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Astron. Astrophys. 345, 137-148 (1999)

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7. Masses of the contact binary and the third component in the system

The systemic velocity of AW UMa determined from the Ondejov spectra does not agree with the values found from the Toledo spectra and there are also differences in its determination among other authors. We will go on to show briefly the evidence for a third body, and hereafter [FORMULA] and [FORMULA] designate the velocities of the mass centres of the binary and triple system, respectively.

McLean (see Rensing et al., 1985) changed its original value [FORMULA] =(-17[FORMULA]7) km s-1 (McLean, 1981) to [FORMULA] = (-9[FORMULA]7) km s-1 (McLean, 1983). Rucinski (1992) excluded four determinations of the RV to reduce the discrepancy in systemic velocity with previous determinations.

We reanalyzed all the original data using the ephemerides (1)-(3). The correction of the phases for the McLean's (1981) data was as large as 10% of the orbital period. The original and the new values of systemic velocities [FORMULA] and amplitudes of the RV curve are given in Table 7.


Table 7. New determination of the spectroscopic elements of AW UMa from published data
* 1988 observations, ** 1989 observations

To find out whether the differences in systemic velocity of binary are real or caused only by the scatter of observations, we have applied zero-point shifts to all available RVs of AW UMa. The individual RVs of the primary component before and after the correction for [FORMULA] are shown in Fig. 9. The sum of squares of residuals for the original data (70287 km2 s-2) is more than three times larger than that for the corrected data (19642 km2 s-2).

[FIGURE] Fig. 9. Radial velocities of the primary component of AW UMa before (top ) and after (bottom ) correction for [FORMULA]

This result as well as the [FORMULA] study indicate that the variations in [FORMULA] are real. We interpret them as evidence for the presence of the third component in the system. It is interesting to note, however, that when previous investigators observed the system over two consecutive seasons, they measured the same [FORMULA] each season (Rensing et al. 1985, Rucinski 1992). A similar effect is seen in our two Toledo observations. One might alternatively conclude that the variations in [FORMULA] are due to systematic effects between different telescopes rather than to a third body. However, systematic effects seem to be ruled out by the use of radial velocity standard stars (except for our Toledo observations). The agreement in the values of [FORMULA] in observations of successive seasons is due to the fact that the period of the third body happens to be comparable to the one-year observing interval.

7.1. New spectroscopic elements of the contact binary

Altogether we have 149 determinations of the RV at our disposal. These data, corrected for particular [FORMULA] and weighted to account for the different qualities of the spectroscopic observations, were used to obtain a more accurate spectroscopic orbit of the contact system. The new spectroscopic elements are given in Fig. 9 (bottom). Adopting a photometric mass ratio q = 0.08 and an inclination angle i = 78.3o, we derive the masses of the components of the contact binary as [FORMULA] = (1.79[FORMULA]0.14) M[FORMULA] and [FORMULA] = (0.143[FORMULA]0.011) M[FORMULA].

One must be aware, however, that the set of RVs of the primary component is quite inhomogeneous due to the different methods used for finding RVs: cross-correlation (McLean, 1981), synthetised profile (Rensing et al., 1985), broadening function with model profiles (Rucinski, 1992) and line measurements (Paczynski, 1964; this paper). Since some methods do not take into account the secondary component, the RV of the primary is underestimated because of the line profile blending with the secondary (Paczynski,1964; Rensing et al., 1985 and this paper). It is important to note that proximity effects in contact binaries tend to make the light center closer to the companion star than is the center of mass and thus tends to underestimate [FORMULA] (Hrivnak, 1988). Rensing et al. (1985), however, state that the distortion effects are not important for AW UMa.

7.2. Parameters of the third component

The third component in the system causes not only changes in the systemic velocity, but also a light-time effect, which can be found in the residuals from the broken-line fit (two sudden period changes). Since the residuals for the third case nearly coincide, henceforth we will assume the first case of period change.

We have tried to find a solution taking into account both effects simultaneously. The main problem is the large number of "free" parameters. Some of them, however, are not independent. If we compare the formulae for the light-time effect (Irwin, 1959):


and for [FORMULA] (e.g. Binnendijk, 1960):


we get the amplitudes as follows:


Excluding of [FORMULA] from the above equations yields:


For [FORMULA] and P in days and [FORMULA] in km s-1 we obtain:


Using the equation (10) we constrained the range of possible periods of the third body. Thereafter we have found the value of period of the third body by a period analysis of the systemic velocity and light-time curves separately.

The amplitude of [FORMULA] residuals is [FORMULA] days ([FORMULA] = 0.0017). The amplitude of the systemic velocity variations [FORMULA] is [FORMULA] = 12.5 km s-1. It is easy to find that for a reasonable range of eccentricities 0[FORMULA]0.9 the orbital period of the third component is in the range 380-880 days. The most significant periods in this range found by the Fourier analysis in systemic velocities [FORMULA] and [FORMULA] residuals from the broken-line fit are 398[FORMULA]5 days and 402[FORMULA]8 days, respectively. The [FORMULA] residuals from the possible fourth body fit provide 407[FORMULA]8 days periodicity. The period of 400 days was used as the initial value for our differential corrections code, which solves the light-time effect and systemic velocity curve simultaneously. In our solution we have put weight 10 to the set of systemic velocities [FORMULA] and 1 to the set of [FORMULA] data since systemic velocities were usually determined from many RV measurements. Individual systemic velocities were weighted according to their errors (for the fitting we have also used two estimates of [FORMULA] from two Toledo spectra).

We have found that the best fit for the third component corresponds to an orbital period [FORMULA] = 398 days (Fig. 10). The systemic velocity of the triple system is [FORMULA] -15.6 km s-1. It is important to note that Rensing et al. (1985) and Rucinski (1992) observed AW UMa in two intervals approximately 400 and 380 days apart, respectively. This is the reason why they did not find a change of the systemic velocity in their spectroscopic data.

[FIGURE] Fig. 10. Systemic velocities and their best fit for a period of 398 days

Although the [FORMULA] fit is perfect, the corresponding fit in [FORMULA] diagram, due to the large scatter of data, is not as good. Hrivnak (1982) estimated that the asymmetry of the LC can cause deviations as large as 0.004 days while the amplitude of the light-time effect caused by the presence of the third body is only about 0.00258 days.

The minimum mass of the third component determined from the mass function and the mass of the contact system is [FORMULA] = (0.85[FORMULA]0.13) M[FORMULA].

The energy distribution of the third light suggests that the third component is a white dwarf (see Sect. 4.2). Therefore it is not expected to be seen on our high dispersion spectra from Toledo. Nevertheless, due to the problems with the exact photometric solution, we cannot exclude the possibility that the third component is a main sequence star. In such a case the ratio of its luminosity and that of the primary component is 0.076[FORMULA]0.040. Thus it could be detected on high-dispersion spectra. The expected range of its RVs is -16 to 58 km s-1, so the lines of the third component are always located in the Doppler core of the primary component lines. This complicates the spectroscopic detection of the third component. This component can cause not only a shift of the line center (affecting [FORMULA] and [FORMULA]) but also the narrowing of the composite line profile. Indeed Mochnacki & Doughty (1972) found the observed profile of H[FORMULA] line to be narrower than the synthetic one.

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© European Southern Observatory (ESO) 1999

Online publication: April 12, 1999