A&A 366, 558-564 (2001)
DOI: 10.1051/0004-6361:20000228
P. Mayer1 - R. Lorenz2 - H. Drechsel2 - A. Abseim1
1 - Astronomical Institute, Charles University,
V Holesovickách 2, 180 00 Praha 8, Czech
Republic
2 - Dr. Remeis-Sternwarte, Astronomisches Institut der
Universität Erlangen-Nürnberg, Sternwartstraße 7,
96049 Bamberg, Germany
Received 27 June 2000 / Accepted 7 November 2000
Abstract
We present an analysis of the early-type quadruple system QZ Car,
consisting of an eclipsing and a non-eclipsing binary. The
spectroscopic investigation is based on new high dispersion echelle and
CAT/CES spectra of H and He lines. The elements for the orbit of the
non-eclipsing pair could be refined. Lines of the brighter component of
the eclipsing binary were detected in near-quadrature spectra, while
signatures of the fainter component could be identified in only few
spectra. Lines of the primary component of the non-eclipsing pair and
of both components of the eclipsing pair were found to be variable in
position and strength; in particular, the He II 4686 emission
line of the brighter eclipsing component is strongly variable. An
ephemeris for the eclipsing binary QZ Car valid at present was derived
Prim. Min. = hel. JD
.
The
relative orbit of the two binary constituents of the multiple system is
discussed. In contrast to earlier investigations we found radial
velocity changes of the systemic velocities of both binaries, which
were used - together with an O-C analysis of the expected light-time
effect - to derive approximate parameters of the mutual orbit of the
two pairs. It is shown that this orbit and the distance to QZ Car can
be further refined by minima timing and interferometry.
Key words: binaries: eclipsing - binaries: spectroscopic - stars: early-type - stars: individual: QZ Car
Morrison & Conti (1980; hereafter MC) remarked that it would be probably wise to spend ones resources on studying a less complicated binary than QZ Car. Certainly this is true when one tries to add new entries to the table of accurate stellar masses and radii. However, QZ Car is an especially remarkable case. Note, e.g., that there is no other star of such late type with the spectral "(f)'' characteristics among stars listed by Conti et al. (1977). The most similar case is perhaps MY Ser of type O8(f), which is another multiple system, and equally difficult to study.
The system was also studied by Leung et al. (1979; hereafter LMS), who confirmed the spectroscopic results of Morrison & Conti (1979). The mass functions suggest that the eclipsing binary component with so far undetected lines is more massive than its binary companion; in the non-eclipsing pair, which has a longer period, the invisible component is several times less massive than the primary component, and therefore probably has very weak, unobservable lines. LMS solved the light curve by Walker and Marino and found a luminosity ratio close to 3:1 for the two binary components, so supporting the hope that the secondary lines might be discernible in high resolution spectra of high S/N. MC analyzed a larger sample of spectra than LMS and found more reliable elements of both binaries. To avoid confusion, we will denote the two binaries in the following in the same way as MC: the long-period binary is called system A (its visible component A1), and the eclipsing binary is referred to as system B (with the brighter, but less massive component B1, and companion B2).
Figure 1: V photometry phased according to ephemeris (1). Crosses - our data, open circles - Christie, triangles - Moffat, points - Walker & Marino | |
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An ephemeris for the eclipsing binary QZ Car valid at present was derived
using the more recent minima (see Table 4), which will be used for
the phasing of the eclipsing system B throughout this paper:
(1) |
Perhaps the best quality light curve by now was obtained by HIPPARCOS (ESA 1997), see Fig. 2. Even this curve is affected by a rather large scatter, which might be due to the close vicinity of similarly bright stars; also short-term intrinsic variability of the star itself could contribute to the photometric scattering. Note that the best fit between photometry in the V bandpass and photometry by HIPPARCOS is obtained for .
Figure 2: HIPPARCOS measurements phased according to ephemeris (1). Data of lower accuracy are plotted as opencircles | |
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In one night, two spectra were obtained in the H region (CAT 5.1 and 5.2 in Table 1; see Fig. 4 for CAT 5.2). These profiles confirm the presence of emission in the Balmer line, as already found by MC. The line is asymmetric - the red wing being less steep, with a peak emission of about 20% above continuum level at zero velocity. The spike at -10 kms-1 is probably due to the Carinae nebulae (MC give a nebular velocity of -27 kms-1). There is a P Cygni-type absorption component centered atabout -250 kms-1, which could be attributed to the expansion velocity of an envelope. On the red side the emission reaches about +500 kms-1. It is of course not possible to judge the nature and origin of the emission from only these two spectra.
