A&A 387, 580-594 (2002)
P. Harmanec1,2 - H. Bozic2,3 - J. R. Percy4 - S. Yang5* - D. Ruzdjak3 - D. Sudar3 - M. Wolf1 - L. Iliev 6 - L. Huang7 - C. Buil8 - P. Eenens9
1 - Astronomical Institute of the Charles University, V Holesovickách 2, 180 00 Praha 8, Czech Republic
2 - Astronomical Institute, Academy of Sciences, 251 65 Ondrejov, Czech Republic
3 - Hvar Observatory, Faculty of Geodesy, Kaciceva 26, 10000 Zagreb, Croatia
4 - Erindale College and Department of Astronomy, University of Toronto, Mississauga, ON L5L IC6, Canada
5 - Department of Physics and Astronomy, University of Victoria, PO Box 3055 STN CSC, Victoria, B.C., Canada V8W 3P6
6 - National Astronomical Observatory, Rozhen, Bulgaria and Isaak Newton Institute of Chile, Bulgarian Branch
7 - Beijing Astronomical Observato
8 - Association des Utilisateurs de Détecteurs Électroniques (AUDE), 28 rue du Pic du Midi,
31130 Quint-Fonsegrives, France
9 - Dept. of Astronomy, University of Guanajuato, 36000 Guanajuato, GTO, Mexico
Received 25 January 2002 / Accepted 25 March 2002
An analysis of numerous homogenized UBV photoelectric observations and red spectra of the Be star V832 Cyg from several observatories led to the following principal findings:
1. Pronounced long-term light and colour variations of V832 Cyg result from a combination of two effects: from the gradual formation of a new Be envelope, and from an asymmetry and a slow revolution of the envelope (or its one-armed oscillation). The colour variations associated with the envelope formation are characterized by a positive correlation between brightness and emission strength, typical for stars which are not seen roughly equator-on.
2. The V magnitude observations prewhitened for the long-term changes follow a sinusoidal orbital light curve with a small amplitude and a period of 281971 which is derived from observations spanning 43 years. This independently confirms a 12-year old suggestion that the star is a spectroscopic binary with a 29-d period. V832 Cyg thus becomes the fifth known Be star with cyclic long-term V/Rvariations, the duplicity of which has been proven, the four other cases being Tau, V923 Aql, Cas and X Per. Therefore, the hypothesis that the long-term V/R variations may arise due to the attractive force of the binary companion at certain phases of the envelope formation is still worth considering as a viable alternative to the model of one-armed oscillation.
3. We have shown that the RV and V/R variations of the H and He I 6678 emission lines are all roughly in phase. In particular, the He I 6678 emission also moves with the Be primary which differs from what was found for another Be binary, Per.
4. We derived the orbital elements and found that in spite of the remaining uncertainties, the basic physical properties of the 282 binary are well constrained.
5. The light minimum of the orbital light curve occurs at elongation when the Be star is approaching us and the object becomes bluest in (B-V) and reddest in (U-B) at the same time. This may indicate that a part of the optically thick regions of the envelope is eclipsed at these orbital phases.
Key words: stars: emission-line, Be - stars: binaries: close - stars: binaries: spectroscopic - stars: fundamental parameters - stars: individual: V832 Cyg
|File||Epoch||No. of||HD comp.||System|
|No.||HJD-2 400 000||obs.||/check|
Observing stations are identified by their file numbers used in the Ondrejov data archives (see column "File No.'') as follows: 1... Hvar 0.65-m reflector, EMI6256 tube; 8... Xing-Long 0.60-m reflector; 20... University of Toronto 0.40-m reflector, Optec SSP-3 photometer; 23... Catalina, original UBV observations; 30... San Pedro Mártir: Older data set: 13C photometry transformed to UBV; Recent data set: UBV photometry with the 0.84-m reflector; 43... AAVSO observers with photoelectric photometers; 44... Mt Palomar 0.51-m reflector, EMI 6094 tube; 52... Rozhen 0.60-m reflector, EMI tube; 61... Hipparcos satellite, magnitudes transformed to Johnson V.
