2.1 Red dwarfs and BY Dra phenomenon

Red dwarfs are main-sequence stars with the mass range from $0.08Mo .$ to $0.5 Mo .$ . The lower mass limit is the critical mass for hydrogen burning in the central cores of stars with solar abundances, while the upper limit corresponds to the spectral class M0. The radii of the red dwarfs span from $0.2R o .$ to about $0.6Ro .$ while their effective temperatures are in the range of $2500 K$ - $4000 K$ . Thus, red dwarf stars are cooler, smaller, and less massive than the Sun. Correspondingly their luminosities range from 0.1% to about 8% of the solar luminosity. They constitute, at least, 80% of the stellar population in the Galaxy.

Remarkable magnetic activity expressed in extremely strong optical flares was first recorded on UV Cet type stars, while periodic brightness variations were observed in binary systems of red dwarfs as distortions of light curves outside eclipses. Kron (1947 , 1952 ) suggested that they are large spots on the stellar surface that cause these distortions. Subsequent observations by Chugainov (1966 , 1971 ) confirmed this hypothesis. Chugainov also showed that spots are much cooler than the undisturbed photosphere and can cover up to 10% of the stellar surface. A spot model for light curve variations developed by Bopp and Evans (1973 ) supported the previous findings. This appeared to be extraordinary compared to the Sun. The star with such spottedness, BY Dra, became a prototype of a group of stars exhibiting similar behaviour. Also, this type of variability is often called the BY Dra phenomenon. It is common among binaries with G-K dwarfs as well.

A typical light curve of such a star has a near-sinusoidal shape with an amplitude about $0.1 mag$ . In addition to the starspot activity, these stars possess powerful chromospheres and coronae, whose activity is exhibited in strong UV, X-ray, and radio emissions and flares.