Publications of the Astronomical Society of Australia (PASA), Vol. 30, e026, 11 pages.
C Astronomical Society of Australia 2013; published by Cambridge University Press.
doi:10.1017/pas.2013.001
GSC 4019 3345: An A-Type Twin Binary
V. Bakış1,2 , H. Bakış1 and Z. Eker1
1 Department of Space Sciences and Technologies, Akdeniz University
2 Corresponding author. Email: volkanbakis@akdeniz.edu.tr
Science Faculty, Antalya, Turkey
(Received October 18, 2012; Accepted January 9, 2013; Online Publication March 1, 2013)
Abstract
Physical dimensions and evolutionary status of the A-type twin binary GSC 4019 3345 are presented. Located at a distance
of 1.1 kpc from the Sun, the system was found to have two components with identical masses (M1,2 = 1.92 M ), radii
(R1,2 = 1.76 R ), and luminosities (log L1,2 = 1.1 L ) revolving in a circular orbit. Modeling the components with
theoretical evolutionary tracks and isochrones implies a young age (t = 280 Myr) for the system, which is bigger than
the synchronization time scale but smaller than the circularization time scale. Nevertheless, synthetic spectrum models
revealed components’ rotation velocity of Vrot12 = 70 km s−1 , that is about three times higher than their synchronization
velocity. No evidence is found for an age difference between the components.
Keywords: binaries: close – binaries: twins – binaries: spectroscopic – eclipses
ability has been discovered by Bakış et al. (2007) and twin
nature of the binary system is concluded in this paper. Since
its discovery, systematic photometry and spectroscopy have
been performed to determine the precise orbital period and
also to test whether or not the two minima in the preliminary
light curve (LC) are precisely equal. Nevertheless, measured
times of minima have shown that the published period of
Porb = 4.077278 days is true with a small update (Section
2.2) and constant with an accuracy of 3 × 10−6 days. Component masses are same within an accuracy of 0.1%.
1 INTRODUCTION
Statistical studies on the mass ratio distribution of binaries
(e.g. Lucy 2006; Simon & Obbie 2009) showed that the frequency of existing twins within the mass ratio 0.98–1.00 is
about 3% among all binaries, at which F, G, and K spectral
type systems dominate. The sample list of twins studied by
Simon & Obbie (2009) consisted of 1 O-type, 1 B-type, 3
A-type, 16 F-type, 11 G-type, and 3 K-type twins. This result enabled Simon & Obbie to suggest that low-mass twins
are formed in binary populations in which the accretion processes have the time to proceed to completion. Therefore,
the discovery of additional twins of earlier spectral types is
important statistically for understanding binary formation
mechanisms. The existence of early-type twins also suggested that the formation of binaries with components more
massive than 1.6 M might be similar to those for the less
massive ones (Zinnecker & Yorke 2007) but other mechanisms might also be important (Simon & Obbie).
In order to test whether late- and early-type systems have
the same formation mechanisms, precise observations and
detailed analysis of early-type twins especially the eclipsing
ones are of special interest. Eclipsing twins are also important astrophysically since they provide the highest precision
astrophysical parameters among the others.
In this paper, we studied the recently discovered twin
eclipsing binary GSC 4019 3345, which is relatively faint
(V12 mag) and relatively long period (Porb = 4.08 days)
among the common eclipsing systems. Its photometric vari-
2 OBSERVATIONS
2.1 Photometry
s
Photometry of GSC 4019 3345 (α = 00h 22m 45.37,
δ =
′
′′
62°20 05 .5) has been carried out in 2004, 2005, 2006, 2007,
and 2009 observing seasons. Observations between 2004 and
2007 are mainly based on the time of minimum observations using several telescopes (0.3- and 0.4-m Cassegrain–
Schmidt) and CCD cameras (SBIG ST10XME and SBIG
ST1001E) of the Çanakkale Onsekiz Mart University Observatory (COMUO) in order to determine the precise orbital
period of the binary system. Only Johnson V-band data were
studied due to its higher quality with respect to other filters
used during the observations between 2004 and 2007. After determining the accurate orbital period of the system,
a 1.22-m telescope of COMUO equipped with ST1001E
1
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Bakış, Bakış and Eker
Figure 1. O − C diagram of GSC 4019 3345. Filled and empty circles are from primary and secondary
times of minima, respectively.
Table 1. Log of photometric observations of GSC 4019 3345.
