International Journal of Astronomy and Astrophysics, 2013, 3, 123-130
http://dx.doi.org/10.4236/ijaa.2013.32014 Published Online June 2013 (http://www.scirp.org/journal/ijaa)
Photometric Study of Three Short-Period Eclipsing
Binaries from the ASAS Catalogue
J. A. Obu1*, P. N. Okeke2
1
Department of Physics, University of Calabar, Calabar, Nigeria
Centre for Basic Space Science, University of Nigeria, Nsukka, Nigeria
Email: *abebeobu@yahoo.com, okekepius@yahoo.com
2
Received January 11, 2013; revised February 10, 2013; accepted February 18, 2013
Copyright © 2013 J. A. Obu, P. N. Okeke. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
We present the results of our study of three previously unstudied short-period eclipsing binaries, namely: ASAS 110609
− 2045.3, ASAS105331 − 7424.7, and ASAS 130057 + 2120.3. Using the visual (V)-band data obtained from the
ASAS catalogue, the orbital and physical parameters of the systems were derived for the first time using the Wilson-Divenney (WD) codes. Our investigation revealed that ASAS 110609 − 2045.3 is a near-contact binary star of the
W Uma type having an angle of inclination of 80˚ ± 1, a mass ratio of about 0.5, an orbital period of 0.2933 ± 0.0130
days, and an effective temperature in the range of 5800 K - 6200 K, making it a G2V-F7V spectral system. ASAS
105331 − 7424.7 was established to be an over-contact binary system of the W Uma type, inclined at 86˚ ± 2 to the line
of sight, having a mass ratio of about 0.9, a period of 0.4825 ± 0.0002, and an effective temperature in the range of 5200
K - 5300 K, making it a K2V-K0V spectral system. A third light factor of just 0.1 was established for the system, however, no evidence of starspots or discs was inferred for either component. ASAS 130,057 + 2120.3 is a W Uma binary
having a mass ratio of about 0.6 in a state of marginal contact. Its orbital inclination is 55˚ ± 1; the effective temperature
is in the range of 6200 K - 6500 K, making it a F7V-F5V stellar system. The system showed evidence of third light,
with a third light factor of 0.6, however, the presence of spots or discs could not be established for either component.
The deduced period was 0.8930 ± 0.0014 days. None of the systems showed any evidence of the O’Connell effect on
either component.
Keywords: Binaries; Eclipsing—Stars; Starspots—Stars; Fundamental Parameters—Individual;
ASAS 110609 − 2045.3; ASAS 105331 − 7424.7; ASAS 130057 + 2120.3
1. Introduction
Eclipsing binary stars are stellar systems consisting of
two gravitationally-bound stars orbiting around their
common centre of mass, with their orbital motion in a
plane sufficiently edge-on to the observer for either total
or partial eclipse to occur when one star passes in front of
its companion. These stellar systems are very important
astrophysical objects because they not only constitute
about one half of all stellar populations [1-3], they serve
as ideal astrophysical laboratories for the determination
of stellar properties such as masses, radii, and temperatures [4]. Their study also yields information on stellar
structure and evolution, and the existence of exoplanets
[5]. In addition, they can be used for the estimation of
cosmic distances and time without external calibration,
test the validity of the theory of general relativity (for
*
Corresponding author.
Copyright © 2013 SciRes.
instance, through the study of binary systems in which
one of the component stars is a compact object such as
neutron stars and black holes).
Binary systems located in clusters, are even more
valuable for study, this because, since all cluster members are presumed to be at the same distance from the
Sun, the binaries in a cluster can be used to determine
cluster the distance. Furthermore, owing to the fact that
they have the same chemical composition and age, but
different masses, cluster members are different from one
to another. Consequently, a study of binary systems,
which are members of a cluster, is important for understanding the evolution of the entire cluster.
Recently, the All Sky Automated Survey (ASAS) [6]
has confirmed the detection of some eclipsing binary
stars from their all-sky survey. Three of these, namely,
ASAS 110609 − 2045.3, ASAS 105331 − 7424.7, and
ASAS 130057 + 2120.3 are believed to have very short
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J. A. OBU, P. N. OKEKE
124
(<1 day) orbital period and are strongly visible in the
visual band. Since the discovery of these objects, no further observational study has been carried out on the systems with a view to characterising their orbital and
physical properties. The objective of this study, therefore,
is to carry a comprehensive photometric study of these
three newly detected short-period eclipsing binaries in
order to: 1) determine their orbital and physical parameters, 2) determine the spectral and luminosity class of the
binary systems and 3) constrain the structure and evolutionary status of the systems.
The light curve analysis was carried out with the Wilson-Divenney (WD) codes [7], while the period analysis
was done with Peranso 2.50 [8]. The visual models were
obtained using the BinaryMaker 3.0 software [9].