The history of early investigation of V832 Cyg has been summarized by Barker (1982). A few sentences of the section "history" in his paper are worth quoting here: "in view of the large variations in the spectrum of 59 Cyg during the last several decades, it is extremely likely that the widely varying velocities (as well as an oft-repeated "SB1" annotation) are the result of different observers measuring different line features at different phases of activity. The present observations show large velocity changes but give no evidence that the star is a binary. Hence, it is assumed here that 59 Cyg is a single star with radial velocity -23 km s-1 as determined in this work." V832 Cyg is actually the brightest component A of a multiple visual system ADS 14526. Component B at a distance of 201 (V = 938, B-V = 022, U-B = 004) is an A8III star and forms a common-motion pair with V832 Cyg. Component C, at 26 is optical.
At about the same time when Barker was preparing his study, Harmanec (1982) speculated that the long-term spectral variations of V832 Cyg could be related to the presence of a companion with a long orbital period. Notably, McAlister et al. (1984) indeed reported the discovery of a speckle-interferometric companion to V832 Cyg (system Aa) at a distance of 021 but no proof of its possible relation to long-term spectral changes is available. Barker (1983) obtained a new series of electronic spectra of the star and, analyzing the H emission profiles, he noted possible periodicity of the V/R ratio with either a 28-d or 14-d period. Tarasov & Tuominen (1987) obtained high-dispersion CCD H spectrograms of V832 Cyg and found periodic radial-velocity (RV hereafter) variations of the absorption core of H and its V/R variations with a 2914 period, the phase of the RV maximum being JD 2 446 614.10. They concluded that V832 Cyg is a spectroscopic binary with a 2914 orbital period. Soon thereafter, Tarasov & Tuominen (1988) analyzed the published spectroscopic data on V832 Cyg along with their additional CCD spectrograms. They improved the value of the orbital period to 27975 and concluded that the orbital period could be detected in the V/R variations of the Balmer lines also in several published data sets. Very regrettably, their detailed study has never been published.
Recently, Rivinius & Stefl (2000) confirmed their result. Measuring the radial velocity of the He I 4471 line in 1990-1998 Heros spectra, they derived the velocity curve with a semiamplitude of 27 km s-1. Using IUE spectra from 1978 to 1994, they refined the value of the orbital period to a value of 281702 which they kept fixed in their orbital solution for the He I 4471 line. They concluded that the orbit is eccentric (e=0.2) and derived the epoch of periastron passage as JD 2 450 018.9 2.5. They also discovered the presence of a weak emission component in the core of the He I 6678 line and suggested possible similarity of V832 Cyg to another Be binary, Per, studied recently by Gies et al. (1993) and Bozic et al. (1995). They interpreted this emission as arising from a part of the Be disk around V832 Cyg illuminated by a hot (and as yet unseen) compact secondary to V832 Cyg in a 2817 orbit.
The purpose of this paper is to investigate the character of the long-term light, colour and emission-line variations of V832 Cyg and to look for possible signatures of its orbital changes.
|56 Cyg||198639||3||5.063 0.004||5.251 0.007||5.351 0.009||0.187||0.101|
|HD 199311||199311||406||6.689 0.010||6.767 0.012||6.866 0.015||0.079||0.099|
|HD 199479||199479||148||6.847 0.012||6.807 0.013||6.595 0.016||-0.040||-0.212|
|HD 199890||199890||3||7.507 0.002||7.409 0.003||7.024 0.007||-0.098||-0.385|
|HR 8161||203245||326||5.762 0.010||5.635 0.010||5.121 0.013||-0.127||-0.514|
|Date of||Epoch||V||B-V||U-B||N of||Source|
|obs.||(HJD-2 400 000)||(mag)||(mag)||(mag)||obs.|
|1955 - 1957 ??||35400::||4.49||-0.03||-0.93||3||Mendoza (1958)|
|1956 - 1963||35655-38300:||4.88||-0.14||-||3||Ljungren & Oja (1964)|
|1962 - 1970||37850-40860:||4.79||-0.07||-0.92||1||Crawford et al. (1971)|
|Oct. 1969 to Sep. 1970||40495-40860||4.87||-0.07||-0.93||1||Lutz & Lutz (1972)|
|1970 - 1971||40800-41230:||4.57||-0.01||-0.99||2||Lutz & Lutz (1977)|
|Sep. 1973 to Aug. 1975||41930-42655||4.67||-0.03||-1.00||?||Warman & Echevaria (1977)*|
|Sep. 1973 to Aug. 1975||41930-42655||4.93||-0.14||-0.95||1||Echevaria et al. (1979)|
The observational data used in this study consist of numerous UBV, BV and V photometric measurements from 9 different observatories for which accurate dates of observations are known. They were secured between the years 1958 and 2000 and consist of both already published observations and new data obtained by us. Basic information is provided in Table 1. As seen there, most of the available data sets were secured differentially but relative to several different comparison stars, and there are also three data sets based on all-sky photometry.