Day
30.09.2004
27.11.2004
02.12.2004
26.06.2005
28.06.2005
30.06.2005
14.08.2005
24.08.2005
20.09.2005
04.10.2005
06.10.2005
21.10.2005
26.10.2005
28.08.2007
31.08.2007
01.09.2007
06.09.2007
02.12.2007
20.08.2009
23.08.2009
25.08.2009
29.08.2009
30.08.2009
31.08.2009
03.09.2009
13.09.2009
19.09.2009
23.09.2009
26.09.2009
28.09.2009
29.09.2009
05.10.2009
06.10.2009
Filter
UBVR
UBVR
UBVR
UBVR
UBVR
UBVR
UBVR
UBVR
BVR
BVR
BVR
BVR
BVR
BVRI
BVRI
BVRI
BVRI
BVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
UBVRI
Table 2. Times of minimum of GSC 4019 3345.
Number of exposures
222
79
132
144
62
110
57
52
35
28
109
57
50
145
187
79
122
102
43
33
35
47
38
32
38
28
16
45
42
39
39
53
50
No.
HJD
(−240 0000)
Error
Type
(pri/sec)
O−C
(days)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
53279.2902
53342.4861
53548.3917
53550.4263
53552.4686
53597.3168
53607.5143
53648.2842
53650.3227
54341.4268
54345.5035
54437.2431
55073.3025
55075.3414
8
11
7
13
6
11
11
6
4
4
7
1
3
6
sec
pri
sec
pri
sec
sec
pri
pri
sec
pri
pri
sec
sec
pri
0.0016
−0.0008
0.0009
−0.0031
0.0006
−0.0016
0.0027
−0.0005
−0.0006
0.0004
−0.0002
0.0001
0.0000
0.0002
CCD has been used in the 2009 observing season to obtain the whole light curve in UBVR and I-band filters. A
total of 15 nights were allocated for the CCD photometry of the system. For differential photometry, GSC 4019
s
δ = 62°18′ 35′ ′ .3, V11.4 mag)
2747 (α = 00h 22m 42.97,
s
δ = 62°21′ 33′ ′ .7,
and GSC 4019 2784 (α = 00h 22m 17.97,
V11.7 mag) were chosen for comparison and as a check
star, respectively. The average standard deviations of a typical observation in UBVR and I bands are σ = 0.058, 0.009,
0.008, 0.008 and 0.009, respectively. The log of photometric
observations is given in Table 1.
The reduction of CCD frames was made by means of
the aperture photometry with C-Muniwin1 package, on
which one of the authors has development contribution. The
1
http://c-munipack.sourceforge.net/
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GSC 4019 3345: An A-Type Twin Binary
1.0
0.5
3850
3900
3950
δ
H
H
H
ζ
-0.5
ε
0.0
4000
4050
4100
4150
4200
4250
4300
1.0
0.5
H
γ
Mg II 4481 A
0.0
-0.5
4400
4500
4600
4700
4800
1.0
0.5
β
0.0
-0.5
4700
H
Normalized Flux
4300
4800
4900
5000
5100
5200
5300
5400
1.0
0.5
Na I D lines
0.0
-0.5
5400
5500
5600
5700
5800
5900
6000
6100
6200
6300
6400
1.0
0.5
H
α
0.0
-0.5
6400
6500
6600
6700
6800
6900
7000
7100
7200
1.0
0.5
0.0
-0.5
-1.0
7200
7400
7600
7800
8000
8200
8400
8600
8800
9000
Wavelength (A)
Figure 2. Observed spectrum of GSC 4019 3345 (at φ = 0.5) (upper) and Vega (lower).
reduction of CCD frames is standard: bias and dark subtraction and flat field correction. The size of apertures during
the computation of magnitudes of stars in the CCD field selected was about three times the Full Width at Half Maximum
(FWHM) of the star profile so that no flux is lost and noise
has no considerable effect. The airmass for program stars has
not been taken into account due to their proximity with less
than 7 arcmin in the sky.
The B and V magnitudes of stars in the same CCD
field of GSC 4019 3345 are available in several survey
catalogs (i.e. Tycho-2, Høg et al. 2000; United States
Naval Observatory (USNO), Monet et al. 1997). Using
these catalog magnitudes of stars, we standardized B and
V magnitudes of GSC 4019 3345 at light maximum as
B = 12.55(0.10) and V = 12.15(0.02).
2.2 Orbital period
A total of 14 times of minima are extracted from the photometric observations of the system between 2004 and 2009.
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Bakış, Bakış and Eker
Table 3. Journal of spectroscopic observations for GSC 4019 3345. S/N refers to the continuum near 6 500 Å.
