PASJ: Publ. Astron. Soc. Japan 61, 499–502, 2009 June 25
c 2009. Astronomical Society of Japan.
An Orbital Period Investigation of the Solar-Type Overcontact Binary V700 Cygni
Fuyuan X IANG, Yongpo T IAN, Xia TAO, and Wenli X IE
Department of Physics, Xiangtan University, 411105 Xiangtan, Hunan, China
[email protected]
(Received 2008 July 14; accepted 2009 January 20)
Abstract
Orbital period changes of the solar-type contact binary V700 Cyg were investigated based on one new eclipse
time combined with the others collected from the literature. A cyclic oscillation, with a period of 39.1 yr and
an amplitude of 0.d 0197, was found to be superimposed on a secular period increase at a rate of dP =dt = +2.8
108 d yr1 . Weak evidence indicates that there exists another small-amplitude period oscillation. The long-term
period increase is in agreement with the conclusion that high-mass ratio W-type overcontact binaries usually show
period increasing. This suggests that it may be in the stage controlled by thermal relaxation oscillations. Cyclic
period oscillation can be explained as being the result of a light-travel time effect via the presence of an additional
body. On the other hand, since both components of V700 Cyg are late-type stars, the period oscillation may be
evidence of magnetic activity cycles of the two component stars.
Key words: stars: binaries — stars: eclipsing — stars: individual (V700 Cygni) — stars: magnetic activity
1. Introduction
V700 Cyg is a short-period (P = 0.d290633) W UMa-type
contact binary. The light variability of the system was discovered by Whitney (1952). After Whitney published the first
minimum times of the light, many authors also made visual,
photographic, photoelectric, and CCD observations (Romano
1969; Hoffmann 1983; Agerer & Hübscher 1995, 1997, 1999;
Niarchos et al. 1997). They presented many minimum timings
in the literature, which enable studying the change in the orbital
period. Qian et al. (2003a) collected all photoelectric and CCD
times of light minima of V700 Cyg published before 2001.
With a new linear ephemeris, they recomputed the O C
values of these times of light minima and concluded that the
orbital period of the system continuously increased at a rate of
dP =dt = +8.41 108 d yr1 .
Since then, some new CCD times of the light minima of
V700 Cyg have been published (e.g., Nelson 2003, 2005;
Dvorak 2005; Hübscher 2005; Hübscher et al. 2006; Kotková
& Wolf 2006; Zejda et al. 2006; Doǧru et al. 2007). This
indicates that the period change of the system needs to be
investigated in detail.
In order to study the period change in V700 Cyg, we
observed it. In section 2, we describe our observation. In
section 3, we calculate O C with the newer ephemeris
formula given by Kreiner et al. (2001) and present the results of
our analyses. Finally, in section 4 we discuss the mechanisms
that may cause changes in the period.
Cassegrain focus, and the size of each pixel was 0:0038. During
the observation, the R filters used are close to the standard that
of Johnson UBVRI system (Yang & Li 1999). The integration
time for each image was 60 s. The coordinates of V700 Cyg,
a comparison star, and a check star are listed in table 1. PHOT
(measure magnitudes for a list of stars) of the aperture photometry package of the IRAF1 was used to reduce the observed
images. The resultant light curve is shown in figure 1. By
using a parabolic fitting method, we determined one time of
light minimum, HJD 2453963.3488 ˙ 0.0001. We used the
light curve in figure 1 in the range of Δm.R/ > 0.9 mag for
determining the eclipse time.
3. Orbital Period Variations of V700 Cyg
Times of light minimum of V700 Cyg published before
2001 were compiled by Kreiner et al. (2001; M. J. Kreiner’s
private communication). Some times of light minimum were
published recently by Doǧru et al. (2007), Zejda et al. (2006),
Hübscher et al. (2006), and Kotkova and Wolf (2006). The
.O C /1 curve computed with the ephemeris given by Kreiner
et al. (2001),
Min. I = 2445207:5126 + 0:29063138 E;
Table 1. Coordinates of V700 Cyg, the comparison, and the check
stars.
˛2000
Star
V700 Cyg
The comparison
The check
2. New CCD Photometric Observations for V700 Cyg
CCD photometric observations of the W UMa-type binary
V700 Cyg were carried out on 2006 August 15 with a PI1024
TKB CCD photometric system attached to the 1.0-m reflecting
telescope at Yunnan Observatory. The effective field of view
of the CCD photometric system was about 6:0 5 6:0 5 at the
(1)
1
h
m
ı2000
s
20 31 05: 3
20h 31m07:s 1
20h 31m01:s 8
ı
38 470 01:005
38ı 470 07:003
38ı 460 19:003
IRAF is distributed by the NOAO, which are operated by the Association of
the Universities for Research in Astronomy, Inc., under cooperative agreement with the NSF.
500
F.-Y. Xiang et al.