Special effort was made to derive improved all-sky values for all comparison stars used, employing carefully standardized UBVobservations secured at Hvar and San Pedro Mártir observatories. The new values are collected in Table 2, together with the number of all-sky observations and the rms errors. They were added to the respective magnitude differences to obtain directly comparable standard UBV magnitudes of V832 Cyg. For the convenience of future investigators, we publish all of our homogenized individual UBV observations together with their HJDs in Table 3.
Some comments on the individual data sets and their reduction follow:
File 1: Hvar These observations were reduced to the standard UBV system via non-linear transformation formulæ using the HEC22 reduction program - see Harmanec et al. (1994) and Harmanec & Horn (1998). The first part of them was secured in the course of the international campaign on photometry of Be stars and has already been analyzed by Hadrava et al. (1989) and by Pavlovski et al. (1997) and published in detail by Harmanec et al. (1997).
During summer and autumn 1999, two of us (PH and HB) obtained dedicated series of observations of V832 Cyg aimed at detection of variations on the time scale of the orbital period and shorter. Since the comparison star originally recommended for the Be campaign, HD 199311, is rather faint for observations of V832 Cyg, we selected and used a brighter comparison star HR 8161 = HD 203245 after verifying its secular constancy. The first part of the 1999 Hvar observations was secured during a commissioning run with a new, computer controlled photometer, while the second part was obtained with the original one. Transformation coefficients were derived separately for these two parts of the data. A few observations were secured during one night in June 2000 with the original Hvar photometer by HB. Numerous observations with the new photometer were again secured during the summer and autumn of 2001. The 1999-2001 observations are published and analyzed for the first time here.
File 8: Xing-Long These observations were also secured as part of the international campaign on photometry of Be stars and reduced using the HEC22 program.
File 20 and 43: Toronto and AAVSO photoelectric program These observations come from the photometric archives of the AAVSO and of JRP. They were secured in support of the international program. The Toronto data were obtained by summer undergraduate research assistants, while the AAVSO V data were obtained by several different AAVSO observers equipped with photoelectric photometers (mostly SSP-3 from Optec). All the observations were reduced by AAVSO or by JRP via linear transformation equations and some results have already been published by Percy et al. (1988,1996,1997), Percy & Bakos (2001) and Landis et al. (1992).
File 23: Catalina These original UBV all-sky observations were published with dates of observations by Johnson et al. (1966). We converted their tabulated JDs into HJDs.
File 30: San Pedro Mártir The older part of these data is based on the all-sky 13C observations which were published by Johnson & Mitchell (1975). They were reduced to the standard UBV system via transformation formulæ, derived and published by Harmanec & Bozic (2001). The formulæ are defined by those good standard stars observed at Hvar (see Harmanec et al. 1994) for which the 13C photometry was also available. The recent part of these observations was secured by PH, MW and PE with the 0.84-m reflector and Cuenta-pulsos photon-counting photometer equipped with an RCA 31034 photomultiplier and UBV filters. These data were also reduced with the HEC22 program, corrected for measured extinction and transformed to the standard Johnson system.
|Figure 1: A plot of the B-V colour index vs. the V magnitude for all calibrated UBV observations of V832 Cyg.|
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File 44: Mount Palomar These V observations were published by Lynds (1959). The new V value of HD 199890 from Table 2 was added to the magnitude differences V832 Cyg - HD 199890 to obtain Vmagnitudes of V832 Cyg comparable to the other data.
