N f Ic f f df

The upper limit of Ic(f) in (6.4.10), C2, is not known but is found by trial and error. The computation of the quantities on the left-hand side of (6.4.7) and (6.4.9) is to be done so as to achieve the least-squares minima of the two sets of data of | O - C |, here defined as:

| o - C| = £ Wj {[1 - iob2s(0j)] - [1 - lu(0;)]} , (6.4.12)

where the weight of a normal point, wj = k/ej; k is arbitrary and ej is the standard deviation of the jth normal point. Computer codes to accomplish the fitting and extraction of the unknowns are described in Cherepashchuk (1973), Cherepashchuk et al. (1973), and Goncharsky et al. (1985). The steps are done as follows:

• the condition cos i < rp is established;

• the quantities rp and i are assumed, and (6.4.9) is solved for Ic(f, rp, i) and the corresponding values of | O - C |rp,;; and

• substitution of Ic(f, rp, i) in (6.4.8) and the solution of (6.4.7), which then provides the function Ip(f, rp, i) and corresponding values of |O - C|rp,;.

The absolute minima of the two sets of (6.4.12) yield the parameters rp, i and the functions Ic (f) and Ip (f). These two functions are used to determine physical characteristics of the WN5 component of V444 Cygni such as the temperature and absorption coefficient over the disk and core radius, r0. The data which were analyzed were taken in a rectified light curve in a 7.5 nm passband centered at X = 424.4 nm in the continuum. The results by Cherepashchuk (1975) are rp = 0.25 ± 0.02, i = 78° ± 1°, Lwr = 0.197 ± 0.03, 2.2 < — < 2.6.

Cherepashchuk notes that the relatively small value of r0 suggests that the WN5 component is the helium remnant core of a star formed as a result of extensive mass exchange in an interacting, massive binary.

Treatment of more complicated cases is illustrated by the solution of the inverse problem for SS433, an interesting, interacting X-ray binary with relativistic jets. Extensive fitting of a model with a thick, precessing accretion disk with an oblate spheroid shape to an extensive body of optical (V-passband) data consisting of 10 light curves representing a range of precessional phases failed to satisfy the level of significance (1% by the accuracy and precision of the data). The results, described in detail by Antokhina & Cherepashchuk (1987) and in Goncharsky et al. (1991), are as follows: The "normal" star fills its Roche lobe; and the equatorial radius of the accretion disk is equal to the maximum radius of the compact object's Roche lobe. The choice of the optimum mass ratio was uncoupled to the temperature of the "normal" star. The model for q > 0.25 is shown in Fig. 6.5 along with a still more complicated model with q = 0.20 (lower three figures).

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