Pav, $\epsilon$ CrA and EF Dra). These systems may be specifically important for studying structure and evolution of a binary. The evolution of these systems is controlled by the primary but the radius of the secondary is controlled by its contact with the primary. The small mass secondary has the large radius not resulting from any evolution of reactions in the core of the secondary and then it could be extremely heated by radiation from the primary. In addition, the secondary of these systems also receives energy through energy transfer from the primary to the secondary. Therefore, the structure and evolution of the secondary of these binaries should be very interesting. Some perplexing phenomena for these binaries could be observed. A similar binary, for example, AW UMa is an A-subtype W UMa binary with 0.080 of a mass ratio. Besides the variable light curve and decreasing period like that of FG Hya, secondary minima of AW UMa are systematically delayed with respect to the expected position in phase 0.5 given by primary minima (Pribulla et al. 1999). In any case, it may be interesting systematically to observe this group of the contact systems with a small mass ratio.

Acknowledgements
The authors would like to thank Dr. S. Qian and Dr. F. Li for their assistance in the observations and thank the unknown referee for his useful comments and improvement of the authors' English. The authors would also like to express their gratitude for the support from the Chinese National Science Foundation Committee and the Chinese Academy of Sciences.


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