File 52: Rozen These UBV observations were secured by one of us, LI, and consist of two parts. The first one was shown in a preliminary graphical form in Kovatchev et al. (1986). These data are on an instrumental UBV system and the B and U magnitudes differ systematically from all other comparable data sets even after the new UBV values for the comparison star used, 56 Cyg = HD 198639, were added to the magnitude differences V832 Cyg - 56 Cyg. Observations secured during two nights in 1990 and 1991 were reduced with the help of the HEC22 program. It turned out that the available observations did not allow us to derive the dead-time of the instrument accurately enough from the available data. The B magnitude of V832 Cyg is bright enough to be sensitive to the exact value of the dead-time coefficient and the values of the (B-V) and (U-B) colours are affected by this uncertainty for both data sets. We, therefore, analyzed only the V observations from Rozen and - as a precaution - we use the earlier data set only for the study of long-term changes.
File 61: Hipparcos These observations were reduced to the standard V and B magnitudes via the transformation formulæ derived by Harmanec (1998). Since the star underwent long-term brightness and colour variations over the period 1989-93, covered by Hipparcos observations, we proceeded in such a way that we first found the mean relation between the V magnitude and the (B-V) colour from all calibrated UBV observations and then we used proper values of (B-V) in the to BV transformation formulæ. As Fig. 1 shows, the (B-V) vs. V relation is nearly linear for V832 Cyg.
To be able to study the relation between the long-term light and spectral changes, we collected all available records of the H profiles of V832 Cyg. New electronic spectra, covering the spectral region near H and available to us consist of the following five data sets:
All spectra at our disposal cover the region of the H profile. The DAO and Reticon spectra also contain the He I 6678 line profile. Samples of the H and He I 6678 profiles of V832 Cyg are shown in Figs. 2 and 3, respectively. One can see that the H profile is dominated by strong emission and exhibits V/R changes. The profile of He I 6678 is composed of a broad absorption and a double emission which exhibits variations in both the line intensity and the V/R ratio.
We obtained and investigated the following characteristics of the H profiles: the peak intensities IV and IR of the violet and red peaks of the double H emission expressed in units of the local continuum, their ratio IV/IR, the line intensity measured by the mean of the two, i.e. (IV+IR)/2 and the equivalent width of the emission profile EW(we omit the usual minus sign for the emission-line equivalent width). Note that our IV/IR ratio differs from the quantity denoted as V/Rin the papers by Doazan et al. (1985,1989) which was defined as (IV-1)/(IR-1). It is necessary to warn that the H emission is so strong that in some profiles even a proper identification of the Vand R peak of the emission is anything but easy. That is why we measured only the total peak intensity (IV+IR)/2 in such profiles when the separate V and R peaks could not be safely identified. The problem is also complicated by the presence of a number of strong telluric lines. For the He I 6678 profiles, we also measured the V and R peaks of the double emission and derived their mean and ratio but we did not measure the equivalent width of these complicated profiles.
|Figure 2: A sample of three H profiles of V832 Cyg identified by the instrument and heliocentric Julian date. The profiles are on a heliocentric wavelength scale (in 'A) and consecutive profiles were shifted for 0.3 in relative intensity.|
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|Figure 3: A sample of the same three He I 6678 profiles of V832 Cyg as H profiles shown in Fig. 2, again identified by the instrument and heliocentric Julian date. The profiles are on a heliocentric wavelength scale (in 'A) and consecutive profiles were shifted for 0.1 in relative intensity.|
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For spectra with higher resolution we also derived the RV of the symmetric bottom parts of the steep wings of the H emission (up to about 1.3 in relative intensity) trying to take into account the distortion caused by the telluric lines. Whenever available, we also measured the RV of the emission wings and of the broad absorption wings of the He I 6678 profile. It turned out that although the H profile is quite complicated and the upper parts of the emission wings may become asymmetric, the settings on the bottom parts of the emission wings can be reproduced quite well as evidenced by the independent measurements in the series of DAO profiles.