2. Selection Criteria
We searched the ASAS catalogue and visually inspected
several thousand individual light curves of eclipsing binaries and extracted photometric data for those systems
that met our specific criteria, which include: 1) those
variable systems conclusively established by ASAS as
eclipsing binary systems; 2) systems for which no detailed study has been carried out on them; 3) systems
with orbital periods of less than one day, selected on the
basis that they might be close; 4) systems whose visual
magnitude V, ranges between 11 and 13. This is to ensure that we are dealing with systems that meet the exposure time limits for set for the observing telescope optics’ spectral resolving power, as this is directly related to
the accuracy of the measurement; 5) systems with light
curves that have a primary eclipse depth greater than 0.1
magnitude and those with well defined photometric
variations; and 6) systems with light curves where the
ratio of eclipse depths are not extreme. This is to ensure
that the secondary spectral lines will be readily detected,
if spectrometric analysis is to be carried out on these
systems.
3. The ASAS Eclipsing Binary Catalogue
The All Sky Automated Survey (ASAS) is blind optical
survey that monitors the variability of stars between 8th
and 14th magnitude in the visual (V) and infrared (I)
bands south of declination +28˚ at the coverage rate of
once in 1 - 3 days. The sky coverage became full in 2006.
These observations which are automated are carried out
at Las Campanas Observatory in Chile. The number stars
observed so far is approximately 20 million; the number
of detected variable sources is approximately 50,000 out
of which 39,000 are new variables. The number of
eclipsing binaries detected is 11,099 [6,10]. The ASAS
catalogue is publicly available, and can be accessed at
http://www.astrouw.edu.pl/asas and
http://www.archive.princeton.edu/asas.
4. Observational Data
The following basic information was extracted from
ASAS and used in the analysis of respective the binary
systems (see Table 1): the epoch of minimum light T0 ,
the Heliocentric Julian Date (HJD) of measurement, the
magnitude of the binary system measured in the visual
passband (Vmax), a preliminary orbital period, and the V
and I colour indices of the eclipsing system. The corresponding J, H, K colour indices were obtained from
2MASS (Two Micron All Sky Survey) and from these
colour indices the spectral class was inferred using the
scheme formulated by [11]. From the spectral class, the
mean effective temperature, Teff , of the systems as defined by [12] was determined using the calibration
scheme of [13].
Table 1. List of information extracted from the ASAS catalogue for the analysis of each binary system under study.
ASAS 110,609 − 2045.3
ASAS 105,331 − 7424.7
ASAS 130,057 + 2120.3
RA: 11:06:09
RA: 10:53:31
RA: 13:00:57
DEC: −20:45:18
DEC: −74:24:42
DEC: 21:20:18
Period (days)
0.293317
0.482494
0.89304
Epoch of primary minimum, T0 (HJD)
2451870.3
2451869.4
2452653.4
Vmax
13.1
13.04
11.92
Vamp
0.91
1.19
0.22
J
12.51
11.33
11.11
H
12.09
10.87
10.91
K
12.04
10.72
10.886
Time span of observations (HJD)
2451871.856 to 2454671.488
2451870.810 to 2454767.867
2452651.870 to 2455038.481
Astrometry (J2000)
Copyright © 2013 SciRes.
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J. A. OBU, P. N. OKEKE
125
5. Data Analysis
a02 N
5.1. Period Analysis
a12 cos 2 xi a02 cos xi
To obtain the most accurate period of the binary systems,
a detailed period analysis of the V-band magnitude data
for each system was done using the Date Compensated
Discrete Fourier Transform (DCDFT) method embedded
in the Peranso software programme. In the programme,
the Fourier integral of the raw magnitude data (obtained
in the time domain), and date of measurement are transformed in a discretised way into the period or frequency
domain taking into account the time of observation as
theoretically formulated by [14]. This is summarised below:
In the classical discrete Fourier transform (DFT) method, designated values f n taken at time tn are assigned to a continuous function f t , so that its discrete
Fourier transform is written as:
Fk
N 1
f n e k n
k 0 to N 1
0
(1)
n0
where N is the number of equispaced subintervals
t P N between 0 and t; n designates the discrete
times at which samples are taken. The inverse Fourier
transform is thus, given by:
fn
1
N
N 1
Fk eik n
0
n 0 to N 1
(2)
2
a22 sin 2 xi a02 sin xi a12 M 2
2
where M cos xi sin xi a02 sin xi cos xi and
c1 a1 fi cos xi
c2 a2 fi sin xi a1a2 c1 M .
S
c12 c22
.
f12
(3)
N is the number of observations in the series, ti , are
the observation dates, xi 2πti , and fi are the
measured m referred to their mean values, i.e. shifted
in a way such that fi 0 . The summations are made
for i 1 to i N .
Next, the range of frequencies to be investigated is
chosen. Usually, the range is taken from 0 to the Nyquist frequency. Then, an appropriate step to be used
in scanning the frequency range is chosen.