Fig. 1. CCD photometric light curves in the R band of V700 Cyg
obtained on 2006 August 15. Those open circles are the magnitude
difference between the comparison and check stars. The filled circles
are the magnitude difference between V700 Cyg and the comparison
star.
is displayed in figure 2, where open circles refer to visual
and photographic data and solid dots to photoelectric or CCD
(hereafter “PC”) observations. It is revealed in the figure that
the change in the orbital period of V700 Cyg may be continuous, and that the variation is very complex. There may
exist a sinusoidal variation that is superimposed on a secular
period increase. This type of period variation, periodic change
superimposed on a secular period change, is not unusual for
W UMa-type binary stars. Some other examples recently
studied are V839 Oph (Akalin & Derman 1997), CK Boo
(Qian & Liu 2000), YY Eri (Kim et al. 1997), V417 Aql (Qian
2003b), RZ Com (Qian & He 2005), BX Peg (Lee et al. 2004),
FG Hya (Qian & Yang 2005), CE Leo (Kang et al. 2004; Qian
2002a), GR Vir (Qian & Yang 2004), AK Her (Awadalla et al.
2004), ER Ori (Kim et al. 2003), XY Leo (Yakut et al. 2003),
IK Per (Zhu et al. 2005), AH Cnc (Qian et al. 2006), AP Leo
(Qian et al. 2007a), UX Eri (Qian et al. 2007b), TY Boo
(Yang et al. 2007), AD Cnc (Qian et al. 2007c), and BI Cvn
(Qian et al. 2008). Therefore, a sinusoidal term was added
to a quadratic ephemeris to obtain a good description of the
.O C /1 data (solid line in figure 2). By assigning a weight
of 1 to the photographic observations and 10 to the PC data,
a least-squares solution yields the following equation:
.O C /1 = 0:0106.˙0:0017/
+1:5.˙0:6/ 107 E + 1:1.˙0:3/ 1011 E 2
+0:0197.˙0:0021/
sin Œ0.ı 0073.˙0:0002/ E + 31.ı9.˙3.ı 4/:
(2)
The quadratic term in equation (2) indicates a long-time period
decrease at a rate of dP =dt = +2.8 108 d yr1 . The
sinusoidal term in equation (2) suggests a cyclic oscillation
with a period of P3 = 39.1 (˙1.1) yr and an amplitude of A3
= 0.0197(˙0.0021), which is more easily seen in figure 3,
where the .O C /2 values from the quadratic part of equation (2) are displayed and the solid line in the figure represents
a fit by the periodic term in equation (2).
A least-squares solution to the residuals of all PC data leads
to the following equation:
[Vol. 61,
Fig. 2. .O C /1 curve of V700 Cyg from the linear ephemeris given
by Kreiner (2001). Open circles refer to visual or photographic observations and solid dots to CCD or photoelectric data. The solid line in
the upper panel represents the combination of a secular period increase
and a cyclic variation. The dashed line refers to the quadratic part in
equation (2). Residuals of .O C /1 with respect to the whole effect
of equation (2) are also displayed in the lower panel. Weak evidence
indicates that there exists a small-amplitude oscillation in the orbital
period (solid line).
Fig. 3. .O C /2 diagram of V700 Cyg after the continuous period
increase is removed. The solid line is its fit by the sinusoidal term in
equation (2). The symbols are the same as those in figure 2.
Re = 0:0012.˙0:0002/
+0:0031.˙0:0004/
sinŒ0.ı 0115.˙0:0007/ E + 208.ı3.˙3.ı 9/;
(3)
which indicates a small-amplitude periodic change with
a period of P4 = 25.0 (˙1.5) yr and an amplitude of A4
= 0.0031 (˙0.0004). However, to check this small-amplitude
periodic change, the system needs long-term photometric
monitoring for high precision eclipse times.
4. Discussions and Conclusions
The general O C trend of V700 Cyg reveals a longterm continuous period increase at a rate of dP =dt = +2.8
108 d yr1 . This kind of period increase can be explained
No. 3]
Orbital Period of the Solar-Type Overcontact Binary V700 Cyg
as being the result of mass transfer from the less massive
component to the more massive one. Assuming a conservative mass transfer, we can estimate that the mass transfer rate
is dM2 =dt = 7.33 108 Mˇ yr1 by using equation (5)
of Kwee (1958). Based on the period changes of 30 W-type
contact binary stars, Qian (2001a) found that systems showing
a period increase usually have a higher mass ratio (q = M2 =M1
> 0.4, where M1 and M2 denote the mass of the primary and
secondary components of the binary), while the periods of lowmass ratio systems (q = M2 =M1 < 0.4) are varying in a secular
decrease. This conclusion was later expanded by Qian (2003a)
to both W- and A-type contact binaries, who gave the relations
between the period variation and the mass ratio and the orbital
period. The long-term period increase of V700 Cyg is in agreement with the conclusions of Qian (2001a, 2003a).
Secular period variations, both decreasing and increasing,
are common for W UMa-type stars. To interpret these changes,
an evolutionary scheme was originally proposed by Qian
(2001a), in which contact binaries are undergoing thermal
relaxation oscillation (TRO) (e.g., Lucy 1976; Flannery
1976; Robertson & Eggleton 1977) with a variable angular
momentum loss (AML) via a change in the degree of contact.