Spectrophotometric quantities and heliocentric Julian dates which we directly derived ourselves from the published profiles are collected in Table 5. Note that we also re-measured the 17 scanner H profiles obtained by Barker (1983) which were later included in the detailed study by Doazan et al. (1985). Otherwise, we directly used the tabulated values from the papers by Doazan et al. (1985,1989) which we do not reproduce here.
The spectrophotometric quantities derived by us from the new electronic spectra can be found in Table 6 while the RVmeasurements are collected in Table 7.
|Figure 4: Long-term H emission line strength, light and colour variations of V832 Cyg.|
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Figure 4 is a plot of the V/R ratio and peak intensity of the H emission, and of V, B-V and U-B individual observations of V832 Cyg vs. time. It shows how complicated and complex the long-term variations of the object are. Inspecting Fig. 4, one can only regret that the very interesting period of the two shell phases centred roughly on JDs 2 441 850 and 2 442 400, and the epoch of the near-absence of the Balmer emission around JD 2 443 200, are so poorly covered by photometric observations. The only existing occasional all-sky UBV observations of the star from that period, collected in Table 4 show that rather rapid and large brightness changes occurred at that time (see, however, a note to this table). It is also seen that the re-appearance of the Balmer emission after JD 2 443 200 was accompanied by a brightnening of the object. As seen in Fig. 5, the photometric spectral class of the object varied from a main-sequence B1 star to a B1 supergiant (after one takes the dereddening into account). All these are clear signatures of a positive correlation between the brightness and emission-line strength as defined by Harmanec (1983,2000) (see also a detailed discussion in Koubský et al. 1997). In this interpretation, the optically dense inner parts of the envelope, a pseudophotosphere, seen under an intermediate angle, simulate an increase of the radius of the star which then appears larger and more luminous then in the period when it is without the envelope. (In contrast to it, for stars seen roughly equator-on, one observes an inverse correlation during which an increase of the emission strength is accompanied by a decrease of brightness of the object, which at the same time moves along the main-sequence towards a cooler spectral subclass in the colour-colour diagram.)
One can also note that after the formation of a new Be envelope, large cyclic V/R variations with about 2-year-long cycles were observed until about JD 2 447 000 when the brightness of the star also reached its contemporary value (between about 47 and 48 in V). The brightening of the object was accompanied by reddening of the (B-V)index. In contrast to this, the (U-B) index showed only rather mild cyclic variations over the whole interval covered by the observations.
|In the text||Figure 5: (U-B) vs. (B-V) colour diagram with the main-sequence and supergiant sequence shown. It is seen that the observations of V832 Cyg correspond to a positive correlation between the brightness and emission-line strength. After dereddening the object moves between B1V and B1Ia in the diagram.|
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We began our analysis by prewhitening the most numerous set of Vobservations for the pronounced and - at some epochs also quite fast - long-term light changes, using Vondrák's (1969,1977) smoothing technique. After some trial we found that the best removal of the long-term changes is obtained when one uses the smoothing parameter equal to .
|Figure 6: A time plot of a longer series of 1999 Hvar V observations, prewhitened for long-term changes. The only significant variations occur on a time scale of days, not on a time scale of hours.|
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It is necessary to say that our photometric observations were not aimed at studies of possible rapid light changes and were not obtained in really long whole-night series. They are, therefore, less ideal for any search for rapid changes. In July 1999, we obtained a series of observations at Hvar in very good weather conditions. This series spans one week in about 02 long series. From it, we see no evidence of significant variations on a time scale of hours exceeding the usual scatter of 002, illustrated by observations of a check star - see Fig. 6. Only gradual changes on a time scale of days are observed.