Figure 3: Examples of profiles of the He I 4922 line. Labels near profiles give phases according to ephemeris (1); the step width between continuum levels is 10% of the normalized flux | |
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Figure 4: Profile of H line (spectrum CAT 5.2) | |
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As known from previous studies, the most prominent feature in the He I 4922 line profile corresponds to the primary component of the long-period binary (A1). In some spectra taken near quadratures of the short-period binary, it is apparent that lines of both stars are present. It is however also evident that all line components are changing their strengths with time or phase. The equivalent width of A1 lines is considerably larger than that of B1 and B2 lines, which makes the disentangling of spectral features a difficult task. We tried to use the KOREL code (Hadrava 1995) for this purpose. The line of star A1 was of course always dominant, and the orbit derived with the KOREL program had appropriate parameters. The short-period orbit is masked to such extent, that the automatic disentangling procedure was not able to extract its spectral features. Therefore, we tried to deconvolve the spectra by multiple Gaussian profile fitting (using MIDAS routines). The positions, depths and widths of the A1, B1 and B2 He I 4922 line components were iteratively optimized, while a fourth component in the blend was attributed to the O II 4925 line of star A1. In a paper on KX Vel (Mayer et al. 1997) we found that in this binary with a spectral type practically identical to A1 the equivalent width of the O II line equals approximately one sixth of the He I 4922 line. Therefore, we assumed the same relative strength for this line here too, and kept the ratio fixed at this value; for the two system B stars, we neglected any contribution of O II 4925 to the blend.
Being aware that automatic procedures can easily converge in local minima of the parameter space, we searched for a best fit solution following both the visual appearance of the computed profile blend and the value of sum of squared residuals O-C. We believe that the values given in Table 1 are the best obtainable. In some cases however it was not possible to fully reconstruct the profile using the four adapted line components. In cases close to conjunction of the short-period orbit, the Gaussian profile parameters have larger error margins than close to quadrature phases.
Among other lines, only He I 4713 and 5015 appear suitable for radial velocity determinations. Unfortunately, the B2 component cannot be identified reliably in any of them.
Conti et al. (1977) classified the integral spectrum as O9.5 Ib(f), i.e., they should have seen He II 4686 in emission. However, such emission is not mentioned in the MC paper, and also Walborn's classification does not refer to it. Our spectra can possibly explain this situation, because emission is also not always visible there. Several examples of the line profile are shown in Fig. 6. Due to the clear variability of the emission, the A1 contribution to the 4686 line is unpredictably affected by the superimposed emission and hence not suitable for radial velocity measurements.
Element | MC solution | MC & |
for He I | present data | |
period | 20 73 | 20 73596 |
semi-amplitude K (kms-1) | 49 | 49.6 |
MC systemic velocity (kms-1) | -7 | -8.1 |
present data systemic velocity (kms-1) | -19.1 | |
eccentricity | 0.34 | 0.342 |
longitude of periastron | 131 | 143.6 |
time of periastron | 2442530.0 | 2442530.49 |
rms of MC data (kms-1) | 11.9 | |
rms of present data (kms-1) | 6.9 | |
(km) | ||
mass function () | 0.21 | 0.218 |
In Table 1, the equivalent widths of component A1 are given. For He I 4922, the values scatter around a mean value of 0.29 Å with a standard deviation of 0.06 Å, while the accuracy of individual values is certainly better than 10%, so some intrinsic variability of the line strengths has to be present. No dependence on phase is apparent. The average value of the width of the A1 component of He I 4713 is 0.27 Å.
The equivalent widths of He I 4713 and 4922 lines of other components are also variable, as is apparent from Fig. 3. For B1 the average value of He I 4922 is 0.10 Å. The maximum EW of the emission seen in the He II 4686 line of component B1 is 0.03 Å.
The period is known from previous studies with an accuracy of about 0.02 days. The mean time interval between the MC spectra and our data is 6200 days (300 periods; 17 years), so there is no problem with determining the number of intermediate epochs. As a matter of fact, periods corresponding to actual cycles 1 can already be ruled out by the MC data. Therefore, a definitely more precise period could be determined using the broad time base between the MC and our data sets without any bias.