No
HJD
(−240 0000)
Exp. time
(s)
S/N
Phase
(φ)
RV1
(km s−1 )
(O − C)1
(km s−1 )
RV2
(km s−1 )
(O − C)2
(km s−1 )
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
55455.2941
55455.3204
55455.5186
55456.3890
55456.4303
55456.4524
55456.5594
55456.5813
55457.2650
55457.2905
55457.3824
55457.5735
55457.5922
55795.2997
55795.3166
55795.3558
55795.3726
55795.3900
55795.5144
55795.5307
55795.5472
55795.5933
55863.2090
55863.2343
55863.2598
55863.3449
55863.3693
55863.4491
1 800
1 800
1 800
1 800
1 800
1 800
1 800
1 800
1 800
1 800
1 800
1 800
1 800
1 200
1 200
1 200
1 200
1 200
1 200
1 200
1 200
1 200
1 800
1 800
1 800
1 800
1 800
1 800
70
120
30
110
130
110
130
72
50
60
50
50
50
50
50
30
40
45
40
40
35
28
85
75
50
120
70
60
0.187
0.194
0.242
0.456
0.466
0.471
0.497
0.503
0.671
0.677
0.699
0.746
0.751
0.577
0.581
0.591
0.595
0.599
0.630
0.634
0.638
0.649
0.232
0.239
0.245
0.266
0.272
0.291
−92.9
−90.9
−103.3
−36.3
−31.7
−36.0
−7.2
−5.3
98.2
92.3
98.1
104.0
104.0
47.0
49.4
54.8
57.0
59.3
74.4
76.2
77.9
82.6
−105.5
−105.8
−110.6
−105.2
−99.2
−101.9
2.5
5.8
−0.9
−5.7
−8.7
−16.8
−3.7
−5.8
5.3
−2.5
−2.8
−1.9
−1.9
−3.5
−1.1
−2.7
−0.5
−1.6
−1.5
−2.5
−0.7
−1.3
−3.8
−3.7
−8.3
−3.4
2.1
−2.8
94.1
96.2
97.3
31.7
29.4
20.7
–
–
−90.1
−94.2
−100.0
−105.9
−105.9
−48.9
−51.3
−56.7
−58.9
−61.2
−76.3
−78.1
−79.8
−84.5
103.6
103.9
109.9
106.3
101.9
100.0
−2.1
−1.4
−6.0
0.9
6.3
1.4
–
–
3.7
1.5
1.9
1.1
1.0
2.1
−0.2
1.4
−0.8
0.3
0.3
1.4
−0.4
0.3
0.9
0.9
6.6
3.5
−0.4
0.0
Figure 3. The Hα (6 563 Å) lines of the components of GSC 4019 3345. Orbital phases are
shown on the right.
The method described by Kwee & van Woerden (1956) was
used for the determination of times of minima. The times
of minima extracted are listed in Table 2 together with their
uncertainties and minimum types. The regression analysis of
the O − C data (for the observing span from 2004 to 2009)
improved the orbital period Porb = 4.077278 days given by
Bakış et al. (2007) and provided the new ephemeris:
Pri HJD = 245 3648.2847(4) + 4.077304(3) × E.
(1)
Based on the new ephemeris (Equation (1)), the calculated
O − C values are also included in Table 2. The O − C
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GSC 4019 3345: An A-Type Twin Binary
Figure 4. Top: spectral disentangling results on selected spectra around Hα. Observations and
fits are shown in black and red, respectively. Middle: reconstructed spectrum of the components.
Bottom: best-fitting orbital solution, where filled and empty squares are of primary and secondary
RVs, respectively.
diagram is shown in Figure 1, where the consistency of the
orbital period is clear with an accuracy better than 3 × 10−6
days.
2.3 Spectroscopy
The spectra of GSC 4019 3345 were taken with the
Faint Object Spectrograph and Camera (TFOSC) of
the TUBITAK National Observatory (TUG), Turkey.
It is attached on the Cassegrain focus of the 1.5m telescope called RTT150 located at Bakırlıtepe
(36°49m N, 30°20m E; altitude = 2 500 m),
Antalya. TFOSC has two main capabilities: (a) direct imaging and (b) low-/medium-resolution spectroscopy, both operated by a Linux operating system. For imaging and spectroscopy the same CCD, which has a field of view of
13.3 × 13.3 arcmin with a chip dimension of 2 048 × 2 048
pixels with a pixel size 15 × 15 µm, is used. The spectrograph
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Bakış, Bakış and Eker
Figure 5. Top: best-fitting LC models in UBVR and I bands. Lower left: primary and secondary minima with theoretical fit.
