A&A 372, 588-593 (2001)
DOI: 10.1051/0004-6361:20010532
E. Rodríguez 1 - J. M. García 2 - S. Martín 1 - A. Claret 1
1 - Instituto de Astrofísica de Andalucía, CSIC,
PO Box 3004, 18080 Granada, Spain
2 -
Departamento de Física, E.U.I.T. Industriales, UPM, Ronda de Valencia 3,
28012 Madrid, Spain
Received 29 September 2000 / Accepted 6 April 2001
Abstract
This paper presents complete uvby light curves for the recently
discovered eclipsing binary system V2154 Cyg. Additional Crawford H
data were also obtained. Three times of primary minima and two secondary
minima are determined. An improved orbital period is found to be 2
6306312.
A detailed photometric analysis is made using the EBOP code. This
eclipsing
binary is probably one of the components of a much wider double star, forming
altogether a triple system. The results show that the eclipsing pair is a
detached system with two late-type stars very different in
size. Masses of about
and
are
inferred for the components by using stellar evolution models. The total
mass of the probable triple system is estimated to be of about
3.5
,
leading to a minimum orbital period of about 140 yr for the
visual pair.
Key words: stars: binaries: eclipsing - stars: individual: V2154 Cyg - stars: fundamental parameters - techniques: photometric
V2154 Cyg (HD 203839, Hip 105584) was discovered as an eclipsing
binary system by the Hipparcos satellite (ESA, 1997) with a period of
P=2
63060 and eclipses depths in the primary and secondary minima of about
3 and 0
05, respectively. Although this remarkable
primary depth and being moderate bright (V=7
8), it had never been
reported as photometric variable.
Hipparcos catalogue reports V2154 Cyg as also a double visual star
(components A and B). Fabricius & Makarov (2000) give a separation of
0
47 between these two components and magnitude differences
of 2
18 and
2
15 in the Tycho
and
passbands.
The eclipsing nature of V2154 Cyg was also discovered, in an independent way
and using uvby photometry, in the year 1996 by Martín et al.
(2001) during the course of a survey for Dor
variables carried out on the open cluster M 39. V2154 Cyg is not a member of
this cluster, but it was used as a check star during these observations.
New observations were collected during 1998 in order to complete the light
curves using Strömgren uvby photometry. Based on these new
observations, together with the old ones obtained in 1996, a photometric
study is presented in this paper using the EBOP code. Section 2 is dedicated to
describe the observations itself while Sect. 3 is devoted to analyse the
light curves. Some conclusions are summarised in Sect. 4.
The observations were carried out during 1998, July to November,
using the 90 cm telescope at the Sierra Nevada Observatory,
Spain. The photometer attached to this telescope is a six-channel uvby
spectrograph photometer for simultaneous measurements in uvby or in the narrow and wide H
channels, respectively, using
uncooled EMI photomultipliers type 9789 QA (Nielsen 1983).
Twenty-eight nights
were devoted to measuring V2154 Cyg using the four uvby filters.
In addition, a few measures were collected in H
around the phase
0.25 of the orbital period.
For these observations, HD 204626 was used as the main comparison
star with HD 204977 as check star. The sequence was, generally,
C1, C2, Var, C1, C2, Var. Sky measurements were made every 2 or 3 cycles depending
of the position of the Moon in the sky. 852 uvby measurements were
collected for the variable, about 800 for C1 and 650 for C2. Each integration
consisted of 35 s for the variable and C1 and 40 s for C2. This means, for any
of the stars, an internal error in each observation better than 0
003 in
the u filter for C2, namely the worst case.
The extinction corrections
were based on nightly coefficients determined from the main comparison star.
Then, magnitude differences of each object relative to C1 were calculated by
means of linear interpolation.
During the observations reported here, neither of the comparison stars showed
any sign of variability. Each night, the standard deviations for C2-C1
differences were always better than 0
010, 0
005, 0
004 and
0
006 for u, v, b and y, respectively. In
addition, the mean values obtained for the C2-C1 differences on each of the
nights were always the same within 0
002, as standard deviation, for any
of the filters. Moreover, when we consider the full sample, the standard
deviations of C2-C1 were found to be of 0
0085, 0
0035, 0
0032
and 0
0043 for u, v, b and y, respectively.
