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Peremennye Zvezdy (Variable Stars) 42, No. 6, 2022 Received 21 June; accepted 30 June. |
Article in PDF |
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DOI: 10.24412/2221-0474-2022-42-35-37
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Third Body in GSC 3937 2349, a New W UMa Variable
Igor Volkov1,2
- Sternberg Astronomical Institute, Moscow University,
Universitetsky Ave., 13, 119992 Moscow, Russia
- Institute of Astronomy of the Russian Academy of Sciences, Pyatnitskaya str., 48, 119017 Moscow, Russia
The analysis of minima timings of the newly discovered
W UMa variable GSC 3937 2349 (
 ,
 )
revealed the light time effect that can be assigned to the third
body in the system. Parameters of the third body orbit were
derived and its mass was estimated, which turned out to be
comparable to the mass of the components of the eclipsing system.
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The variable star GSC 3937 2349 was discovered and classified as
an EW eclipsing variable by Peter Frank and Wolfgang Moschner
during unfiltered CCD observations of V1049 Cyg (Moschner et al.,
2016). They derived the period of the variable and found the
amplitude of its light variation to be
for Min I and
for Min II in the instrumental system of their CCD
photometer. The amplitude of brightness variations of the star
seems to be somewhat too low for this class of stars and could
indirectly indicate the presence of an additional light source in
the system.
Recently, the same authors (Moschner et al., 2021) published a total of 46 minima timings that showed a deviation from the linear formula given in their first paper. The authors suggested the existence of the third body on a highly eccentric orbit or mass ejection from one of the components of the binary as the reason for the abrupt change of the period.
Based on the published observations, I assumed that LIght Time Effect (LITE) can explain the behavior of the O-C residuals. The model of a close binary system rotating in a circular orbit (phase of the secondary minimum is equal to 0.5) with a remote third component was adopted. In the absence of LITE, one can calculate times of minima as:
is initial epoch, 
is the cycle number, and 
is
the period of the eclipsing star, the same for primary and
secondary eclipses in present case. An additional delay or advance
due to LITE, for any observed eclipse, is given by the next
formula (Irwin, 1952, 1959):
, 
, 
, and 
are respectively the
semi-major axis, eccentricity, inclination, and periastron
longitude of the eclipsing pair's orbit around the third body,
while 
is the true anomaly of the position of the eclipsing
pair's mass center on the orbit and 
is the speed of light. The
transition time, 
, of the eclipsing pair's mass center from
the periastron point of its orbit and the orbital period, 
,
are other two parameters of equation (2) that come from the
definition of .
A simultaneous search for , , , , ,
, and was carried out by the least squares method.
As a result, it turned out that the observed pattern of the course
of O-C residuals can be represented with acceptable accuracy
within the framework of the adopted model. The orbit of the third
component turned out to be weakly elliptical, 
, with a
period of revolution 
years. If we accept a rough
estimation of the eclipsing pair mass,
, then
we get
; thus, the third component
turned out to be the most massive member of the triple system. If
it is an ordinary star, its luminosity should even exceed the
luminosity of the main components of the system. This may explain
the reduced depth of the minima discussed earlier. The obtained
and give the following linear formula:
 |
(3) |
The deviations of observed times of minima from this formula due
to LITE reach 
minutes. The corresponding plot is presented
in Fig. 1, upper panel. To get better precision, one needs to
substitute the parameters from Table 1 into eq. (2). After
subtraction of such corrections, one can obtain the plot presented
in the lower panel of Fig. 1. The mean error for a single time of
minimum is presented in the last line of Table 1.
 |
Fig. 1. Top: Phased plot of O-C residuals from eq. (1). The red curve corresponds to the third body's orbit. Bottom: Residuals after LITE subtraction. The earliest obtained data point, 6 years prior to the start of modern observations, is highlighted in blue. |
2MASS gives for the star
, indicating
under the assumption of zero interstellar reddening.
Earlier, we have already noted that the photometric parallax of a
star has little dependence on the interstellar extinction, see
Volkov et al.(2010). Therefore, taking the dereddened color index
as the first approximation, I estimated the distance to the system
by the indirect method (Volkov et al., 2017): 
pc,
which gives the interstellar reddening
from
Green et al. (2015). Thus, the dereddened color index is 
, and the spectrum of the star is K0, typical of W UMa stars.
| Elements | |
| (HJD), 2 400 000 + |
59240.0(5) |
| , days |
1421(1) |
| , degrees |
311.4(3) |
|
0.10(1) |
 , au |
1.39(1) |
 , days |
0.00084 |
Acknowledgements. I express my gratitude to Wolfgang Moschner, member of the BAV, who drew my attention to the problem. I would like to express my sincere appreciation to Dr. N.N. Samus for fruitful discussion.
This study was supported by a scholarship of Slovak Academic Information Agency SAIA.
References:
Green, G.M., Schlafly, E.F., Finkbeiner, D.P., et al., 2015, Astrophys. J., 810, 25
Irwin, J. B., 1952, Astrophys. J., 116, 211
Irwin, J. B., 1959, Astron. J., 64, 149
Moschner, W., Frank, P., and Bernhard, K., 2016, BAV Journal, 11, 1
Moschner, W., Frank, P., and Bernhard, K., 2021, BAV Journal, 59, 1
Volkov, I.M., Volkova, N.S., and Chochol, D., 2010, Astron. Rep., 54, 418
Volkov, I. M., Chochol, D., Grygar, J., et al.,, 2017, Contrib. Astron. Observ. Skalnate Pleso, 47, 29