close

Вход

Забыли?

вход по аккаунту

?

1538-3873%2Faa8bb0

код для вставкиСкачать
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
https://doi.org/10.1088/1538-3873/aa8bb0
© 2017. The Astronomical Society of the Pacific. All rights reserved. Printed in the U.S.A.
Is There a Substellar Object Orbiting the Solar-like Stable
Contact Binary V2284 Cyg?
1
2
J.-J. Wang1, L.-Q. Jiang2, B. Zhang3, S.-Q. Zhao1, and J. Yu1
China University of Petroleum–Beijing at Karamay, Anding Road 355, 834000 Karamay, China; 2016592016@cupk.edu.cn
School of Physics and Electronic Engineering, Sichuan University of Science Engineering, 643000 Zigong, China; jianglinqiao11@163.com
3
Yunnan Observatories, Chinese Academy of Sciences, P.O. Box 110, 650216 Kunming, China
Received 2017 June 29; accepted 2017 September 11; published 2017 October 24
Abstract
V2284 Cyg is a neglected W UMa-type binary star for photometric investigations. Monitored by the Kepler Space
Telescope from 2009 to 2013, its light curves are continuously stable, suggesting that both components are inactive
during this time interval. Based on the short-cadence observations, we determined the photometric solutions by
using the 2013 version of the Wilson-Devinney code. These parameters reveal that V2284 Cyg is a W-type system
with a degree of contact factor of f=39.23% and a mass ratio of q=2.90. Meanwhile, hundreds of times of
minimum light were obtained and applied to analyze the orbital period changes. In the O-C diagram, a smallamplitude cyclic oscillation (A3=0.00030 days and T3=2.06 years) superimposed on a secular decreasing was
found. The continuous decreasing may be a result from the mass transfer from the more massive component to the
less massive one. With the long-term decreasing of the orbital period, this binary will evolve into a deeper contact
system. Because the light curve is stable, the cyclic variation is plausibly explained as the light-travel time effect
(LTTE) due to the presence of an additional body. The mass of the companion is M3 sin i¢ = 0.036 ( 0.003) M. If
the orbital plane inclination is a random distribution, it is a brown dwarf with 66.7% probability. Therefore, the
companion of V2284 Cyg is possibly the first candidate of the brown dwarf orbiting around contact binary, where
both component are sharing a common convective envelope.
Key words: (stars:) binaries (including multiple): close – stars: solar-type – stars: evolution
Online material: color figure
et al. 2000). Blättler & Diethelm (2000) published one light
curve without filter, which belonged to the typical EW type. Its
range of light curve variability is 12 m. 71–13 m. 45 in the V–band
given by Kazarovets et al. (2003). The VIc light curves with
larger scatter were obtained from the All Sky Automated
Survey 3-North station (Pigulski et al. 2009). Until 2013, the
high-precision Kepler space mission of V2284 Cyg spanned
about more than 1400 days with long-cadence exposure and
22.3 days of with short cadence. The spectral type of this
binary system was identified as G7 from the LAMOST spectra
of some EW-type binaries (Qian et al. 2017). In this paper, we
use the Kepler data of V2284 Cyg to understand its orbital
period changes, configuration, and evolution.
1. Introduction
The Kepler space mission is designed to continuously
observe more than 150,000 stars to accomplish the science goal
of detecting Earth-size planets around those stars. Based on the
high-precision Kepler photometry, stars orbiting the eclipsing
binaries are found in some systems, i.e., HD 181068 (Derekas
et al. 2011) and KOI-126 (Carter et al. 2011). Borkovits et al.
(2013) measured eclipse timing variations (ETVs) of close
binary HD 181068 from the Kepler observations to prove the
cyclic variation of O-C curve result from the gravitational
perturbations of the third body. Meanwhile, as discussed in
some binaries, e.g., IK Per (Zhu et al. 2005), AD Cnc (Qian
et al. 2007b), RZ Com (Qian & He 2005), DD Com (Zhu
et al. 2010), GSC 03526-01995 (Liao et al. 2012), and XY LMi
(Qian et al. 2011b), their light curves in different seasons
indicate that there are stellar dark spots on the surface of at least
one component. The Kepler Space Telescope provides a good
chance to understand the third body, magnetic activity of close
binaries in unbroken time.
V2284 Cyg (KIC 11245381) was discovered by the Robotic
Optical Transient Search Experiment (ROTSE-I) (Akerlof
2. Observation
The continuous Kepler photometric data of V2284 Cyg with
long-cadence mode (LC; one point every 29.4 min) covers over
1400 days from quarter 0 to 17. The short-cadence (SC; one
point every 30 seconds) data spans 22.3 days in 2013, only
one-quarter 17. All data are available athttp://archive.stsci.
edu/pub/kepler/. In these Kepler data, the header keyword
“SAP-QUALITY” refers to the trustworthiness of each
1
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
observation. If the “SAP-QUALITY” flag is equal to zero, then
the observation is good. We analyze all good data and convert
pdcsap-flux into magnitudes with Mag = -2.5 ´ log Flux .
The photometric error for individual observation is less than
0.001 mag.
With the linear ephemeris equation from the website of
Kepler Eclipsing Binaries ,
Min. I (BJD) = 2454953.641745 + 0 d. 3069920 ´ E ,
Wang et al.
the orbital period without changes in three days, when the other
observational points are far away from the median more than
half period, plus or minus the times of the orbital period
(P = 0 d. 3069920 ) are applied for moving these points into the
new periodic light curves around the median point, e.g., when
the BJD of these observations off the medians point are
0.5∼1.5 times period, then minus one period; −2.5∼−1.5
times period off the median, plus two times period. These
corrected points are shown in the graph in the bottom of
Figure 3, and show nicely the shape of the light curve of V2284
Cyg. After that, the part of these points (the gray circles) are
used for deriving the times of light minimum (×) with
secondary polynomial fitting (lines). Through means of the
above method, hundreds of times of minimum light are
determined from long-cadence data. Meanwhile, we also obtain
some times from short-cadence data. All times from Kepler
data are listed in Tables 1–3.
We combined these times of light minimum and those
collected from O-C gateway (http://var.astro.cz/ocgate/) to
analyze O–C changes. To compute the (O - C )1 values with
the ephemer Equation (1), the Heliocentric Julian Date (HJD)
in O-C gateway are converted into the BJD (Dai et al. 2010).
The corresponding O-C diagram is plotted in the upper panel of
Figure 4, where the filled circles refer to the primary times of
minimum light, the open circles to the secondary ones.
To describe the trend of the O-C curve well, a periodic term
superposed on the secular decrease is required:
(1 )
the Kepler light curves along with their magnitudes and phases
are displayed in Figure 1, where these curves in five successive
years (2009 to 2013) are obviously stable. We also found the
light curves of V2284 Cyg are typical EW type and symmetric,
properties that reveal both components have similar
temperature.
Significantly, the short-cadence data have been available
since 2013 December 5, and this one month of data contains
nearly 50% as many points as the 5 years of long-cadence data.