Lower right: RV curves of the components together with the theoretical model; filled and empty squares are for primary and
secondary components, respectively.
was designed to provide a continuous wavelength coverage
between 330 and 1 200 nm and has a resolution range of
R(λ/δλ)205–5 099 with a different wavelength interval.
The grisms are used to change the resolutions. The list of
available grisms and the resulting resolutions is given in the
instrument’s manual.2
In this project, we have chosen the highest available resolution mode (R5 099) of TFOSC, which provides a continuous wavelength coverage of 330–900 nm in 11 échelle
orders. All spectra presented in this paper are obtained in
three observing sessions (2010 September, 2011 August, and
2011 October). The total number of spectra obtained for GSC
4019 3345 is 28. We have observed radial velocity (RV) standard star Vega (α Lyrae) in each observing night in order to
standardize our RV measurements.
Comparison spectra of the iron–argon arc lamp for the
wavelength calibration were recorded before and after each
exposure. For the exact time of the stellar observation, the
dispersion solution was interpolated between the two spectra
of the arc lamp. A set of white lamp images was taken every
night for flat-fielding.
2
http://www.tug.tubitak.gov.tr/rtt150− tfosc.php
Table 4. Spectroscopic orbital parameters of GSC 4019 3345.
Parameter
P (days)
T0 (HJD − 245 0000)
K1 (km s−1 )
K2 (km s−1 )
e
w (°)
Vγ (km s−1 )
q
rms (km s−1 )
Value
4.077304
3 648.2846 ± 0.0001
105.0 ± 0.8
105.1 ± 0.8
0.03 ± 0.01
273 ± 16
−0.80 ± 1.30
1.00 ± 0.01
2.8
All spectra were reduced with the Image Reduction and
Analysis Software (iraf).3 The reduction is standard for
échelle spectra: bias subtraction, scattered light correction,
aperture extraction, flat-field correction, and dispersion solution for wavelength calibration.
An observed sample spectrum at phase φ 0.5 of GSC
4019 3345 and of Vega (α Lyr) with the same instrument is
3
iraf is distributed by the National Optical Astronomy Observatories, which
are operated by the Association of Universities for Research in Astronomy
Inc., under cooperative agreement with the National Science Foundation.
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GSC 4019 3345: An A-Type Twin Binary
Table 5. Results from the simultaneous solution of UBVR and I-band LCs and RVs. Adjusted and fixed parameters are
presented in separate panels of the table. Uncertainties of adjusted parameters are given in parentheses.
Parameter
Symbol
Value
T0
Teff2
L1 /L1+2 (U)
L1 /L1+2 (B)
L1 /L1+2 (V)
L1 /L1+2 (R)
L1 /L1+2 (I)
1,2
r1,2
i
q
a
e
Vγ
2 453 648.2848 (0.0002)
8600 (260)
0.506 (0.010)
0.497 (0.007)
0.496 (0.005)
0.504 (0.003)
0.499 (0.005)
10.56 (0.23), 10.51 (0.25)
0.104 (0.002), 0.106 (0.002)
85.8 (0.1)
1.000 (0.002)
16.76 (0.14)
0.0 (0.14)
0.0 (0.4)
Orbital period (days)
Albedo
Gravity-darkening exponent
Primary surface temperature (K)
Linear limb-darkening coefficient for U, B, V, R, I
Linear limb-darkening coefficient for U, B, V, R, I
Non-linear limb-darkening coefficient for U, B, V, R, I
Non-linear limb-darkening coefficient for U, B, V, R, I
Rotation rate
P
A1,2
τ 1,2
Teff1
x1
y1
x2
y2
F1,2
4.077304
1.0
1.0
8600
0.640, 0.750, 0.645, 0.522, 0.419
0.243, 0.319, 0.282, 0.241, 0.209
0.641, 0.750, 0.645, 0.522, 0.410
0.243, 0.319, 0.282, 0.241, 0.209
1.0
Chi-square for UBVRI light curves
χ 2 min
0.108, 0.016, 0.033, 0.013, 0.018
Adjusted parameters:
Time of primary minimum (HJD)
Secondary surface temperature (K)
Primary light contribution in the U band
Primary light contribution in the B band
Primary light contribution in the V band
Primary light contribution in the R band
Primary light contribution in the I band
Surface potentials
Mean relative radii
Orbital inclination (°)
Mass ratio
Semi-major axis (R⊙ )
Orbital eccentricity
Systemic velocity (km s−1 )
Fixed parameters:
presented in Figure 2. All spectra observed around the Hα
region are also shown together with orbital phases in Figure 3 in order to show the phase distribution of the observed
spectrum and Doppler shifts of the component stars during
the orbital motion. The journal of observations including
observing times, mean signal-to-noise ratios (S/N) at 650
nm and exposure times is given in Table 3.
