7 The mutual orbit of both binaries

From our detailed line blend fitting we found that the systemic velocities of both binaries changed on a time base of approximately 17 years by -11 and +36 kms^-1 for systems A and B, respectively. The errors are difficult to estimate due to reasons discussed above, but the opposite sense of the changes supports the idea that it is due to the mutual orbital motion of the two binary constituents of the multiple system. MC noted that within three years no change was recognized; we therefore assume that the radial velocity change found by us has been monotonic in time, and its effect can be measured only on such a long time base. The amount of velocity changes strongly contradict the idea that masses of both binaries are nearly equal. But of course one should be aware that such conclusions depend on the essentially unknown uncertainty in determination of systemic velocities.

Therefore, only rough estimates for parameters of the mutual orbit can be given. The period might be of the order of several decades, not necessarily 25 years or shorter, as suggested by LMS. The $\gamma$velocity by Feast et al. (1956) does not contradict a period of about 50 years. Then the semi-axis might be larger than previously assumed, perhaps about 50 AU, and the hope that systems A and B can be separated by means of speckle interferometry increases. Note that Mason et al. (1998) made an attempt to resolve the system in 1994.31, and gave an upper limit for the separation of 0.30 mas.

7.1 Expected light-time effect

Caused by the orbital motion of both binaries around the common mass center, the light-time effect in times of eclipse minima of system B should be observable (see, e.g., Lorenz et al. 1998). Its semi-amplitude in days is

$$A = a_{\rm B} \sin i \cdot \sqrt {1 -{\rm e}^2 \cos^2 \omega} /173.15,$$

where $a_{\rm B}$ is the semimajor axis of the orbit of the binary B around the common mass center in AU, and e and $\omega$ are the elements of this orbit. The published times of minima are collected in Table 4. Values of O-C are calculated according to the ephemeris (Mayer et al. 1998)

$${\rm Prim.\, Min. = hel~JD}\,\,2441033.06 + 5\hbox{$.\!\!^{\rm d}$ }99857 \cdot E$$ (2)

and plotted in Fig. 7. The curves in this graph were calculated mainly in order to demonstrate that good minimum timing is appropriate to find the orbital parameters. Since we are lacking a sufficient data sample to extract more precise information, circular orbits were assumed, and two trial curves were calculated for the following parameters: semi-amplitude $A = 0\hbox{$.\!\!^{\rm d}$ }20$, and;
1. $P_{\rm mutual}$ = 40 years, time of conjunction JD 2449200;
2. $P_{\rm mutual}$ = 50 years, time of conjunction JD 2450000.
In both cases, the linear ephemeris was optimized to fit the observations. Clearly, also shorter as well as longer periods would be compatible with the data.

 

 

Table 4: The published times of minima for QZ Car

HJD-2400000	m.e.	Epoch	O-C	Source
41033.06	0.200	0.0	0.000	Walker & Marino 1972
42472.64	0.100	240.0	-0.077	Moffat 1977
43192.40	0.200	360.0	-0.145	Morrison & Conti 1980
48501.160	0.030	1245.0	-0.120	HIPPARCOS
48687.160	0.020	1276.0	-0.075	Mayer et al. 1992
49422.039	0.005	1398.5	-0.021	Mayer et al. 1998

The mutual orbit radial velocities are connected with the light-time effect parameters as $K_{\rm B} = 5156\,A/P_{\rm mutual}$, where $K_{\rm B}$ is in kms^-1 and $P_{\rm mutual}$ in years. In our examples, the semi-amplitudes are 25.8 and 20.6 kms^-1, respectively. The radial velocity curve of the better observable component A1 should be shifted in phase by +90$^\circ$ against the O-C curve. It appears that the trend of the $\gamma$ velocities as given by the Feast et al. (1956), MC and in this paper does not contradict this expectation.

Figure 7: O-C graph of times of minima published for QZ Car. The full line represents the light-time effect with an assumed period of 40 years, the dashed line with a period of 50 years (see text)