4. Photometric light-curves and their analysis
4.1. Normal points and Fourier analysis of the mean light-curves
All our individual observations of AW UMa were used to construct 250 normal points of the mean light-curve (henceforth LC) in each passband. Each normal point is the mean value of brightness in ranges of 0.004 of the orbital phase and was calculated using 12 individual observations in average. The numbers of individual points coming into one normal point were used as weights. The mean UBV LCs were used for a Fourier analysis. The resulting Fourier coefficients are given in Table 4.
Table 4. Fourier coefficients of the mean light-curves
Due to the fact that AW UMa is an A-type contact binary with a slightly hotter (and more massive) primary, the coefficient is negative in all passbands. As , the half amplitude of the light changes is nearly the same in all passbands (as indicated by A2). The coefficient , reflecting the O'Connell effect, has its largest absolute value in U. As it is positive, the maximum I is somewhat brighter. There is no significant O'Connell effect in B and V. Comparison of the absolute values of coefficients shows that all types of asymmetries of the LC increase from V to U.
The rough estimate of the main photometric elements from Fourier coefficients fails in systems with 0.2 (Rucinski, 1973). As this is the case of AW UMa, we have not made this estimate.
4.2. Photometric elements
The UBV LCs were analyzed using the synthetic LCs and the differential corrections code developed by Wilson & Devinney (1971) (W&D). Particular numbers of individual points coming into one normal point were used as weights. Mode 3 of the W&D code was employed assuming synchronous rotation and blackbody radiation. We have assumed = 7175 K and solved all LCs simultaneously. The input parameters were taken from Hrivnak (1982). The differential corrections code was run until the output corrections were smaller than the probable errors of the elements.
The LC analysis of contact systems is complicated by strong correlations between some elements (see Wilson & Biermann, 1976). Moreover, a LC solution is usually insensitive to bolometric albedo and, to a smaller extent to gravity and limb darkening. Our solution of the LC of AW UMa was aimed at detection of the third light which could be ascribed to a possible third component (see Sect. 7). In previous studies (Hrivnak, 1982; Mochnacki & Doughty, 1972; Wilson & Devinney, 1973) the third light was set to zero. In solution 1 (see Table 5) we have fixed several parameters () from the study of Hrivnak (1982). The limb darkening coefficients () were taken from Grygar et al. (1972). The range of photometric and spectroscopic ratios found in previous studies varies from 0.0716 (Wilson & Devinney) to 0.08 (Mauder, 1972) and from 0.07 (McLean, 1981) to 0.086 (this paper) respectively. Due to problems with convergence of solution 1, we have held the mass ratio fixed at values from 0.071 to 0.082 (with the step of 0.001). For the third light was negative in the V filter, so these unphysical solutions were omitted in further discussion. For the positive third light in all passbands increased with q. The weighted sum of squares reached a minimum for , but varied in other solutions only within a few%. The solution with fixed = 0 led to q = 0.071.
Table 5. Photometric elements of AW UMa and their probable errors . Parameters not adjusted in the first solution were denoted by a superscript "a".
We have also tried to adjust all parameters (except ). Although the fit of the LC is better, the resulting values of differ from the theoretical values. On the other hand, the derived value of is closer to the spectroscopic mass ratio found from the Toledo spectra (see Sect. 6).
The normal points as well as the LC from solution 2 are depicted in Fig. 3. Although the fits of the B and V LCs are quite good, there is a significant difference between the fit and the mean U LC around the maximum II. Furthemore, there are difficulties with exact fitting of the minima. A non-uniform distribution of the temperature on the surface of the components, caused by spot(s) as well as the presence of circumstellar matter can be responsible for these differences. Since Maceroni & van't Veer (1993) demonstrated that the determination of the position of spots is not unique, we have not tried to improve the solutions by spots.
The most interesting result of our analysis is the detection of the third light, which increases from V to U (solution 2). It is hard to know if the derived values of L3 tell us something physical about the system, or if they are parameters which adjusted to fit some of the complications in the LCs. In Sect. 7 we derived the mass of the third body as = (0.850.13) M. If it is a main-sequence star, its luminosity has to be L3 = 0.0760.040 L1 (L , Allen, 1976), with the maximum of energy distribution in V, which is not observed. The derived energy distribution is more compatible with the presence of a white dwarf in the system and/or of a hot polar region (not being eclipsed) on the contact binary.
In further calculations we have adopted and from our LC solutions.
© European Southern Observatory (ESO) 1999
Online publication: April 12, 1999