Furthermore, a frequency analysis was performed to these data in order to
investigate the existence of possible small variabilities in any of the
comparison stars. When a Fourier analysis was applied (using the method
described in Rodríguez et al. 1998) to the v filter,
we obtain C2
and C1 not showing any sign of variability within about 0
001, in the
range from 0 to 30 cd-1. Similar results were obtained for the other
two b and y filters. Hence, C1 and C2 can be considered as
constant stars.
To transform our data into the standard uvby
system, we have used
the same procedure described in Rodríguez et al. (1997).
The data obtained, as magnitude differences variable
minus C1 in the standard system versus Heliocentric Julian Day, are listed in
Table 1. This table is available via ftp at the CDS and can also be
requested from the authors. The data have also been
deposited in the Commission 27 IAU Archives of Unpublished Observations, file
343E. These standard data,
together with those obtained on 9 nights during 1996 (Martín et al.
2001), are used in
the following section to analyse the light curves of V2154 Cyg. In total, 976
data in each of the four uvby are used. Nearly all phases have been
covered at least twice.
Derived standard
indices for V2154 Cyg and the two comparison stars are given in
Table 2 together with relevant catalogue information on these stars. These
derived Strömgren values are in very good agreement with those found in the
bibliography (e.g. Hauck & Mermilliod 1998) and also
with those published in Martín et al. (2001).
Variable | Comp. 1 | Comp. 2 | |
HD no. | 203839 | 204626 | 204977 |
SAO no. | 50783 | 50910 | 50959 |
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21![]() ![]() ![]() |
21![]() ![]() ![]() |
21![]() ![]() ![]() |
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48
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48
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47
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l | 91![]() |
92![]() |
92![]() |
b | -1![]() |
-2![]() |
-3![]() |
Sp. type | F0 | A0III | B9V |
V | 7
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7
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8
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|
b-y | 0
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0
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0
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|
m1 | 0
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0
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0
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|
c1 | 0
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1
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0
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|
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2
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2
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2
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Three times of light minima were obtained for the primary minimum and other
two for the secondary one during the observations collected in 1998. They are
the only times of minima available for this binary system up to date and are
listed
in Table 3. These times of minima were determined using the method described
in Rodríguez et al. (1990) where each light minimum is
derived as average
of the four uvby bands. The estimated uncertainties in determining a
time of minimum is of about 0
0005 and 0
0015 for the primary and
secondary eclipses, respectively.
In order to improve the period determination of this binary system,
a frequency analysis
was utilised making use of least-squares algorithms better than the classical
O-C method, because of the short baseline in time available from the times
of minima.
In this way, a period of P1=2
63068 was found as the best solution
for our data with a baseline of 2.3 years.
This derived period is slightly longer than that of P2=2
63060 given
by the Hipparcos catalogue (ESA 1997). To verify the
reliability of these determinations, the Hipparcos data were corrected to
make compatible with our data in the y filter. Consequently, the
baseline of the full sample is much longer (8.9 years). When all the data are
phased using linear ephemeris with origin in time
T0=2451048
6170 (our
first time of primary minimum) and periods of P1 or P2, we obtained that
P1 is slightly long while P2 is slightly short. Then, a new frequency
analysis was performed for the full sample and a new best solution was found
as P3=2
6306312 with an errorbar of
.
The
Hipparcos data are reconciled with the ones collected by us when
altogether are phased using a new linear ephemeris with T0 and P3.
Assuming this linear ephemeris, our uvby data were phased and plotted in
Fig. 1. The bottom panels in each graph show the corresponding magnitude
differences of C2-C1.