More importantly, the time resolution is higher. With an orbital
period of only 7.4 hours, only 15 points per eclipse were
obtained from the long-cadence observation, but the shortcadence data provide hundreds of points per eclipse. The
unbroken short-cadence light curves along with their magnitude and BJD times are plotted in Figure 2, which confirmed
that the components are continuously stable in 22.3 days. The
light curves with SC mode in the last panel of Figure 1 are
nearly the same as LC mode ones in the other panels. This
phenomenon suggest V2284 Cyg is a truly stable binary star
from 2009 to 2013.
Min. I (BJD) = 2454953.64249 (  0.00003)
+ 0 d. 30699175 (  0.00000001) ´ E
- 1.83 (  0.16) ´ 10-11 ´ E 2
+ 0.00030 (  0.00003) sin [0 . 146676 ´ E
+ 85 . 96 (  5 . 18)].
3. Times of Minimum Light and Orbital
Period Changes
The continuous Kepler photometric data of V2284 Cyg with
LC mode covers over 1400 days from 2009 to 2013. From the
upper panel of Figure 3, the LC photometric readouts are coadded for 29.4 min, about 15 points were obtained for one
complete period (P = 0 d. 3069920) of V2284 Cyg, and cannot
outline the features of eclipse. Thus, the lower time-resolutions
data are difficult to determine the high-precision times of
minimum light. Is such a large amount of LC data not used in
computing the times of minimum light? Traditionally, the
eclipse times are determined with the normal continuous
observations of one complete eclipse. Therefore, we assumed
that the orbital period does not change in three days; successive
144 observations make up of one periodic light curves with
clear shape in the bottom of Figure 3. In this way, all LC data
can be divided into many time segments to compute the eclipse
times.
In the process of analyzing one segment, we find the
Barycentric Julian date (BJD) of the median point of these data
in continuous three days; this median is displayed as the gray
circle in the upper panel of Figure 3. Second, due to assuming
(2 )
The quadratic term in Equation (2) indicates a long-term period
decrease at a rate of dP dt = -4.35 ( 0.39) ´ 10-8 d yr−1.
The cyclic oscillation is shown in the middle panel of Figure 4,
which reveals a periodic variation with a small amplitude of
A3=0.00030 days and a short period of T3 = 2.06 yr . The
residuals with this Equation (2) are plotted in the bottom panel
of Figure 4.
4. Photometric Solutions with the
Wilson-Devinney Program
As those observed in some W UMa-type binaries such as AL
Cas (Qian et al. 2014b), LU Lac (Liao et al. 2014), AP Leo
(Qian et al. 2007a), and EM Psc (Qian et al. 2008c), the light
curves of V2284 Cyg are symmetric, which is very useful to
determine reliable photometric parameters. The 2013 version
of Wilson-Devinney program (Wilson & Devinney 1971;
Wilson 1979, 1990; Van Hamme & Wilson 2007; Wilson 2008;
Wilson et al. 2010; Wilson 2012) has expanded the previous
2
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
Figure 1. Kepler light curves of V2284 Cyg in successive five years. The crosses (+) refer to the observations in which errors are individually less than 0.001mag.
3
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
According to spectral type G7 (Qian et al. 2017) and
logG = 4.303, it is inferred that star 1 is in main sequences
with 5568K (Cox 2000). The eclipse depths at both minima are
similar, which indicates that the temperatures of the components are close to each other. Considering the convective
atmospheres of the late-type components, we took the same
values of the gravity-darkening coefficients and the bolometric
albedo, i.e., g1 = g2 = 0.32 (Lucy 1967) and A1 = A2 = 0.5
(Ruciński 1969) into our computing. The bolometric logarithmic law (LD=−1) was introduced into differential corrections program to calculate the limb-darkening coefficients. We
use the high-resolution, short-cadence light curves as shown as
the last panel of Figure 1 to analyze the configuration of
V2284 Cyg.
The mass ratio of V2284 Cyg were still not published, thus
the q-search method was used to determine the mass ratio.
Many sets of solutions are derived with mass ratio from 0.20 to
4.40 with step 0.01. The relation between the resulting sum (Σ)
of weighted square residuals and mass ratio (q) is displayed in
Figure 5. In q-search, the suitable mass ratio converged at
q=2.71 for the minimum residuals. Therefore, we chose the
initial value of the mass ratio q as 2.71, and made the mass ratio
an adjustable parameter to perform the differential corrections.
The converged parameters are listed in Table 4; the mass ratio
and the temperature indicates that V2284 Cyg is a W-type
contact binary. The theoretical light curve in Figure 6 gives
complete eclipses, which suggests that the q-search give a
reliable mass ration (Terrell & Wilson 2005).
Figure 2. Part of the Kepler short-cadence observations in some times. The dot
refer to the observations in which errors are individually less than 0.001mag.
5. Discussion and Conclusion
W UMa-type binary stars are usually monitored by groundbased telescopes. The light curves of some contact binaries,
such as CSTAR 038663 Qian et al. (2014a), CU Tau (Qian &
Yang 2005), EQ Tau (Li et al. 2014), UX Eri (Qian
et al. 2007c), CW Cas (Wang et al. 2014), and BI CVn (Qian
et al. 2008b) are variable on the timescale of days, months, and
years. These variations are evidence of magnetic activity on the
stellar photosphere of the components. On the other hand, the
light curves of some contact binaries do not have the obvious
variations, e.g., GSC 0763-0572 (Wang et al. 2012), RT Lmi
(Qian et al. 2008d), BO CVn, and SS Com (Qian & Zhu 2006),
which indicates that the activities of the component may be
stable. However, due to the lack of continuous and unbroken
timeseries photometry, stable binaries are doubtful. The Kepler
Space Telescope provides the opportunity to understand the
stable binaries, V2284 Cyg is our target star. Compared with
the Kepler long-cadence observations from 2009 to 2013, there
are no changes over the interval of years. The unbroken 22.3
days short-cadence light curves shown in Figure 2 are without
changes and are nearly the same as the long-cadence ones.
Figure 3. Part (continuous 144 points) of the light curve of V2284 Cyg as an
example. Upper panel: the LC continuous 144 points from the Kepler mission.
The gray circle indicates the median of these points. Bottom panel: the black
circles refer to the points merged 144 points into a period, the gray circles
represent the part of 144 points to calculate the times of minimum light by
using the quadratic function. The line is the quadratic fitting and the×is the
positions of times of light minimum.
25 photometric bands up to 93, including the Kepler–band. The
W-D code still does not need to input limb-darkening
coefficients by band; negative control integer LD is for
internally calculating the limb-darkening coefficients by
subroutine LIMDARK. The program itself output them by
the Light Curve program, which is based on the limb-darkening
tables calculated with the method of Van Hamme (1993).