3 SPECTROSCOPIC ORBIT SOLUTION
Relatively sharp spectral lines (see Figure 2) of GSC 4019
3345 may allow a direct measurement of RVs by the Gaussian
fitting to the line profiles. However, for most of the spectra
of low S/N (see Table 3), weak lines become less reliable
for RV measurements. Therefore, we avoided using crosscorrelation or line-fitting techniques, but preferred to use
a spectral disentangling method, the code korel (Hadrava,
1995), which is able to use all spectral information in spectral
regions selected. Using the light contributions of the components, korel solves the pure Keplerian orbit, excluding
eclipse effects on RVs, the so-called Rossiter–McLaughlin
effect, and measures the RVs simultaneously. Additionally,
it gives the disentangled spectrum of the component stars
if the light contribution at the observed phases is provided
correctly. In this study, the light contributions of the components are taken from the light-curve solution (Section 4),
which are almost same for both components at out-of-eclipse
phases except during the eclipses where the light contribution
of the eclipsed component diminishes.
Since korel accepts input spectrum with 2n data points,
our spectra had to be re-binned. Therefore, we re-sampled
our spectra to have 1 024 data points so that each pixel corresponded to 26 km s−1 . The orbital period is adopted from
Equation (1) and kept fixed, while the time of periastron passage T0 , orbital eccentricity e, longitude of periastron w, and
velocity semi-amplitudes K1,2 have been converged during
the orbital solution. The orbital solution yielded a small eccentricity (e = 0.03). The systemic velocity Vγ is measured
by cross-correlating the spectrum at the time of conjunctions
(φ = 0.497, 0.503), with the RV standard star Vega (α Lyrae)
as template. The final RVs are given in Table 3 and adopted orbital parameters with their uncertainties are given in Table 4.
The best-fitting reconstructed spectra, together with observed
one at two particular orbital phases (φ = 0.60, 0.70), and the
Keplerian orbital model are shown in Figure 4.
4 SIMULTANEOUS SOLUTION OF LIGHT AND
RADIAL VELOCITY CURVES
The whole set of photometric data for LC analysis consists
of 442 measurements in the U band, 578 in the B band, 890
in the V band, 572 in the R band, and 574 data points in the
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Bakış, Bakış and Eker
Table 6. Close binary stellar parameters of GSC 4019 3345. Errors are given in parentheses.
Parameter
Spectral type
Mass (M )
Radius (R )
Separation (R )
Orbital period (days)
Orbital inclination (°)
Mass ratio
Eccentricity
Surface gravity (cgs)
Integrated visual magnitude (mag)
Integrated color index (mag)
Intrinsic color index (mag)
Color excess (mag)
Visual absorption (mag)
Individual visual magnitudes (mag)
Temperature (K)
Luminosity (L )
Bolometric magnitude (mag)
Absolute visual magnitude (mag)
Bolometric correction (mag)
Velocity amplitudes (km s−1 )
Systemic velocity (km s−1 )
Computed synchronization velocities (km s−1 )
Observed rotational velocities (km s−1 )
Distance (pc)
Age (Myr)
Orbital angular momentum (cgs)
Proper motion (mas yr−1 )
Space velocities (km s−1 )
Symbol
Primary
Secondary
Sp
M
R
a
P
i
q
e
log g
V
B−V
(B − V)0
E(B − V)
Av
V
Teff
log L
Mbol
Mv
BC
K1,2
Vγ
Vsynch
Vrot
d
t
J1 , J2
µα cos δ, µδ
U, V, W
A4 V
1.92 (0.01)
1.76 (0.05)
A4 V
1.92 (0.01)
1.76 (0.05)
I band. The relatively low number of U-band data is due to
the tracking errors of the telescope in long exposures during
the U-band observations. The relatively high number of Vband data is due to the existence of extra V-band observations
covering 2004–2007 observing seasons.