HJD | Type |
2400000.+ | |
51031.5184 | Sec |
51048.6170 | Pri |
51060.4547 | Sec |
51098.5991 | Pri |
51106.4905 | Pri |
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Figure 1:
uvby light curves of V2154 Cyg relative to ![]() |
Open with DEXTER |
The light curves of V2154 Cyg do not show notable distortions outside the eclipses and the bottom of the secondary minimum appears flat, being this eclipse relatively shallow although clearly defined at phase 0.5. This appearance indicates that the eclipses are complete, primary being annular and secondary being total, and seems to be originated by two well-detached components with very different surface brightnesses.
The photometric analysis of the uvby light curves has been carried out with the EBOP code (Etzel 1981) which is based in the Nelson-Davis-Etzel (NDE) model (Popper & Etzel 1981). This model has proved to yield reliable photometric elements for detached binaries, like V2154 Cyg, where the proximity effects are not very important. The last version, named EBOPC, which permits the treatment for systems showing apsidal motion (Giménez & Quintana 1992, Giménez & Díaz-Cordovés 1993) was used throughout, although apsidal motion is not relevant for the present analysis.
Several basic assumptions were made for solving the four light
curves of V2154 Cyg. Theoretical limb darkening coefficients (x),
as derived by Díaz-Cordovés et al. (1995),
for uvby bands were
adopted. Gravity darkening coefficients (y) for convective
atmospheres (Lucy 1967; Kitamura & Nakamura 1983) have been
used. These values are lower than those corresponding to
radiative envelopes frequently obtained with the formulae by
Martynov (1973). We have verified that the use of either of
these values has negligible effects on the final elements
derived for V2154 Cyg. After some preliminary trial solutions,
circular orbit was assumed. The amount of third light L3 is not
negligible
because the visual component B is at 0
47 and therefore is
unresolved in our photometric measurements. From the magnitude
differences between the visual components derived from the Hipparcos data
(Fabricius & Makarov 2000), we obtained a L3 contribution of
11% in terms of the total light of the system (0.119 in y and
0.116 in b). L3 was included as a free parameter in some of the
computations and in the analysis of the v and u curves.
In absence of a spectroscopic mass ratio, q, we made several attempts to derive a wise value for this parameter. Residuals become slightly lower in the y filter for q=0.68, but the values pointed out are different for the other colours, the shorter the wavelength the smaller the mass ratio (q=0.58, 0.52 and 0.44 for b, v and u, respectively). This is somehow expected because the light curves of V2154 Cyg do not contain enough information to discriminate the q parameter. We have finally chosen q=0.55, obtained as the ratio of the individual masses of the components calculated from the mass-effective temperature empirical relation for main sequence stars given by Habets & Heitnze (1981).
This rough estimation is sufficient for the photometric
analysis of V2154 Cyg, in view of the fact that changing q by 0.1, does not significantly affect the geometrical elements
derived. The assumption is no longer valid when the objective is
to establish reliable absolute dimensions for the system.
The relevant parameters to be determined from the fits are: the
radius of the primary component, r1, the ratio of radii,
k=r2/r1, the orbital inclination, i, and the ratio of central
surface brightnesses, J2/J1. Phase shifts and the photometric
scale factor were always left as free parameters. Light curves
have been analysed separately for each of the four uvby filters.
When
solved with k as free parameter, the convergence indicates an average value
,
but clearly correlated with the amount of third light L3 and
the orbital inclination i. Values of k ranging from 0.47 to 0.53, coupled with
the appropriate i and L3 values, provide equally good (minimum) residuals
between the synthetic and observed light curves.
After computing several grid solutions for fixed values of k and L3, we
have used the observed L3 values for y and b colours to
constrain the acceptable range in k. We found k=0.498 and 0.500 for y and
b filters, respectively, so we have finally adopted k=0.499 as the best
solution. L3 for v and y bands are obtained through the
convergence process with k fixed in that value.
Inferred photometric elements for each passband are presented in Table 4.
Good interagreement is found for the solutions in all colours. Table 5 lists
the adopted mean photometric elements for the eclipsing binary. Flux and
luminosity ratios given there correspond to the mean geometrical elements.
Quoted errors correspond to a realistic estimation of the uncertainties caused
by slight changes on the adopted input parameters.