4
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
Table 1
Times of Light Minimum from Kepler Data
Times
2456392.3586718
2456392.5123448
2456392.6656818
2456392.8194331
2456392.9726642
2456393.1264825
2456393.2796834
2456393.4335778
2456393.5867304
2456393.7404222
2456394.0473889
2456394.3544041
2456394.5076448
2456394.6612635
2456394.8146124
2456394.9683741
2456395.1215460
2456395.2751942
2456395.4285697
2456395.5824412
2456395.7355784
2456395.8893660
2456396.0425520
2456396.1963570
2456396.3495460
2456396.5032774
2456396.6565524
2456396.8104274
2456396.9635676
2456397.1173903
2456397.2706017
2456397.4243723
2456397.5775942
2456397.7311062
2456397.8846092
2456398.0382675
2456398.1915836
2456398.3453752
2456398.4985606
2456398.6523105
2456398.8055639
2456398.9593891
2456399.1126024
2456399.2663347
2456399.4195248
2456399.5733010
2456399.7265407
2456399.8802884
2456400.0335672
2456400.1872809
2456400.3405492
2456400.4943262
2456400.6475338
2456400.8013016
2456400.9545096
2456401.1082885
2456401.2615410
2456401.4152481
2456401.5685465
Errors
Times
Errors
Times
Errors
Times
Errors
0.000044
0.000087
0.000054
0.000090
0.000040
0.000090
0.000055
0.000133
0.000068
0.000092
0.000061
0.000080
0.000053
0.000085
0.000042
0.000074
0.000038
0.000102
0.000034
0.000088
0.000033
0.000091
0.000035
0.000096
0.000038
0.000091
0.000033
0.000126
0.000038
0.000110
0.000034
0.000111
0.000035
0.000094
0.000036
0.000092
0.000044
0.000149
0.000045
0.000098
0.000036
0.000135
0.000034
0.000112
0.000037
0.000110
0.000034
0.000095
0.000035
0.000104
0.000038
0.000144
0.000039
0.000135
0.000042
0.000138
0.000036
0.000133
0.000033
2456405.2525259
2456405.4061130
2456405.5595198
2456405.7131171
2456405.8664742
2456406.0200756
2456406.1734958
2456406.3270706
2456406.4804683
2456406.6341278
2456406.7874225
2456406.9410460
2456407.0944260
2456407.2482149
2456407.4014375
2456407.5549787
2456407.7084689
2456407.8618636
2456408.0154611
2456408.1692136
2456408.3224503
2456408.4757984
2456408.6296317
2456408.7828549
2456408.9364006
2456409.0902112
2456409.2433837
2456409.3971860
2456409.5503687
2456409.7041062
2456409.8573456
2456410.0110758
2456410.1643682
2456410.3181822
2456410.4713624
2456410.6250923
2456410.7783363
2456410.9319391
2456411.0853932
2456411.2391541
2456411.3923653
2456411.5462371
2456411.6993834
2456411.8531855
2456412.0063721
2456412.1601576
2456412.3133697
2456412.4668810
2456412.6203669
2456412.7737679
2456412.9273310
2456413.0811637
2456413.2343190
2456413.3879328
2456413.5413008
2456413.6948683
2456413.8482977
2456414.0020453
2456414.1552560
0.000032
0.000095
0.000033
0.000101
0.000036
0.000094
0.000034
0.000086
0.000033
0.000091
0.000035
0.000089
0.000031
0.000122
0.000035
0.000085
0.000034
0.000092
0.000031
0.000128
0.000033
0.000108
0.000117
0.000102
0.000035
0.000126
0.000032
0.000114
0.000032
0.000099
0.000032
0.000088
0.000035
0.000109
0.000031
0.000094
0.000035
0.000074
0.000033
0.000103
0.000038
0.000112
0.000034
0.000111
0.000037
0.000096
0.000034
0.000087
0.000033
0.000118
0.000038
0.000124
0.000034
0.000081
0.000032
0.000099
0.000030
0.000095
0.000038
2454992.9375646
2454993.0904610
2454995.3935370
2454995.5462922
2454997.3886961
2455003.9890801
2455004.1415948
2455006.4447241
2455006.5981672
2455008.9002430
2455011.3566276
2455013.8125914
2455018.5709358
2455021.0271081
2455023.4843910
2455023.6359641
2455025.9384110
2455026.0927482
2455028.3937477
2455028.5484329
2455030.8502151
2455033.4599487
2455035.9154050
2455038.3718886
2455038.5250720
2455040.8279552
2455040.9803726
2455043.2838216
2455043.4365554
2455045.7393695
2455045.8931520
2455048.1949484
2455048.3496705
2455050.8048710
2455053.2601014
2455053.4143204
2455055.7159010
2455055.8704850
2455058.4797587
2455058.6330609
2455061.0886715
2455064.7724500
2455067.0748990
2455067.2292750
2455069.5314197
2455069.6850162
2455071.9876439
2455072.1406013
2455074.5962695
2455077.0528106
2455079.6617233
2455081.9648742
2455082.1178993
2455084.5742712
2455087.0306290
2455090.2533612
2455090.4065656
2455094.3978997
2455094.5513236
0.000921
0.000160
0.000417
0.000635
0.000893
0.000488
0.000083
0.000107
0.000041
0.000052
0.000105
0.000278
0.000006
0.000238
0.000514
0.000053
0.000047
0.000062
0.000080
0.000145
0.000122
0.000274
0.000055
0.000023
0.000057
0.000051
0.000076
0.000075
0.000120
0.000050
0.000108
0.000073
0.000290
0.000037
0.000054
0.000072
0.000084
0.000061
0.000056
0.000043
0.000048
0.000230
0.000043
0.000120
0.000128
0.000064
0.000139
0.000031
0.000045
0.000011
0.000044
0.000051
0.000110
0.000165
0.000326
0.000318
0.000206
0.000162
0.000872
2455135.9966412
2455138.4518131
2455140.9077496
2455143.3634777
2455145.8193863
2455145.9729815
2455148.2757016
2455148.4288593
2455150.7313282
2455150.8848550
2455153.1869175
2455153.3412149
2455157.7920374
2455157.9458093
2455160.2483019
2455160.4016322
2455162.7040049
2455165.1596790
2455167.7697477
2455170.2253635
2455172.6815284
2455177.5929582
2455177.7467404
2455180.0497802
2455180.2024738
2455186.6501454
2455189.1054544
2455189.2591915
2455191.5613555
2455191.7152998
2455194.0176142
2455194.1713044
2455196.4733666
2455196.6267402
2455198.9299597
2455199.0824110
2455201.3855030
2455201.5388142
2455203.9943315
2455206.4495731
2455206.6035129
2455208.9065205
2455209.0601744
2455211.3620901
2455211.5165607
2455213.8182632
2455213.9721914
2455217.1967605
2455217.3481154
2455222.2605350