The catalog of the 2MASS survey gives the infrared magnitudes of GSC 4019 3345 as J = 11.139 ± 0.024, H =
11.040 ± 0.026, and K = 11.001 ± 0.020, which yields the
system color J − H = 0.099 ± 0.050, implying a spectral
type of A4–A5V (Covey et al. 2007). Since both components
in the light curve have the same color, we can use the system color as the temperature indication for the component
stars. Following temperature–spectral-type calibration tables
of Straižys & Kuriliene (1981), we adopted a temperature of
8 600 K as an input temperature for the primary during the simultaneous analysis of LCs and RV data. The solutions have
been carried out using the w-d program (Wilson & Devinney
1971; Wilson 1979, 1990). Eclipse effects in the RVs are
taken into account during the solution. The logarithmic bolometric and monochromatic limb-darkening coefficients were
interpolated from van Hamme’s (1993) tables. In the gravitydarkening law (T g(τ /4) ), the gravity-darkening exponent τ
was taken to be 1.0 for each component, which corresponds
to β = τ /4 = 0.25, as suggested by Lucy (1967) for earlytype non-convective stars. A bolometric albedo was also set
to 1.0 as suggested by Ruciński (1973) for early-type non-
16.76 (0.14)
4.0773040 (0.0000003)
85.8 (0.1)
1.000 (0.002)
0.0
4.227 (0.011)
4.227 (0.014)
12.15 (0.02)
0.40 (0.10)
0.12 (0.10)
0.28 (0.10)
0.88 (0.10)
12.02 (0.05)
8 600 (310)
8 600 (570)
1.19 (0.09)
1.19 (0.14)
1.78 (0.18)
1.78 (0.22)
1.79 (0.22)
1.79 (0.35)
−0.01 (0.04)
−0.01 (0.04)
104.0 (0.1)
104.1 (0.1)
−0.8(1.3)
22 (1)
22 (1)
70 (20)
70 (20)
1 104 (64)
280 (40)
2.326 (13)x1052 , 2.329 (22)x1052
−2.8 (4.1), −3.6 (4.1)
15 (19), 8 (11), −17 (22)
convective stars. Both fixed and adjusted parameters during
the solutions are presented in Table 5.
The w-d program yielded a unique detached system with
two equal components within the uncertainty box of output
parameters. Table 5 lists the output parameters with their
uncertainties. Figure 5 shows the best-fitting LC and RV
models together with the observations.
5 DISCUSSION AND CONCLUSIONS
5.1 Close binary astrophysical parameters
Using the parameters of Table 5, which lists the results of
simultaneous solutions of light and RV curves, fundamental
astrophysical parameters of GSC 4019 3345 were computed
and are listed in Table 6. Velocity semi-amplitudes of component stars in Table 6 are derived from the theoretical RV
curve of simultaneous wd solutions, which are 1 km s−1
smaller than given in Table 4. The temperature Teff1 = 8 600
K, mass M1 = 1.92 M⊙ , and radii R1 = 1.77 R of the
components correspond to a spectral type of A4 in the main
sequence (MS; e.g. Straižys & Kuriliene 1981). This result is
in very good agreement with the infrared colors of the system
(Section 4).
To obtain the space velocity of the system, we used the
center-of-mass velocity, distance, and proper-motion values
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9
GSC 4019 3345: An A-Type Twin Binary
Determination of the spectral types for the component stars
allows us to interpret their intrinsic colors. Following the
spectral type–intrinsic color calibration tables of Fitzgerald
(1970), the intrinsic color of the system is adopted to be (B
− V)0 = 0.12 mag. Hence, using the observed color of B −
V = 0.40, the color excess is found to be E(B − V) = 0.28
mag, which yields the visual absorption in the direction of
GSC4019 3345 to be Av = 3.1 × E(B − V) = 0.88 mag. The
unreddened Johnson V magnitude (V0 = V − Av = 11.27
mag) of GSC 4019 3345, when combined with the light contributions as derived from the light-curve analysis, yields the
intrinsic V magnitudes of the component stars, mV12 = 12.02
mag. Using Mv = 4.75 mag as the absolute visual magnitude
of the Sun and bolometric corrections BC12 = −0.01 mag
for the primary and the secondary, from Straižys & Kuriliene
(1981), bolometric and absolute visual magnitudes of the
close binary components are derived (see Table 6). The visual magnitude and distance modulus indicate a photometric
distance of 1 104 ± 64 pc to GSC 4019 3345.