In the next step, we searched the more recent and reasonably homogeneous prewhitened V observations for periodicity over the whole range of periods from 3000 days down to 02 using Stellingwerf's (1978) PDM method. In particular, we analyzed 344 individual V observations after HJD 2 451 000 secured at Hvar, San Pedro Mártir and by AAVSO observers. Thanks to a large difference in local time between North America and Mexico on one side, and Hvar on the other, this data set is suitable for a test on the presence of rapid changes. Figure 7 shows the PDM periodogram. It is clearly seen that the light of V832 Cyg varies with a frequency of about 0.035 c d-1, i.e. with a period close to 282. The same conclusion follows also from the analysis of the V/R variations of the H profile from the quiet epoch (after JD 2 446 500).
|Figure 7: Stelligwerf's PDM periodogram of V photometry prewhitened for long-term changes.|
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|Figure 8: Stelligwerf's PDM periodogram of V photometry prewhitened for long-term changes (upper panel) and of the IV/IR ratio of the double H emission (bottom panel).|
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In Fig. 8 we compare the periodograms of the V residuals and the V/R ratio in the neighbourhood of the orbital period. The deepest minima in both periodograms correspond to the same value of the orbital period of about 2819.
At this stage, it seems appropriate to say a few words about Hipparcos photometry. It appears to us that this precious data set seems to be overinterpreted by some investigators. While the set is basically free from the usual one-day aliases occurring for observations from the Earth, it has its own, very selective time distribution as was pointed out by Stefl et al. (1998) and recently discussed by Percy et al. (2002a,2002b) and Jerzykiewicz & Pamyatnykh (2000). Besides, it usually represents something like 100 data points per one object. For completeness, we also ran a PDM period search on Hipparcos data prewhitened for the long-term changes, again over the interval of periods down to 02. Notably, we did not detect any significant period near 0280 but a rather well defined periodicity of 220286 - see Fig. 9. This shows how dangerous it is to search for periodicity in a limited data set which displays only mild variations. We cannot confirm the 22 period from other data and believe it to be an accidental, formal fit for one limited data set, not a real periodicity.
For completeness, we also show a phase diagram for the best "period" near 0280, namely 0277253. It is seen that the phase curve for this period does not look very convincing but it shows certain organized structure, not just a white noise. We also note that all the reports of possible rapid changes cluster around a similar value of 026-028, the sub-feature separation detected by Yang being about 1/4 of that value. Since V832 Cyg lies in the region of the HR diagram where Cep pulsational instability occurs, it is conceivable that it is a pulsating star. In the light of what was said above, however, we postpone the investigation of possible rapid changes until new, dedicated series of observations are available.
|In the text||Figure 9: Phase diagrams for the best-fit "period" of 220286, and for the best "period" near 0280, for the Hipparcos photometry alone (again prewhitened for the long-term changes).|
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We therefore take for granted that - apart from the long-term changes - the brightness of V832 Cyg varies slightly with the orbital period. We formally used the program FOTEL (Hadrava 1990), designed for orbital solutions of spectroscopic binaries, to derive a quantitative description of the light curve and an improved value of the orbital period. The results are summarized in Table 8 for two different solutions, based on individual and common zero points of the magnitude scale for individual data sets. We deliberately used a reference epoch of minimum light close to the epoch of periastron passage derived by Rivinius & Stefl (2000) to allow a direct comparison with their RV curve. Note that we obtained a slightly different - and presumably also a more accurate - value of the orbital period since our data span a longer period of time than theirs: from 1958 to 2001. We verified that the light minimum occurs at the same phase for our improved value of the orbital period for the early, intermediate and new V data subsets. In the following discussion we shall adopt the linear ephemeris from solution 1.
|Element||solution 1||solution 2|
|P (d)||28.1971 0.0038||28.1918 0.0035|
|50013.71 0.35||50013.61 0.39|
|A (mag)||0.00807 0.00060||0.00751 0.00063|
Figure 10 shows the light curve based on all V observations and also the light curve based on 1-d normal points derived from the same data.
|Figure 10: The orbital V magnitude light curve of V832 Cyg plotted for the ephemeris of solution 1: = HJD 2 450 013.71+281971E. Individual observations are shown in the upper panel while the bottom panel shows the 1-d normal points.|
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|Figure 11: The orbital light and colour curves based on Hvar and San Pedro Mártir observations prewhitened for long-term changes. The ephemeris of solution 1 was used: = HJD 2 450 013.71+28 .|
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To study also the colour variations, we extracted 1-d normal points from prewhitened Hvar and San Pedro Mártir observations and show their phase diagrams in Fig. 11. One can see that the object gets slightly bluer in (B-V), and redder in (U-B) near the light mininum.