2455224.7170982
2455224.8700095
2455227.1729920
2455236.0759719
2455236.2284472
2455238.6847850
2455241.1403931
2455243.5955226
2455246.0524054
0.000522
0.000149
0.000275
0.000789
0.000039
0.000101
0.000472
0.000572
0.000142
0.000966
0.000216
0.000869
0.000038
0.000109
0.000595
0.000432
0.000218
0.000118
0.000508
0.000144
0.000459
0.000056
0.000097
0.000561
0.000509
0.000415
0.000094
0.000057
0.000329
0.000746
0.000929
0.000325
0.000041
0.000131
0.000429
0.000623
0.000117
0.000067
0.000976
0.000078
0.000681
0.000136
0.000037
0.000622
0.000485
0.000997
0.000169
0.000552
0.000262
0.000091
0.000387
0.000732
0.000107
0.000615
0.000364
0.000935
0.000060
0.000047
0.000164
5
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
Table 1
(Continued)
Times
2456401.7222723
2456401.8755220
2456402.0292360
2456402.1824786
2456402.3361961
2456402.4895124
2456402.6432121
2456402.7965345
2456402.9502223
2456403.1036029
2456403.2568934
2456403.4105308
2456403.5641944
2456403.7175489
2456403.8711672
2456404.0245298
2456404.1781642
2456404.3315107
2456404.4852985
2456404.6385216
2456404.7919953
2456404.9455176
2456405.0991583
Errors
Times
Errors
Times
Errors
Times
Errors
0.000125
0.000034
0.000107
0.000034
0.000088
0.000033
0.000123
0.000032
0.000119
0.000031
0.000101
0.000036
0.000112
0.000028
0.000100
0.000033
0.000098
0.000033
0.000138
0.000032
0.000088
0.000029
0.000105
2456414.3087910
2456414.4622611
2454954.7153049
2454954.8703365
2454957.1720290
2454957.3262162
2454959.7819831
2454962.0834029
2454962.2377306
2454965.6147461
2454965.7682453
2454968.2239665
2454970.6798696
2454973.1359697
2454975.5912121
2454978.0479659
2454980.5037982
2454980.6578094
2454982.9597910
2454983.1137013
2454985.4158628
2454985.5694830
2454988.0256241
0.000096
0.000031
0.000729
0.000664
0.001006
0.000285
0.000068
0.000169
0.000391
0.000037
0.000102
0.000399
0.000854
0.000099
0.000049
0.000171
0.000299
0.000779
0.000891
0.000347
0.000053
0.000070
0.000402
2455096.8533397
2455097.0078728
2455099.4629239
2455101.9193136
2455102.0726680
2455104.5292102
2455106.9845255
2455109.4403513
2455109.5946116
2455111.8964342
2455112.0505984
2455115.2742250
2455117.7284632
2455120.1851606
2455120.3391623
2455122.6406079
2455122.7961039
2455126.1722434
2455128.4744753
2455128.6279257
2455130.9302625
2455131.0839301
2455133.5399931
0.000289
0.000718
0.000049
0.000097
0.000059
0.000663
0.000204
0.000291
0.000735
0.000912
0.000297
0.000756
0.000051
0.000110
0.000038
0.000325
0.000603
0.000131
0.000780
0.000251
0.000330
0.000796
0.000063
2455248.6622915
2455251.1173324
2455251.2711086
2455253.5739472
2455253.7271574
2455256.0295121
2455256.1833139
2455258.6390257
2455260.9414974
2455261.0948801
2455263.3980040
2455263.5507823
2455265.8536289
2455268.3093059
2455268.4633619
2455270.9186862
2455273.3744855
2455277.8267533
2455280.1282230
2455280.2821453
2455282.7386618
2455285.1939892
2455287.6497777
0.000929
0.000053
0.000872
0.000066
0.000052
0.000405
0.000668
0.000267
0.000045
0.000182
0.000375
0.000696
0.000086
0.000287
0.000883
0.000377
0.000119
0.000235
0.000079
0.000113
0.000603
0.000924
0.000035
GM
⎛ 1
P˙
1 ⎞
= 3M˙2 ⎜
⎟
⎝ M1
P
M2 ⎠
2
timescale of the more massive component ( RL2 ~ 2.8´
107 yr ). With the orbital period decreasing due to thermal
conservative mass transfer, the degree of overcontact become
higher. Therefore, this system will evolve into a deeper
overcontact binary.
The cyclic oscillations in the O-C diagram were usually
explained by the light-travel time effect via the presence of a third
body (Liao & Qian 2010; Zhu et al. 2013a, 2013b) or magnetic
activity cycles of the cool components (Applegate 1992). As
mentioned earlier, the light curves of V2284 Cyg obtained from
2009 to 2013 are stable, which indicates that the components are
inactive during the time interval. Thus, the most plausible
mechanism to explain the cyclic variation in the O-C diagram is
the light-travel time effect that was used to search for planets
orbiting evolved binary stars (Qian et al. 2011a, 2012, 2015). The
presence of a companion object produces the relative distance
changes of the eclipsing pair as it orbits the barycenter of the triple
system. With the same method used by Zhu et al. (2013a, 2013b),
the parameters of the third body are determined and shown in
Table 5.
The A3 and T3 are the period and the amplitude of the cyclic
oscillation, respectively. The results are f (m ) = 0.0000322 M
and M3 sin i¢ = 0.036 M. If the orbital inclination of the third
body i¢ is 90°, we can estimate its mass as M3 = 0.036 M,
the corresponding orbital distance between the circumbinary
brown dwarf and the central binary is about 1.95 au. When
These phenomena reveal that V2284 Cyg is a truly stable
binary star from 2009 to 2013.
The short-cadence light curves from the Kepler space
mission were merged into 400 normal points, which were
analyzed by use of the 2013 version of W-D program. The
solutions suggest that V2284 Cyg is a contact binary with a
degree of contact of f=39.23%, where both components share
a common convective envelope. Based on a mass ratio of
q = M2 M1 = 2.90 and the temperature difference of
DT = T1 - T2 = 287K , this system is a typical W-type contact
binary. Assuming the spectral type of the more massive
component is G7V, its corresponding mass is estimated as
M2 = 0.86 M (Cox 2000). The derived mass of the hotter
component is M1 = 0.30 M.