Z=0.02, Y=0.28, M=1.921Msun
Primary Star
Z=0.02, Y=0.28, M=1.919Msun
Secondary Star
Z=0.02, M=1.9Msun
Z=0.02, M=1.9Msun
2.5
Luminosity, log L, (Lsun)
5.2 Distance
gsc40193345
3
2
1.5
1
0.5
0
4.05
4
3.95
3.9
3.85
3.8
Temperature, log Teff, (K)
3.75
3.7
3.65
3.6
gsc40193345
2
Z=0.02, Y=0.28, M=1.921Msun
Primary Star
Z=0.02, Y=0.28, M=1.919Msun
Secondary Star
Z=0.02, M=1.9Msun
Z=0.02, M=1.9Msun
2.5
Surface Gravity, log g, (cgs)
of the system, which are given in Table 6. The proper-motion
data were taken from the Tycho-2 Catalogue (Høg et al.
2000). The system’s space velocity components (U, V, W),
which are given with their errors in Table 6, were calculated
using Johnson & Soderblom’s (1987) algorithm.
3
3.5
4
4.5
5
4.2
4.1
4
3.9
3.8
Temperature, log Teff, (K)
3.7
3.6
3.5
5.3 Evolutionary scenario
The evolutionary status of GSC 4019 3345 has been investigated in the planes of log Teff –log L and log Teff –log g (Figure
6), using the latest evolutionary models and isochrones of
Girardi et al. (2000; for the MS) and Siess et al. (2000; for
the pre-main sequence, PMS), which include mass loss and
moderate overshooting. As can be seen from Figure 6, the
MS evolutionary tracks calculated for the components’ mass
(M1,2 = 1.92 M ) show that both stars are in very early
stages of their main-sequence lifetime. Different metal abundances imply different ages. Therefore, we have calculated
three isochrones with a very low (Z = 0.0001, Y = 0.23), a
solar, and a higher (Z = 0.040, Y = 0.40) metal abundance.
The isochrones generated for the solar metal content imply
a mean age of 280 ± 40 Myr for the system. The 6.3 Myr
and 4 Gyr ages are indicated by the isochrones of higher and
lower metal abundances.
In the case of detached binary systems, non-synchronous
rotation can be used as an indicator for young age of the system. In order to find the rotation velocity of the components,
the Mg ii 4 481 Å line in the disentangled spectrum was
modeled with the synthetic spectrum calculated using the
Local Thermodynamic Equilibrium (LTE) Kurucz (1993) atmosphere models, with new opacity distribution functions
provided by Castelli & Cacciari (2001). The synthetic model
calculation was achieved with the synthe routine (Kurucz
1993). Solar metal abundance and a microturbulence velocity
Figure 6. Evolutionary tracks in the log Teff –log L (top) and log Teff –log
g (middle) planes. In the top and middle panels, solid and dashed lines are
the evolutionary tracks for MS and PMS stages, respectively. MS evolutionary tracks for the exact masses of the components are indistinguishable.
The PMS evolutionary tracks are calculated for M = 1.9 M⊙ . Isochrones
generated with different metallicities in the log Teff –log g plane (bottom).
of 2 km s−1 were assumed in the model atmosphere calculations. The instrumental broadening of TFOSC was estimated
to be 40 km s−1 from Fe–Ar lines.
The best-fitting model atmosphere revealed the atmosphere parameters as Teff = 8 500 ± 300 K, log g = 4.25 ±
0.25 cgs, and Vrot sin i = 70 ± 20 km s−1 . The synthetic Mg
ii 4 481 Å line produced according to the model atmosphere
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10
Bakış, Bakış and Eker
Figure 7. Synthetic spectra calculated with various projected rotational velocities fitted
on the disentangled Mg ii 4 481 Å line.
well fitted to the component spectra (Figure 7). The effective temperature used in model atmosphere fitting is found
to be in good agreement with the temperature used in the LC
analysis, and the observed rotation velocities of the components (Vrot = 70 km s−1 ) are about three times higher than
the computed ones (Vsynch = 22 km s−1 ), which imply a very
young age for the system that did not yet have the time to
synchronize their rotations with the orbit.
6 CONCLUDING REMARKS
1. There were only three A-type twins known among the
binary systems with reliable spectroscopic data. Early-type
(OBA) twins have great importance since their formation
scenario is not very well known as of low-mass twins of F, G,
and K spectral types. The precise physical parameters derived
for GSC 4019 3345 in this study increased the number of
early-type known twins to four.
