Cherepashchuks Model

Et ex oriente lux (And from the East, Light)

Cherepashchuk's approach is widely used in Russia, and we might even apply the term "Russian school" to those who use the light curve modeling procedures described by Cherepashchuk. Since the work by Cherepashchuk (1966), there is a strong focus on EBs with extended atmospheres10 such as the Wolf-Rayet binary V444 Cygni [Cherepashchuk (1975), Cherepashchuk & Khaliullin (1976)] and X-ray binaries. The light curve models are mostly spherical models with enhanced features for atmospheric eclipses, which are interpreted to include disks. The least-squares problem is solved with great attention to the ill-posed character of the general light curve analysis problem (Cherepashchuk et al. 1967). The methods are based on regularization algorithms by Tikhonov (1963a, b). They are more recently described in Tikhonov & Arsenin (1979). An English translation outlining the method is given in Tsesevich (1973, pp. 237-244). There is a strong mathematical background in the Russian school on ill-posed problems in the sense of Hadamard, and the reader should not be surprised to find Fredholm integral equations of the first kind involved in the light curve analysis as, for example, in Cherepashchuk etal. (1975).

The models describe semi-transparent emitting disks surrounded by nonemis-sive atmospheres. In the simplest case, the stars are uniform, circular disks without reflection effect enhancements. In the case of extended atmospheres, a distinction is made between the radii of the luminous disks and those of the larger absorbing disks. In Cherepashchuk's notation, in which components 1 and 2 are identified with the notation for the distances f and p, respectively, from the disk centers, the luminosity of the system is rrfc r rpc

L = Lf + Lp = 2n / Ic(f)fdf + 2n / Ic(p)pdp = 1, (6.4.1)

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