Besides the O-C diagram shown in Figure 4, the long-term
decreasing and the cyclic oscillation are found. The orbital
period of V2284 Cyg is decreasing at a rate of
dP dt = -2.67 ( 0.27) ´ 10-7 d yr−1, which may be a result
of conservative mass transfer from the more massive star to the
less massive one. Based on the well-known equation
(3 )
the mass transfer at a rate of dM2 dt = -1.36 ´ 10-7 M yr-1
was determined. The timescale of mass transfer is
t ~ M2 M˙2 ~ 0.66 ´ 107 yr , which is close to the thermal
6
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
Table 2
Times of Light Minimum from Kepler Data
Times
2455287.8026120
2455290.1064091
2455290.2586434
2455292.5621085
2455292.7148846
2455295.0178162
2455295.1710522
2455297.6267866
2455300.0827547
2455302.5380020
2455302.6933212
2455305.1489696
2455307.4505354
2455307.6043468
2455313.7442388
2455316.2009074
2455316.3526312
2455318.6565500
2455321.1121134
2455321.2652169
2455323.7205553
2455326.1762057
2455328.6326696
2455331.0880447
2455333.5445514
2455333.6989707
2455336.0013493
2455336.1542700
2455339.2247070
2455341.6812292
2455341.8330453
2455344.1368896
2455344.2897284
2455346.5924530
2455346.7457108
2455349.0483515
2455349.2017383
2455351.6575694
2455354.1138163
2455359.0250332
2455359.1791325
2455361.4813821
2455361.6345814
2455363.9370783
2455364.0909369
2455366.3925786
2455366.5477161
2455369.0032198
2455373.6074559
2455373.7609903
2455376.0640431
2455376.2167299
2455378.5199379
2455378.6724743
2455381.1286212
2455386.0399673
2455386.1940431
2455388.4964271
2455388.6499811
Errors
Times
Errors
Times
Errors
Times
Errors
0.000257
0.000308
0.000827
0.000064
0.000049
0.000377
0.000676
0.000263
0.000215
0.000608
0.000423
0.000129
0.000895
0.000161
0.000047
0.000301
0.000743
0.000064
0.000363
0.000816
0.000321
0.000134
0.000700
0.000963
0.000891
0.000212
0.000399
0.000571
0.000061
0.000434
0.000587
0.000127
0.000051
0.000226
0.000884
0.000712
0.000425
0.000094
0.000552
0.000056
0.000117
0.000514
0.000466
0.000144
0.000894
0.000325
0.000772
0.000327
0.000382
0.000687
0.000034
0.000290
0.000901
0.000142
0.000578
0.000072
0.000224
0.000386
0.000715
2455426.4095158
2455426.5635473
2455429.0193102
2455432.3950858
2455437.3077433
2455437.4613849
2455439.7640775
2455439.9169756
2455442.2198884
2455442.3735020
2455444.6756776
2455444.8296372
2455447.2853908
2455449.5876021
2455449.7410559
2455452.1967067
2455457.1090362
2455459.5652005
2455461.5598889
2455464.3242735
2455464.4764567
2455469.3885208
2455471.8448143
2455474.3006496
2455474.4543847
2455476.7562705
2455479.3671471
2455481.6685287
2455481.8217000
2455484.1244793
2455484.2780303
2455486.7335997
2455489.1900431
2455491.6449774
2455494.8698248
2455495.0223652
2455497.3243439
2455497.4786978
2455499.7807086
2455499.9346068
2455502.2360766
2455502.3908969
2455504.8461268
2455507.3025610
2455509.7584611
2455512.2144124
2455514.6696066
2455514.8226856
2455517.1268021
2455517.2789493
2455519.7351978
2455522.0373868
2455522.1913229
2455525.4147582
2455525.5677522
2455527.8712787
2455528.0233946
2455530.3270512
2455532.9360877
0.000505
0.000542
0.000168
0.000406
0.000082
0.000160
0.000429
0.000597
0.000102
0.000040
0.000448
0.000632
0.000258
0.000050
0.000095
0.000494
0.000838
0.000298
0.000966
0.000554
0.000409
0.000048
0.000409
0.000085
0.000051
0.000379
0.000861
0.000859
0.000279
0.000392
0.000740
0.000993
0.000960
0.000076
0.000655
0.000382
0.000351
0.000957
0.000068
0.000046
0.000376
0.000588
0.000950
0.000283
0.000897
0.000047
0.000054
0.000355
0.000854
0.000944
0.000904
0.000675
0.000413
0.000055
0.000087
0.000504
0.000478
0.000125
0.000724
2455589.4214165
2455589.5763636
2455591.8773443
2455592.0322672
2455597.0981825
2455599.5520023
2455599.7066062
2455602.0083083
2455602.1630879
2455604.4642976
2455604.6189479
2455607.0747462
2455609.3769081
2455614.4423234
2455616.8987437
2455617.0509954
2455619.3543554
2455619.5070833
2455621.9630522
2455624.4195294
2455624.5727301
2455626.8752349
2455627.0291120
2455629.4851766
2455631.9406068
2455634.2439650
2455642.6861445
2455642.8385238
2455645.1415105
2455647.5971998
2455647.7504505
2455650.2070229
2455652.6621385
2455655.1179567
2455655.2725423
2455657.5741443
2455657.7280357
2455660.0303236
2455660.1838249
2455662.6400112
2455665.2491287
2455667.5519510
2455667.7048111
2455670.0077548
2455670.1607916
2455672.4635318
2455672.6170282
2455674.9192632
2455675.0733681
2455677.3735698
2455677.5294195
2455680.5986037
2455683.0541689
2455683.2082729
2455685.5106973
2455685.6639653
2455687.9671003
2455688.1195388
2455690.4228048
0.000207
0.000881
0.000657
0.000406
0.000441
0.000057
0.000920
0.000177
0.000921
0.000597
0.000436
0.000091
0.000644
0.000054
0.000487
0.000474
0.000126
0.000846
0.000136
0.000311
0.000810
0.000068
0.000083
0.000589
0.000227
0.000850
0.000558
0.000459
0.000150
0.000299
0.000039
0.000437
0.000096
0.000362
0.000601
0.000932
0.000274
0.000937
0.000143
0.000586
0.000130
0.000785
0.000225
0.000358
0.000722
0.000089
0.000039
0.000500
0.000584
0.000609
0.000235
0.000236
0.000623
0.000387
0.000032
0.000089
0.000573
0.000382
0.000231
2455735.8566928
2455738.0051001
2455738.1593304
2455741.2289560
2455743.6854795
2455743.8390030
2455746.1413020
2455746.2946964
2455748.5975873
2455748.7504889
2455751.2067750
2455753.6627870
2455756.1180180
2455758.5744689
2455758.7277777
2455761.0302457
2455761.1841764
2455763.6398831
2455766.0958057
2455771.7751895
2455771.9294843
2455774.2309368
2455774.3847689
2455776.6871779
2455776.8404936
2455779.2965550
2455784.2081103
2455786.6646078
2455786.8175205
2455789.1201005
2455791.5758783
2455791.7294110
2455794.0319920
2455794.1859870
2455796.4880390
2455796.6416193
2455798.9442932
2455799.0972829
2455801.5521450
2455804.7768551
2455804.9308366
2455807.3856856
2455809.8422135
2455809.9956421
2455812.2977532
2455812.4518303
2455814.7541497
2455814.9074829
2455817.2107729
2455817.3633852
2455819.6660164
2455819.8192424
2455822.1216294
2455822.2752283
2455824.7314473
2455827.1871805
2455829.6433009
2455829.7960693