The size of the secondary component is about half of the primary,
while the luminosity ratio indicates very dissimilar
components. The fractional radii are small, meaning in practice
that both stars have little oblateness (0.0025 for the primary
and 0.00095 for the secondary) and that this binary can be
considered as a detached system.
parameter | u | v | b | y |
J2/J1 | 0.122 | 0.129 | 0.194 | 0.249 |
4 | 3 | 3 | 4 | |
r1 | 0.1448 | 0.1443 | 0.1437 | 0.1433 |
10 | 8 | 8 | 12 | |
k(=r2/r1) | 0.499 | 0.499 | 0.499 | 0.499 |
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88.65 | 88.83 | 88.70 | 88.50 |
18 | 15 | 10 | 10 | |
u1 | 0.70 | 0.73 | 0.67 | 0.59 |
u2 | 0.95 | 0.90 | 0.85 | 0.76 |
y1 | 0.49 | 0.42 | 0.37 | 0.32 |
y2 | 0.66 | 0.56 | 0.49 | 0.42 |
Phase shift | -41 | -59 | -59 | -58 |
(10-5) | ||||
mag. quad. | 0.330 | 0.699 | 0.444 | 0.205 |
L1 | 0.974 | 0.971 | 0.957 | 0.946 |
L2 | 0.026 | 0.029 | 0.043 | 0.054 |
L3 | 0.101 | 0.100 | 0.116 | 0.119 |
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0.0080 | 0.0034 | 0.0032 | 0.0038 |
parameter | u | v | b | y | mean |
r1 | 0.1440 | ||||
20 | |||||
k(=r2/r1) | 0.499 | ||||
20 | |||||
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88.6 | ||||
0.5 | |||||
J2/J1 | 0.119 | 0.125 | 0.191 | 0.251 | |
L2/L1 | 0.026 | 0.029 | 0.044 | 0.058 |
Figure 2 shows the observed and calculated y light curve
together with the corresponding (O-C) residuals plotted against
the orbital phase. The (b-y) and (u-b) colour index variations are also shown.
No systematic trends are appreciable in the
(O-C) plots and the residuals correspond to the expected values from
the observational scatter typical of each colour.
Individual photometric uvby indices for each component, listed
in Table 6, are derived by using the joint indices out of
eclipses and the luminosity ratios at each bandpass as given in
Table 5. We must
point out that these indices, particularly m1 and c1,
may have some systematic effects due to the adopted third light and its
correlation with the other photometric elements.
The indices listed for the component 1 are compatible
with those obtained directly from observations at phase 0.5, during the
total secondary eclipse, where the combined light of L3 and the primary
eclipsing component is measured.
![]() |
Figure 2: y light curve and (b-y) and (u-b) colour index variations of V2154 Cyg-C1 together with the synthetic y light curve and residuals. |
Open with DEXTER |
A
value of 2
678 can be determined for the primary component of
the eclipsing pair assuming that the corresponding variation in (b-y) and
are identical.
This assumption is not valid for the secondary. By using the
Smalley & Kupka (1997) calibration, an effective temperature value of
T1=6700 K is found for the hotter component. Assuming a null reddening
(which is valid for the primary), a value of about T2=5000 K is derived
for the secondary component making use of the Kurucz (1993) and
Bell & Gustafsson (1989) calibrations.
This is consistent with a temperature difference of about 1800 K
derived from the surface flux ratios J2/J1
and the flux scale given by Popper (1980).
As for the visual companion V2154 Cyg B, the small separation
(0
47) and the common proper motions reported (Dommanget &
Nys 2000) may indicate that is gravitationally bound to the A star,
forming a
wide binary system. Then V2154 Cyg could be a triple system. This is not an
unusual configuration and several cases of eclipsing binaries being members of
triple or multiple systems have been described in the literature (e.g.,
Andersen et al. 1990; Van Leeuwen & Van Genderen 1997).
This association is
however not fully confirmed because the distance modulus derived from B-V
index of the B component, assuming null reddening, is not compatible with the
distance to the system of 88 pc measured by the Hipparcos satellite
(ESA 1997). Information about its radial velocity will help to better
solve
this contradiction. Although the luminosity ratio of the components of the
eclipsing pair is rather low, it might be detected also as a double-lined
spectroscopic binary by using high resolution and S/N ratio instrumentation.