We first tried to obtain a solution of our radial velocity data alone. However, due to a gap in the phase coverage of the velocity curve, the correlation among spectroscopic elements turned out to be strong, and solutions tended to be non-unique: e.g., possible solutions implied a relatively broad parameter range for K1. More decisive results were expected when our data were combined with the older published data. However, a combined solution of different data sets requires the assumption of different velocities for widely separated epochs. In view of the long-term radial velocity changes due to the mutual orbit of the two binary systems A and B, different values of velocities are to be expected for data with long time separations. MC also noted a discrepancy between velocities obtained from different lines, so the intended combination of the MC and LMS data with our measurements required some caution. Therefore, we only considered He I measurements. Since LMS give velocities calculated from a combination of He I and Si IV lines, we restricted our data sample to the rather homogeneous set of He I velocities by MC and ourselves.
Our results are listed in Table 2 and compared with the original MC results. The solutions somewhat depend on the assumed data weighting. Since the rms values for MC velocities and for our data were about 12 and 7 kms-1, respectively, we gave the MC velocities a weight of 1, to ECHELEC velocities a weight of 2, and to CAT velocities a weight of 3. An independent solution of the MC data confirmed the original results by MC.
The large rms value of our high resolution data is somewhat unexpected and must be due to intrinsic variability of unknown nature. The error of fitting the Gaussians to line profiles is not larger than 2 kms-1. The deviations of the velocities from the anticipated orbital curve therefore represent real shifts of line positions.
In Fig. 5, velocities published by Feast et al. (1956) and Buscombe & Kennedy (1966) are also shown for comparison. Mean velocities per plate are used here in the case of Feast et al. data. They follow our A1 radial velocity curve reasonably, and their velocity can be calculated as kms-1. It is however difficult to comment on the data by Buscombe & Kennedy. The apparent difference in the velocities will be discussed in Sect. 7.
Figure 5: Radial velocities of the A1 component derived from He I lines. The theoretical curves are calculated according to elements in the last column of Table 2 for MC (full line) and present (dashed line) velocities. Triangles correspond to MC data, plus signs to the present data, open circles to data by Feast et al., asterisks to those of Buscombe & Kennedy, and crosses are values by Stickland | |
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Spectrum | Phase | (kms-1) | (kms-1) |
ECH 2 | 0.2304 | 262 | |
ECH 3 | 0.2402 | 251 | |
ECH 4 | 0.2502 | 261 | |
ECH 12 | 0.2453 | 263 | -219 |
CAT 3 | 0.2419 | 269 | |
ECH 14 | 0.6064 | -195 | |
ECH 15 | 0.7441 | -258 | |
ECH 16 | 0.7516 | -257 | |
ECH 17 | 0.7763 | -248 | |
ECH 19 | 0.7293 | -271 | 83 |
CAT 6 | 0.7549 | -251 |
Figure 6: Examples of profiles of the He II 4686 line. The dotted curves indicate the expected photospheric profiles, see text. The line at bottom center corresponds to the velocity | |
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As already noted above, the line He II 4686 is strongly variable. For instance in one spectrum the line is clearly in emission (ECH 15), in another spectrum taken only one hour later (ECH 16) the profile does not rise above continuum at all, see Fig. 6. The photospheric profiles of He II 4686 are expected to be similar in shape (albeit of different depth) to those of He I 4922. As illustration, Fig. 6 depicts a few of such profiles; their depth has been decreased such that they fit that part of the line wing, which is not affected by emission. The width of the emission profiles is quite large. It is therefore suggested that the emission is not originating within a possible disk around the B1 component, but comes from a region closer to the B system mass center - e.g. from the L1point. Accordingly, it can be anticipated that no emission is present in spectra taken at phases near eclipse minima.
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 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.
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
(2) |
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 , where is in kms-1 and 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 against the O-C curve. It appears that the trend of the 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) | |
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Some conclusion about the mutual orbit of both binaries were reached. This orbit possesses a period of several decades, and it is demonstrated that it will be worth to further follow its evolution by evaluation of the light-time effect and probably also by speckle interferometry. A highly accurate distance will be found by a combination of these methods in the future. In this respect, the system is similar to SZ Cam (Mayer et al. 1994, Lorenz et al. 1998, Harries et al. 1998) and V505 Sgr (Mayer 1997; Ibanoglu et al. 2000).
Acknowledgements
The authors are indebted to Dr. Stickland for providing them a preliminary version of his study of QZ Car.