2455832.0981019
0.000674
0.000954
0.000084
0.000607
0.000054
0.000178
0.000887
0.000178
0.000434
0.000639
0.000036
0.000704
0.000053
0.000135
0.000045
0.000553
0.000528
0.000149
0.000325
0.000152
0.000916
0.000590
0.000477
0.000039
0.000119
0.000345
0.000053
0.000511
0.000450
0.000182
0.000293
0.000054
0.000867
0.000375
0.000049
0.000083
0.000661
0.000336
0.000705
0.000356
0.000727
0.000046
0.000073
0.000059
0.000458
0.000578
0.000037
0.000206
0.000714
0.000255
0.000345
0.000805
0.000072
0.000068
0.000702
0.000282
0.000208
0.000051
0.000556
7
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
Table 2
(Continued)
Times
2455390.9522649
2455391.1056867
2455393.4080799
2455393.5624154
2455395.8640817
2455396.0181680
2455398.3210435
2455398.4738028
2455401.6972344
2455401.8503225
2455404.1529748
2455404.3066833
2455406.6087101
2455406.7630289
2455409.2186640
2455411.5208336
2455411.6742819
2455413.9766019
2455414.1301253
2455419.0426210
2455421.4974839
2455423.9538820
2455424.1073270
Errors
Times
Errors
Times
Errors
Times
Errors
0.000092
0.000899
0.000508
0.000565
0.000891
0.000213
0.000773
0.000138
0.000335
0.000652
0.000119
0.000037
0.000566
0.000538
0.000199
0.000966
0.000155
0.000469
0.000589
0.000640
0.000052
0.000103
0.000049
2455535.3910747
2455537.8474681
2455538.0016476
2455540.3031022
2455540.4580388
2455542.7586666
2455542.9137941
2455545.8290445
2455548.2846844
2455548.4398833
2455550.7409286
2455550.8956536
2455569.6217189
2455572.0780805
2455574.6865630
2455576.9897463
2455577.1420624
2455579.4455559
2455579.5977405
2455581.9012869
2455582.0539896
2455584.5102659
2455586.9658837
0.000044
0.000095
0.000060
0.000482
0.000525
0.000640
0.000148
0.000087
0.000077
0.000044
0.000156
0.000979
0.000142
0.000800
0.000152
0.000787
0.000209
0.000349
0.000692
0.000105
0.000042
0.000568
0.000182
2455693.0315993
2455695.4880067
2455697.9436965
2455700.3995424
2455705.3113407
2455705.4650713
2455708.3820022
2455708.5338591
2455710.9910538
2455713.4464084
2455715.9029120
2455716.0557412
2455718.3584498
2455718.5119219
2455720.8141762
2455720.9679633
2455723.4236023
2455725.8795158
2455728.3359766
2455730.7911876
2455733.2469109
2455733.4007650
2455735.7034968
0.000050
0.000539
0.000161
0.000303
0.000051
0.000065
0.000427
0.000407
0.000044
0.000089
0.000338
0.000784
0.000072
0.000056
0.000336
0.000738
0.000295
0.000136
0.000746
0.000991
0.000056
0.000217
0.000382
2455835.4758844
2455837.9310925
2455838.0847318
2455840.3878289
2455840.5414401
2455842.9976070
2455843.1499945
2455845.4533708
2455845.6066911
2455847.9089155
2455848.0625925
2455850.5190850
2455852.9739773
2455853.1275439
2455855.4297138
2455855.5841500
2455857.8865102
2455858.0400613
2455860.4956792
2455862.9511561
2455866.1752761
2455866.3288172
2455868.7848867
0.000047
0.000099
0.000480
0.000156
0.000040
0.000949
0.000917
0.000305
0.000929
0.000078
0.000060
0.000598
0.000110
0.000995
0.000519
0.000739
0.000951
0.000335
0.000079
0.000458
0.000165
0.000799
0.000936
Table 3
Times of Light Minimum from Kepler Data
Times
2455871.2404216
2455873.6961548
2455873.8498075
2455876.3062467
2455878.7618183
2455881.2176429
2455883.8275743
2455886.1295966
2455886.2831804
2455888.5858951
2455888.7390320
2455891.0415589
2455891.1953128
2455893.4974237
2455893.6516032
2455896.1081786
2455899.3307843
2455899.4839470
2455901.9392488
2455906.8523465
2455907.0050676
2455909.3081356
2455911.9174291
2455914.3733495
2455916.8290498
2455919.2847052
2455921.8947314
2455924.1968101
Errors
Times
Errors
Times
Errors
Times
Errors
0.000248
0.000145
0.000060
0.000583
0.000119
0.000647
0.000235
0.000063
0.000113
0.000497
0.000517
0.000123
0.000059
0.000417
0.000697
0.000294
0.000831
0.000193
0.000970
0.000499
0.000562
0.000160
0.000900
0.000381
0.000135
0.000526
0.000189
0.000926
2456012.4570539
2456014.2982130
2456016.9084858
2456017.0616189
2456019.5175664
2456021.9729906
2456022.1270254
2456024.4295284
2456026.8850941
2456027.0395360
2456029.3408705
2456029.4955558
2456031.9511693
2456032.1038938
2456034.5604034
2456037.0160420
2456039.4718505
2456041.9272326
2456042.0823194
2456044.5379474
2456046.8406868
2456046.9935337
2456050.2168487
2456052.6724420
2456055.1281181
2456055.2828090
2456057.7385908
2456060.1943206
0.000085
0.000172
0.000336
0.000748
0.000054
0.000034
0.000530
0.000166
0.000189
0.000915
0.000612
0.000523
0.000097
0.000998
0.000632
0.000267
0.000133
0.000527
0.000517
0.000158
0.000769
0.000269
0.000232
0.000140
0.000554
0.000514
0.000151
0.000292
2456153.6735818
2456153.8267572
2456156.2828846
2456158.5858645
2456158.7391008
2456161.1946742
2456163.6507002
2456166.1064095
2456168.5611781
2456168.7161538
2456171.9384547
2456174.3953685
2456174.5486800
2456176.8510676
2456177.0042461
2456179.3070417
2456179.4606721
2456181.7630958
2456181.9162281
2456184.3718991
2456189.2838624
2456191.7401344
2456191.8936658
2456194.1957041
2456196.6512414
2456196.8060778
2456199.1070902
2456199.2616036
0.000368
0.000790
0.000078
0.000192
0.000720
0.000321
0.000156
0.000646
0.000769
0.000157
0.000134
0.000220
0.000987
0.000203
0.000043
0.000766
0.000411
0.000084
0.000099
0.000270
0.000069
0.000458
0.000623
0.000131
0.000245
0.000749
0.000748
0.000386
2456284.6044611
2456284.7581764
2456287.0607762
2456287.2140975
2456289.5164582
2456289.6703291
2456291.9723249
2456292.1266675
2456294.5824018
2456297.0380376
2456299.4940165
2456301.9500095
2456306.2482439
2456306.4009985
2456322.6722850
2456325.1266772
2456327.5833947
2456327.7373199
2456330.0391736
2456330.1936657
2456332.6486882
2456335.2579899
2456337.7135548
2456340.1701828
2456342.6258720
2456342.7802558
2456345.2359935
2456347.5376348
0.000058
0.000164
0.000447
0.000606
0.000107
0.000050
0.000421
0.000615
0.000238
0.000122
0.000538
0.000052
0.000316
0.000754
0.000987
0.000059
0.000100
0.000038
0.000437
0.000593
0.000060
0.000062
0.000142
0.000139
0.000382
0.000644
0.000257
0.000216
8
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
Table 3
(Continued)
Times
2455924.3504493
2455926.6527326
2455926.8062058
2455929.2621930