In fact, the system may show three sets of lines due to the unavoidable
inclusion of the (also faint) B component within the slit of the
spectrograph.
If we consider that A and B constitute a wide pair at a distance of 88 pc,
the separation of 0
47 is equivalent to a minimum
separation of 41 AU. Assuming a total mass of about 3.5
for the
triple system and a circular orbit, we can obtain a minimum orbital period of
140 yr for the possible wide pair. With such a period, no third
light-time effect is noticeable within the span of our photometric
observations, but a long term monitoring of minima might allow to
measure it. Less straightforward, also long term optical interferometric
observations should provide the basic parameters of this wide orbit.
Since the radial velocity curves of V2154 Cyg are not available yet,
its absolute dimensions cannot be derived and the system cannot be
used as a reliable test to the evolution theory. However, it is
interesting to investigate the capability of prediction of stellar
models when only a few observational constraints are available. In this way,
we have used the stellar evolution code by Claret (1995) assuming the
solar chemical composition and a mixing-length parameter of 1.52.
The computations were carried out without mass loss.
By using as indicators the derived effective temperature
of the primary, mass ratio q and ratio of radii k
we have computed a series of couple of models. The results indicate that both
components are not too much evolved with masses of about
1.4 and 0.8
for
the primary and secondary, respectively. The inferred surface gravities are
consistent, within the present uncertainties, with the derived values of q
and k.
The above numerical experiment, though instructive, is not definitive
of course. Even considering the severe limitations to interpret
the evolutionary history of V2154 Cyg one interesting aspect should be
remarked: the mass range we are dealing. Clausen et al. (1999)
pointed out that the two components of a sample
of eclipsing binary systems in the mass range of 0.7-1.0
with
accurate absolute dimensions were not fitted by a single isochrone.
The "theoretical'' mass of the secondary falls just in this problematic
interval. It would be very interesting to obtain through
spectroscopic studies the absolute dimensions not only to test the
evolutionary models but also to check if the discrepancy in age is
also present in this system.
System (A+B) | Comp. 1 | Comp. 2 | Star B | |
V | 7
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7
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11
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10
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b-y | 0
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0
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0
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0
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m1 | 0
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0
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0
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0
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c1 | 0
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0
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0
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0
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2
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2
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- | - |
We present for the first time complete uvby light
curves for the recently discovered eclipsing binary system V2154 Cyg based in
simultaneous measurements collected in the four filters. Times of primary and
secondary minima are determined and an improved orbital period of
2
6306312 is found by means of frequency analysis. They are the only times
of minima available for this binary system up to date.
The behaviour of the light
curves indicates that the eclipses are complete, annular for the primary and
total for the secondary, being originated by two well-detached components with
very different surface brightnesses.
An analysis of the photometric
elements was carried out using the EBOP code.
The results show that V2154 Cyg is a
detached system with two late-type components very different in size (k=0.499)
and mass ratio of q=0.55 with T1=6700 K and T2=5000 K. Stellar evolution
models have been also used to gain some more insight about this system.
The results indicate that both components are not too much evolved with
masses of about
and
.
In order to obtain reliable absolute dimensions for the components of the system, the photometric elements determined in this paper should be supplemented by accurate spectroscopic parameters from radial velocity observations. Spectroscopic observations will provide basic information on this possible triple system and, in particular, on the interesting eclipsing binary formed by two late-type components, being the secondary a low-mass star, which light curves do not show significant evidences of wave-type distortions normally associated to stellar activity. Spectroscopic data would also be very interesting in order to check if a discrepancy in age is also present in this system.
Acknowledgements
This research was supported by the Junta de Andalucía and the Dirección General de Enseñanza Superior e Investigación Científica (DGESIC) under project PB98-0499. This research has made use of the Simbad database, operated at CDS, Strasbourg, France. We like to thank the referee for very helpful remarks.