In Fig. 12 we show the orbital variations of the IR/IV ratio of the H and He I 6678 emission lines from all spectra taken after JD 2 446 650, i.e. in the epoch without large cyclic IR/IV changes. One can see that the curve for the H line has a more complicated phase dependence than the almost perfectly sinusoidal He I 6678 IR/IV curve. The minima of both curves occur somewhat earlier than the light minimum.
Finally, we also analyzed the RV curves. Figure 13 shows the velocity curves based on the RV measurements of the bottom part of the H emission wings and on the wings of the double He I 6678 emission. One can see a clear sinusoidal variation of the H emission RVs with the orbital phase. It is also significant that the epoch of the RV minimum of the H emission, HJD 2 450 013.81 0.62, is identical to the epoch of minimum light.
A notable thing is that the He I 6678 emission also roughly follows the RV curve of the V832 Cyg primary, though with a larger amplitude and some shift in phase, and does not define a RV curve with a large amplitude in antiphase to the RV curve of the H emission as was found by Gies et al. (1993) and Bozic et al. (1995) for Per. The larger scatter along the RV curve is understandable since the He I 6678 emission line is very weak and the measurements can also partly be affected by possible weak subfeatures moving across the He I 6678 line profile. Besides, one can suspect that some additional emission is affecting the RVof the He I 6678 emission near RV maximum. A closer inspection of Fig. 13 reveals that it is still conceivable that in all phases outside the RVmaximum the He I 6678 emission closely follows the RV curve of the H emission. This has to be verified with a more numerous data set.
|Figure 12: The orbital IR/IV curve of H and He I 6678 lines plotted for the ephemeris of solution 1: = HJD 2 450 013.71+28 .|
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|Figure 13: The RV curves based on RV measurements of the bottom part of the H emission wings (top) and wings of the double He I 6678 emission in DAO, Ondrejov and Rozen spectra. The ephemeris of solution 1 was used: = HJD 2 450 013.71+28 .|
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Let us first try to estimate the basic physical properties of the primary
component of the 282 binary. One can obtain an estimate of the radius of the
primary using dereddened V0 magnitude, effective temperature and
the Hipparcos parallax of 000290
(Perryman et al. 1997). The best estimate of the properties of
the underlying star comes from the epoch near JD 2 443 000 when the star
was almost without emission. The mean value of 5 UBV observations
available to us from that epoch (year 1977) is
A standard dereddening leads to
The primary of V832 Cyg is a rapid rotator. Hutchings & Stoeckley (1977) derived v sin i = 450 km s-1 and this value agrees well with our He I line profiles. Chauville et al. (2001) derived v sin i = km s-1 from high-dispersion spectra obtained in 1992. The often quoted value of 260 km s-1, published by Slettebak (1982), is too low. For our estimate of the radius and mass of the primary, the Keplerian velocity at the equator of the primary is 620 km s-1. For instance for v sin i = 450 km s-1 this implies that the inclination of the rotational axis must be higher than 46. One also gets a lower estimate of the corotation period near the primary as 043.
|Element||TT||RS||H emis.||He I 6678 emis.||He I 6678 abs.|
|P (d)||28.1971fixed||28.1702 0.0014||28.1971fixed||28.1971fixed||28.1971fixed|
|46627.98 0.34||50013.6||50013.81 0.62||50010.23 0.66||50010.1 1.2|
|e||0 fixed||0.20 0.08||0 fixed||0 fixed||0 fixed|
|K (km s-1)||52.6 1.3||27.2 8.5||13.0 1.0||31.3 1.6||25.4 3.0|
|(km s-1)||21.4 2.3||-||-16.49 0.76||-4.7 2.1||-14.1 3.2|
|No. of RVs||13||46||30||29||29|
|rms (km s-1)||7.98||?||3.08||8.43||13.0|
We therefore believe that the determination of the true orbital RVcurve can best be obtained from the RV measurements of the wings
emission as we did here and as Bozic et al. (1995)
did earlier for Per. Note that it is very probable that
the rotational velocity of the circumstellar disk decreases with
increasing distance from the star. One can, therefore, assume that
any possible asymmetries in the distribution of the circumstellar matter
will affect the central parts of the emission profiles more than the outer
wings of the emission which reflect the motion of the inner and
probably more axially symmetric parts of the disk. If the disk is
centred on the primary, the outer wings of the Balmer emission
should reflect the true orbital motion of the primary. Indeed, the
RV curve of the emission wings is circular and has an amplitude of only
13 km s-1 - see Table 9. Consequently, we base our
estimate of the properties of the binary system on this RV curve.