2. Both components of GSC 4019 3345 occupy the same
location on the Hertzsprung-Russell (H-R) diagram according to the derived luminosity, effective temperature, and surface gravity values. Hence, evolutionary status (ages) is similar for both components. This means that both components of
GSC 4019 3345 passed the mass accretion phase during the
formation at the same time within the derived parameters’
uncertainty boxes. On the contrary, it is not possible with
present accuracy to prove or disprove that GSC 4019 3345
contradicts with Parenago 1802, the low-mass binary with an
age difference between the components (e.g. Stassun et al.
2008), since the age difference between the components of
Parenago 1802 is on the order of several hundred thousand
years that is beyond the accuracy of the present study.
3. The synchronization time scale for the component stars
of GSC 4019 3345 is, following Zahn (1977), on the order of
3 Myr. Nevertheless, the orbital circularization time scale is,
again following Zahn (1977), on the order of 570 Myr. The
age of GSC 4019 3345 is clearly higher than the synchronization time scale but lower than the circularization time scale
of the system. According to the estimated system age, the
system should have been in a non-circular orbit with a pseudosynchronized rotation. Supersynchronism itself is unusual
for a binary with circular orbit since tidal synchronization
proceeds faster than tidal circularization. However, such unusual supersynchronism is also found in the M35 open cluster
(τ = 150 Myr) in a binary (Porb = 10.3 days) having circular orbit with four times supersynchronous rotation (Meibom
et al. 2006). Obviously, such systems are challenges for the
present tidal evolution theory.
Higher resolution spectroscopy of the system is strongly
needed to study the spectral lines in the individual spectrum
of the components. This will enable one to know the metal
content of the components, which will provide more reliable
age estimates for GSC 4019 3345.
ACKNOWLEDGMENTS
Photometric observations are granted by the Çanakkale Onsekiz Mart University Observatory. Spectroscopic observations are
granted by the TUBITAK National Observatory with the project
code 11BRTT150-202-0. We thank Drs Afşar Kabaş and Naci Erkan
for their help during the photometric observations. We thank the
referee for useful comments that contributed to the scientific improvement of the manuscript.
REFERENCES
Bakış, V., Bakış, H., Demircan, O., Erdem, A., & Cicek, C. 2007,
ASPC, 370, 251
Castelli, F., & Cacciari, C. 2001, A&A, 380, 630
Covey, K. R., et al. 2007, AJ, 134, 2398
Fitzgerald, M. P. 1970, A&A, 4, 234
Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C., 2000, A&AS,
141, 371
Hadrava, P. 1995, A&AS, 114, 393
Høg, E., et al. 2000, A&A, 355, 27
Johnson, D. R. H., & Soderblom, D. R. 1987, AJ, 93, 864
Kurucz, R. L. 1993, CD-ROM 13, 18 (http://kurucz.harvard.edu)
PASA, 30, e026 (2013)
doi:10.1017/pas.2013.001
Downloaded from https://www.cambridge.org/core. IP address: 18.206.13.133, on 15 Jun 2020 at 00:28:05, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms.
https://doi.org/10.1017/pas.2013.001
GSC 4019 3345: An A-Type Twin Binary
Kwee, K. K., & van Woerden, H. 1956, BAN, 12, 327
Lucy, L. B. 1967, ZA, 65, 89
Lucy, L. B. 2006, A&A, 457, 629
Meibom, S., Mathieu, R. D., & Stassun, K. G. 2006, ApJ, 653,
621
Monet, D., Canzian, B., Harris, H., Reid, N., Rhodes, A., & Sell, S.
1997, A Catalog of Astrometric Standards, US Naval Observatory Flagstaff Station
Ruciński, S. M. 1973, AcA, 23, 79.
Siess, L., Dufour, E., & Forestini, M. 2000, A&A, 358, 593
11
Simon, M., & Obbie, R. C. 2009, AJ, 137, 3442
Stassun, K. G., Mathieu, R. D., Cargile, P. A., Aarnio, A. N.,
Stempels, E., & Geller, A. 2008, Natur, 453, 1079
Straižys, V., & Kuriliene, G. 1981, Ap&SS, 80, 353
van Hamme, W. 1993, AJ, 106, 2096
Wilson, R. E. 1979, ApJ, 234, 1054
Wilson, R. E. 1990, ApJ, 356, 613
Wilson, R. E., & Devinney, E. J. 1971, ApJ, 166, 605
Zahn, J. P. 1977, A&A, 57, 383
Zinnecker, H., & Yorke, H. W. 2007, ARA&A, 45, 481
PASA, 30, e026 (2013)
doi:10.1017/pas.2013.001
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https://doi.org/10.1017/pas.2013.001