2455933.5604025
2455933.7130910
2455936.1690941
2455938.6251737
2455941.0803018
2455941.2345006
2455943.5366556
2455943.6911673
2455945.9923515
2455946.1470254
2455948.4487539
2455948.6025772
2455953.2074600
2455956.7378865
2455959.9617004
2455962.2640704
2455962.4170394
2455964.7198539
2455964.8727534
2455967.1755712
2455967.3290522
2455972.2411181
2455974.6969422
2455977.1523019
2455977.3067700
2455979.6085841
2455979.7625358
2455982.0650969
2455982.2182756
2455984.5212276
2455984.6743828
2455987.8971636
2455988.0518062
2455992.9634661
2455999.8702870
2456000.0237571
2456002.4801304
2456004.9359634
2456007.3917351
2456009.8471373
2456012.3035477
Errors
Times
Errors
Times
Errors
Times
Errors
0.000160
0.000398
0.000630
0.000072
0.000289
0.000903
0.000047
0.000589
0.000100
0.000987
0.000285
0.000764
0.000879
0.000346
0.000057
0.000080
0.000969
0.000774
0.000161
0.000895
0.000155
0.000435
0.000608
0.000105
0.000084
0.000248
0.000132
0.000579
0.000503
0.000947
0.000151
0.000707
0.000320
0.000319
0.000936
0.000187
0.000818
0.000132
0.000067
0.000060
0.000621
0.000246
0.000261
0.000787
0.000054
2456062.8039805
2456065.2594439
2456067.7153602
2456070.3254200
2456072.6275715
2456072.7811782
2456075.2379478
2456075.3905136
2456077.6924104
2456077.8462748
2456081.0703646
2456081.2230890
2456083.5264250
2456085.9811809
2456086.1351850
2456088.5910032
2456091.0466917
2456093.5023660
2456093.6564788
2456095.9585040
2456096.1123258
2456098.4144015
2456098.5681403
2456100.8719563
2456103.9401916
2456104.0940466
2456108.3908267
2456110.8476648
2456111.0012368
2456113.4566947
2456115.9133307
2456116.0661348
2456118.5223344
2456120.9787329
2456130.3418831
2456132.7973848
2456135.2535614
2456135.4073954
2456137.7093671
2456141.3937276
2456143.8495393
2456146.3051198
2456148.9149043
2456151.2171131
2456151.3707641
0.000315
0.000080
0.000515
0.000221
0.000849
0.000168
0.000899
0.000389
0.000920
0.000122
0.000742
0.000571
0.000780
0.000202
0.000842
0.000408
0.000093
0.000364
0.000722
0.000909
0.000314
0.000037
0.000113
0.000716
0.000088
0.000054
0.000116
0.000086
0.000045
0.000037
0.000217
0.000937
0.000054
0.000525
0.000088
0.000344
0.000945
0.000291
0.000936
0.000348
0.000093
0.000463
0.000211
0.000035
0.000234
2456201.5633397
2456201.7174751
2456203.5583944
2456207.7031734
2456207.8573253
2456210.1588072
2456210.3139846
2456212.6150726
2456212.7691757
2456215.0709275
2456215.2247705
2456217.5274212
2456217.6804792
2456220.1368295
2456222.5921008
2456222.7456755
2456225.0489119
2456225.2017067
2456227.5047041
2456227.6575091
2456230.1142366
2456232.5696208
2456232.7236884
2456235.0252154
2456235.1798628
2456241.0123264
2456243.4676771
2456243.6214483
2456251.6033035
2456254.0592655
2456254.2123788
2456256.5150756
2456258.9706114
2456259.1242094
2456261.5806834
2456264.0363060
2456266.4922118
2456269.7158567
2456269.8691665
2456272.1713383
2456272.3247733
2456274.6271590
2456274.7809953
2456277.2367968
2456279.6931469
0.000049
0.000090
0.000296
0.000076
0.000042
0.000374
0.000707
0.000982
0.000263
0.000042
0.000159
0.000402
0.000655
0.000154
0.000135
0.000298
0.000252
0.000835
0.000168
0.000058
0.000605
0.000101
0.000049
0.000299
0.000752
0.000222
0.000660
0.000305
0.000764
0.000612
0.000355
0.000238
0.000116
0.000089
0.000543
0.000167
0.000328
0.000114
0.000999
0.000176
0.000063
0.000664
0.000457
0.000127
0.000548
2456347.6916400
2456350.1475803
2456352.6034198
2456352.7568074
2456355.0597908
2456355.2127656
2456357.5148247
2456357.6674105
2456361.1989019
2456363.6548212
2456363.8088211
2456366.1110781
2456366.2645030
2456368.7206394
2456373.6321849
2456373.7857729
2456376.0885266
2456376.2415095
2456378.5442497
2456381.1539404
2456383.6098411
2456386.0653496
2456386.2188977
2456388.5210731
2456388.6754769
2456394.9686802
2456397.4243048
2456399.8799838
2456402.3364100
2456404.7920463
2456407.2483628
2456407.4013060
2456409.7042349
2456409.8568234
2456412.1599795
2456412.3132023
2456419.8343054
2456422.2907308
2456422.4447235
0.000082
0.000454
0.000900
0.000173
0.000680
0.000297
0.000809
0.000517
0.000214
0.000672
0.000421
0.000035
0.000109
0.000525
0.000106
0.000120
0.000500
0.000528
0.000132
0.000881
0.000264
0.000078
0.000067
0.000436
0.000669
0.000549
0.000206
0.000174
0.000719
0.000049
0.000677
0.000329
0.000272
0.000797
0.000079
0.000099
0.000790
0.000300
0.000125
SDSS J143547.87+373338.5 (Qian et al. 2016), FN Lyr
and V894 Cyg (Li & Qian 2014). To date, no substellar objects
orbiting the low-mass contact binaries are found. If it is confirmed
in the future, the companion of V2284 Cyg is the first
brown dwarf candidate that is orbiting around contact binaries
where both components are sharing a common convective
envelope.
the orbital inclination i¢ of the third body is larger than 30°, the
mass of the tertiary component is less than 0.072 M, which is the
limit of the stable hydrogen burning in the core. By considering a
random distribution of the the orbital inclinations, the third body
is a brown dwarf with 66.7% probability. Similar substellar
objects are found in other systems: HW Vir (Qian et al. 2008a;
Lee et al. 2009), HS 0705+6700 (Qian et al. 2009, 2013),
9
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Wang et al.
Figure 6. Theoretical light curve calculated with the W-D program. The circles
refer to the average observations with Kepler short cadence.
Figure 4. The O-C diagram for V2284 Cyg with respect to Equation (1). Upper
panel: the solid line refers to a combination of a quadratic decrease and a cyclic
period change; Middle panel: the solid line for the cyclic variations (P=2.06
years, A=0.00030 days). Bottom panel: the residuals with respect to
Equation (2).
(A color version of this figure is available in the online journal.)
Table 4
Photometric Solutions of V2284 Cyg
Figure 5. Relation between Σ and q. The minimum residuals are achieved
at q=2.71.
To further understand the properties of the contact binary
system and its substellar companion, spectroscopic and multicolor photometric observations are required.
