## 4. Photometric light-curves and their analysis## 4.1. Normal points and Fourier analysis of the mean light-curvesAll 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.
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
A 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 elementsThe 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
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 L In further calculations we have adopted and from our LC solutions. © European Southern Observatory (ESO) 1999 Online publication: April 12, 1999 |