In Table 10 we give them for the two extremes of possible
orbital inclination, making a reasonable assumption
that the equatorial plane of the primary and the orbital plane of the binary
coincide. One can see that the dimensions of the binary system are quite well
constrained. No matter whether one adopts our circular orbit and
K1=13 km s-1 based on the broad wings of the H
the eccentric orbit with K1 = 27.2 km s-1 advocated by
Rivinius & Stefl (2000), the separation of the components
must be about 90
and the mass ratio between about 0.1 and 0.2. For
the mass of the primary appropriate for its effective temperature
the expected mass of the secondary should be between 1 and 2 .
This implies an expected semi-amplitude of the secondary between
about 60 and 150 km s-1.
The IV/IR orbital variations, detectable after HJD 2 446 650 when the slowly revolving elongation of the envelope vanished, which are depicted in Fig. 12, deserve a few comments.
|Element||H||H "eccentric''||He I 6678|
|P (d)||28.1971 fixed||28.1965 0.0049||28.1971 fixed|
|50010.77 0.43||50007.62 0.70||50012.09 0.18|
|e||0.0 fixed||0.524 0.096||0.0 fixed|
|A (mag)||0.0548 0.0041||0.0664 0.0083||0.0618 0.0016|
|No. of obs.||44||44||36|
In passing, we also note that there is no unambiguous direct evidence of the secondary spectrum at the moment. The origin of the weak He II 4686 emission line (amounting to 0.5 per cent of the continuum radiation), detected in the mean Heros spectrum by Rivinius & Stefl (2000), is not quite clear. The authors say only that the spectra were "RV corrected" but they do not say how. Should the He II emission line be associated with the secondary, its RV curve should have an amplitude of about 100 km s-1 which should be tested with future high-resolution and high-S/N spectra.
|Figure 14: Recorded orbital motion of the closer visual component ADS Aa.|
|Open with DEXTER|
Figure 14 is a plot of the position angle and separation of the closer visual component to V832 Cyg, ADS 14526Aa, based on data published by Hartkopf et al. (2001). Evidence of the orbital motion is obvious. It is interesting to attempt rough estimates of the orbital period of this closer visual pair. Using the observed parallax, the largest recorded angular separation of 022 and Kepler's Third Law (assuming a total mass of 13 ), one arrives at an orbital period of 183 years. Assuming a uniform change of the position angle with time, one gets 193 years to complete one full 360 cycle. No matter how rough both these estimates are, it seems that the orbital period of the Aa system may be about 200 years.
We acknowledge the use of Hvar UBV observations of the star obtained as a part of the international Be program, which were obtained by a number of observers and published by Pavlovski et al. (1997) and Harmanec et al. (1997) as well as the V observations provided by AAVSO. Two of the Ondrejov Reticon spectra were obtained by Ms. D. Korcáková and Dr. P. Skoda. The use of the computerized bibliography from the Strasbourg Astronomical Data Centre is also gratefully acknowledged. This study was realized as a part of the research projects J13/98 113200004, AV 0Z1 003909 and K2043105. PH, PE and MW acknowledge the support from the collaborative program KONTAKT ME402(2000) and CONACyT which allowed a direct collaboration and obtaining several important data sets used. JRP acknowledges a research grant from NSERC Canada. In the early stages, this study was also partly supported from the grant A3003805 of the Granting Agency of the Academy of Sciences of the Czech Republic and from the project K1-003-601/4 of the Academy of Sciences of the Czech Republic.