Parameters
Photometric
Elements
Errors
g1 = g2
A1 = A2
LD
x1bol
x 2bol
x1Kepler
x 2Kepler
T1
T2
q (M2 M1)
Win
Wout
i
L1 (L1 + L 2 ) (Kepler)
l3(Kepler)
W1 = W2
r1 (pole)
r1 (side)
r1 (back )
r2 (pole)
r2 (side)
r2 (back )
f
Sw (O - C )2
0.32
0.5
−1 (logarithmic)
0.514
0.525
0.582
0.620
5568K
5281K
2.90
6.4836
5.8662
81.461
0.3281
−0.0695
6.2414
0.2755
0.2876
0.3236
0.4506
0.4540
0.5119
39.23%
0.0024371
Assumed
Assumed
Assumed
Assumed
Assumed
Assumed
12K
±0.06
±0.345
±0.0045
±0.0025
±0.0802
±0.0019
±0.0020
±0.0025
±0.0067
±0.0092
±0.0124
12.99%
Karamay (No.RCYJ2016B-03-006), the research fund of
Sichuan University of Science and Engineering (No.2015RC42),
and the National Natural Science Foundation of China (No.
U1631108).
The data of V2284 Cyg in the paper were obtained by the
Kepler mission. This work was supported by Research
Foundation of China University of Petroleum-Beijing At
10
Publications of the Astronomical Society of the Pacific, 129:124202 (11pp), 2017 December
Qian, S.-B., Dai, Z.-B., Zhu, L.-Y., et al. 2008a, ApJ, 689, 49
Qian, S.-B., Han, Z.-T., Fernández Lajús, E., et al. 2015, ApJS, 221, 17
Qian, S.-B., Han, Z.-T., Soonthornthum, B., et al. 2016, ApJ, 817, 151
Qian, S.-B., & He, J.-J. 2005, PASJ, 57, 977
Qian, S.-B., He, J.-J., Liu, L., Zhu, L.-Y., & Liao, W.-P. 2008b, AJ, 136, 2493
Qian, S.-B., He, J.-J., Soonthornthum, B., et al. 2008c, AJ, 136, 1940
Qian, S.-B., He, J.-J., & Xiang, F.-Y. 2008d, PASJ, 60, 77
Qian, S.-B., He, J.-J., Zhang, J., et al. 2017, RAA, 17, 87
Qian, S.-B., Liu, L., Liao, W.-P., et al. 2011a, MNRAS, 414, 16
Qian, S.-B., Liu, L., Zhu, L.-Y., et al. 2011b, AJ, 141, 151
Qian, S.-B., Liu, L., Zhu, L.-Y., et al. 2012, MNRAS, 422, 24
Qian, S.-B., Shi, G., Zola, S., et al. 2013, MNRAS, 436, 1408
Qian, S.-B., Wang, J.-J., Zhu, L.-Y., et al. 2014a, ApJS, 212, 4
Qian, S.-B., Xiang, F.-Y., Zhu, L.-Y., et al. 2007a, AJ, 133, 357
Qian, S.-B., & Yang, Y.-G. 2005, AJ, 130, 224
Qian, S.-B., Yuan, J. Z., Soonthornthum, B., et al. 2007b, ApJ, 671, 811
Qian, S.-B., Yuan, J. Z., Xiang, F.-Y., et al. 2007c, AJ, 134, 1769
Qian, S.-B., Zhou, X., Zola, S., et al. 2014b, AJ, 148, 79
Qian, S.-B., & Zhu, L.-Y. 2006, AJ, 131, 1032
Qian, S.-B., Zhu, L.-Y., Zola, S., et al. 2009, ApJ, 695, 163
Ruciński, S. M. 1969, AcA, 19, 245
Terrell, D., & Wilson, R. E. 2005, AP&SS, 296, 221
Van Hamme, W. 1993, AJ, 106, 2096
Van Hamme, W., & Wilson, R. E. 2007, ApJ, 661, 1129
Wang, J. J., Qian, S. B., He, J. J., Li, L. J., & Zhao, E. G. 2014, AJ, 148, 95
Wang, J. J., Qian, S. B., Zhao, E. G., et al. 2012, PASJ, 64, 83
Wilson, R. E. 1979, ApJ, 234, 1054
Wilson, R. E. 1990, ApJ, 356, 613
Wilson, R. E. 2008, ApJ, 672, 575
Wilson, R. E. 2012, AJ, 144, 73
Wilson, R. E., & Devinney, E. J. 1971, ApJ, 166, 605
Wilson, R. E., Van Hamme, W., & Terrell, D. 2010, ApJ, 723, 1469
Zhu, L. Y., Qian, S.-B., et al. 2010, AJ, 140, 215
Zhu, L. Y., Qian, S. B., et al. 2013a, AJ, 145, 39
Zhu, L. Y., Qian, S. B., et al. 2013b, AJ, 146, 28
Zhu, L.-Y., Qian, S.-B., Soonthornthum, B., & Yang, Y.-G. 2005, AJ, 129
2806
Table 5
Orbital Parameters of the Period Changes
Parameter
Value
A3 (day )
T3 (year )
a¢12 sin i ¢
f (m )
M3 sin i ¢
a3 (i ¢ = 90)
0.00030 (0.00003)days
2.08 years
0.058 (0.005)AU
3.22 (0.01) ´ 10-5 M
0.036 (0.003) M
1.68 (0.03)AU
Wang et al.
References
Akerlof, C., Amrose, S., Balsano, R., et al. 2000, AJ, 119, 1901
Applegate, J. H. 1992, ApJ, 385, 621
Blättler, E., & Diethelm, R. 2000, IBVS, 4985, 1
Borkovits, T., Derekas, A., Kiss, L. L., et al. 2013, MNRAS, 428, 1656
Carter, J. A., Fabrycky, D. C., Ragozzine, D., et al. 2011, Science, 331, 562
Cox, A. N. 2000, Allen’s Astrophysical Quantities (New York: Springer), 389
Table 15.8
Dai, Z. B., Qian, S. B., Fernandez, L. E., & Baume, G. L. 2010, MNRAS,
409, 1195
Derekas, A., Kiss, L. L., Borkovits, T., et al. 2011, Science, 332, 216
Kazarovets, E. V., Kireeva, N. N., Samus, N. N., & Durlevich, O. V. 2003,
IBVS, 5422, 1
Lee, J. W., Kim, S.-L., Kim, C.-H., et al. 2009, AJ, 137, 3181
Li, K., Qian, S. B., Hu, S. M., & He, J. J. 2014, AJ, 147, 98
Li, L.-J., & Qian, S.-B. 2014, MNRAS, 444, 600
Liao, W. P., & Qian, S. B. 2010, MNRAS, 405, 1930
Liao, W. P., Qian, S. B., & Liu, N. P. 2012, AJ, 144, 178
Liao, W.-P., Qian, S. B., Zhao, E.-G., & Jiang, L.-Q. 2014, NewA, 31, 65
Lucy, L. B. 1967, Zeitschrift fur Astrophysik, 65, 89
Pigulski, A., Pojmański, G., Pilecki, B., Szczygieł, D. M., et al. 2009, AcA, 59, 33
11
Документ
Категория
Без категории
Просмотров
0
Размер файла
1 766 Кб
Теги
1538, 3873, 2faa8bb0
1/--страниц
Пожаловаться на содержимое документа