This evolutionary scenario was later supported by the period
changes of early-type contact binaries and near-contact binary
stars (Qian 2001b, 2002b). Qian (2003a) obtained some
statistical relations of contact binaries, and pointed out that
the combination of the TRO and the variable AML should
drive W UMa-type binaries to oscillate around a critical mass
ratio, while the critical mass ratio varies with the mass of
the primary component. The long-term period increase may
suggest that V700 Cyg is in the TRO-controlled stage of this
evolutionary scheme.
After the continuous period increase was removed from the
.O C /1 diagram, the .O C /2 curve in figure 3 revealed
a periodic oscillation.
Since V700 Cyg is such a short-period system, the variation
of .O C /2 can not be explained as apsidal motion. The period
oscillation of the system may be caused by a light-travel time
effect of a third companion.
The orbital period of the third body rotating around the
eclipsing pair is about 39.1 yr. However, since early data
were observed visually and photographically, which show large
scatter, information on the orbital eccentricity of the third body
is not clear.
By considering that the third body is moving in a circular
0
orbit and using a12
sin i 0 = A c, where i 0 is the inclination
of the orbit of the third component and c is the speed of light,
0
0
a12
sin i 0 was calculated to be a12
sin i 0 = 3.4(˙0.4) AU.
Then, a computation with
4 2
0
.a12
sin i 0 /3
(4)
GT 2
yields a small mass function of f .m/ = 2.6(˙0.8) 102 Mˇ
for the assumed companions. With the absolute parameters,
M1 = 0.92 Mˇ, M2 = 0.60 Mˇ, R1 = 1.04 Rˇ, R2 = 0.86 Rˇ,
determined by Niarchos et al. (1997), a calculation using
f .m/ =
f .m/ =
.M3 sin i 0 /3
;
.M1 + M2 + M3 /2
ΔQ
ΔJ
ΔE
ΔΩ=Ω
ΔT
B
Primary
Secondary
3.85 (˙0.41) 10
1.48 (˙0.16) 1047
5.75 (˙1.19) 1039
0.000155 (˙0.000016)
1.49 (˙0.16) 1043
7.73 (˙0.62)
49
(5)
yielded the lower limit of the third body’s mass, M3
> 0.47 ˙ 0.06 Mˇ, and the upper limit of its orbital radius, A3
< 11.07 ˙ 1.18 AU.
V700 Cyg is a solar-type binary. The cyclic period changes
may be caused by magnetic activity cycles of the components. To explain a quasi-periodic orbital period changes
in binaries containing at least one convective star, Applegate
(1992) suggested a theory that invokes possible magnetic
cycles. Subsequently, Lanza et al. (1998, 2002) improved it.
According to this model, while the star goes through its activity
cycle, a certain amount of angular momentum is periodically
exchanged between the inner and outer parts of the convection
zone. Thus, the rotational oblateness of the star also changes.
The change of rotational oblateness is transferred to the orbit
by gravity, which causes an orbital period variation.
With the absolute parameters obtained by Niarchos et al.
(1997), we can calculate the separation to be a = 2.12 Rˇ by
using Kepler’s third law. If the period of the magnetic activity
cycle is P = 39.1 yr, the value of the amplitude, ΔP , of the
orbital period modulation can be computed by the formula
ΔP = 2APe =T , where A, Pe , and T are the amplitude of
O C , the ephemeris period and the modulation period. The
computed result is ΔP = 2.52 106 d. With the model of
Lanza et al. (1998, 2002) and the above parameters, the corresponding results were obtained, and are shown in table 2. In
this table, ΔQ is the required quadrupole moment, ΔJ is
the angular-momentum transfer, ΔE is the energy required to
transfer the angular momentum, ΔΩ=Ω is the variation of the
differential rotation, ΔT is the variation of the kinetic energy,
and B is the mean subsurface magnetic field.
In summary, by means of an analysis of the O C curve,
we have found that the period of V700 Cyg contains a secular
increase with a rate of dP =dt = +2.8 108 d yr1 , while it
undergoes oscillaton with a period of 39.1 yr and an amplitude
of about 0.0197 d. The increase in the period may be caused
by mass transter between the two components, and the period
oscillation of the system may be due to the light-travel time
Table 2. Values of parameters mentioned in the magnetic activity cycle mechanism.
Parameters
501
Unit
9.48 (˙1.01) 10
3.66 (˙0.39) 1046
3.48 (˙0.74) 1038
0.000038 (˙0.000004)
3.66 (˙0.39) 1042
4.80 (˙0.45)
48
g cm2
g cm2 s1
erg
—
erg
kG
502
F.-Y. Xiang et al.
effect of a third companion, or magnetic activity cycles of the
components, or both. In orde to check this conclusion, more
accurate epochs of the minimum light are need.
This work is partly supported by Scientific Research Fund
of Hunan Provincial Education Department (No. 08A072),
Chinese Natural Science Foundation (No. 10878012) and
Xiangtan University Natural Science Foundation (No.
07QDZ25). New observations of the system were obtained
with the 1.0-m telescope at Yunnan Observatory. The authors
thank the referee for useful comments and suggestions that
help to improve the original manuscript.
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