Once the frequency range and the step of scanning are
chosen, the value of S for each trial frequency was
computed, and the function S plotted.
From the value of for which S is maximum, the
period P, of the variation of the source is obtain as
P 1 .
k 0
where 0 2π N .
However, because photometric magnitude data such as
those from ASAS are not evenly well-sampled, in our
computational period analysis using the Peranso software [8], we used the embedded date compensated discrete Fourier transform (DCDFT) algorithm. The
DCDFT method as the name suggests, takes the time of
observation into account, meaning that the data no longer
has to be regularly sampled and, its underlying principle
corresponds to a curve fitting approach using a sinusoid-plus-constant model. Its algorithm is summarised
below.
The spacing between observations which in our case
is roughly three days was noted.
From it the spacing, the Nyquist frequency
(defined as the frequency of a sinusoid exactly
one-half that of the sampling frequency) was obtained.
The deviations from the mean value fi of the differential the magnitude m, were computed and
the standard error of measurements noted.
For each trial frequency one coefficient of spectral correlation S was obtained by the following formulae [14]:
Copyright © 2013 SciRes.
5.2. Light Curve Analysis
The number of geometrical and physical parameters that
enters the model of an eclipsing binary star is quite substantial (see Table 2); so that the task of the modelling is
to take these parameters and uniquely compute synthetic
light curves as predicted by the theory. This is referred to
as the direct problem: given the list of parameters, synthetic light curves are uniquely determined. In practice
however, photometric modelling involves exactly the
opposite: given the observational data, a set of parameters is determined for which the model yields a matching
synthetic curve. This is referred to as the inverse problem.
In this inverse problem-solving scheme, the solutionseeking process of an eclipsing binary data is formulated
as a nonlinear least-squares problem in which observed
curves are compared with model (synthetic) curves. In
our work, the optimisation of the agreement between the
observed and synthetic curves of the systems was carried
out computationally using the Wilson-Devinney (WD)
code.
As with other minimisation algorithms, the WD algorithm minimises the discrepancy between observational
and synthetic curves. This discrepancy is quantified in
terms of a cost function 2 , given by
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126
Table 2. A summary of the light curve solutions obtained from the photometric analysis of the binary systems under study.
Parameters
ASAS 110,609 − 2045.3
ASAS 105,331 − 7424.7
ASAS 130,057 + 2120.3
Inclination (˚)
80 ± 1
86 ± 2
55 ± 1
Mass ratio
0.5
0.9
0.6
Period (days)
0.2933 ± 0.0130
0.4825 ± 0.0002
0.8930 ± 0.0014
Effective temperature
5800 - 6200
5200 - 5400
6200 - 6500
1
2.921975
3.510969
3.010781
2
2.921975
3.510969
3.010781
L1 (solar units)
0.561155
0.510844
0.52343
L2 (solar units)
1.598379
0.681080
1.613038
Mean radius (1)
0.442641
0.400802
0.435176
Mean radius (2)
0.338254
0.382330
0.345871
Surface area (1) (solar units)
2.506699
2.042681
2.396313
Surface area (2) (solar units)
1.449540
1.848952
1.515361
Volume (1) (solar units)
0.360898
0.266694
0.341757
Volume (2) (solar units)
0.159746
0.230725
0.170806
Reflection effects (bolometric albedo)
0.5
0.5
0.5
Third light
0.5
0.1
0.6
Spots
No evidence
No evidence
No evidence
Disks
No evidence
No evidence
No evidence
k2 k i Fi obs Fi syn
Nk
1
2
i 1
k2
i Fi obs Fi syn (4)
Nk
i 1
for the k passband, where N k and k are, respecttively, the number and standard deviation of observational data points in that passband; i are individual
weights, k 1 k2 are passband weights; F obs is the
observed flux at the given phase and F syn is the synthetically-computed flux at the same phase. The weighted variance is given by:
th
sk2
1 Nk
i Fi obs F syn
N k 1 i 1
2
,
(5)
so that the passband cost function 2 , may be expressed as:
k2 N k 1
sk2
k2
(6)
.
The overall cost function is a sum of individual cost
functions for each observed curve, thus
M
M
sk2
k 1
k 1
k2
2 k2 N k 1
.
(7)
where M is the number of curves. If k are properly
Copyright © 2013 SciRes.
estimated, the ratio sk k is of the order of unity and
2 , of the order N tot k N k . This is used by the
code to parameterise 2 , values as:
2 N tot
(8)
It is this cost coefficient , that directly measure the
goodness of fit; if the value is ~1, the discrepancy between the model and observations is small and the fit is
satisfactory, and vice versa.
While carrying out the optimisation of agreement between the observed and synthetic curves, the orbits were
assumed to be circular and so the orbital eccentricity, e of
each of the systems was set at zero. The limb-darkening
coefficients were interpolated from van Hamme’s table at
the respective values suggested for convective and radiative stars [15]. Because of the convective nature of the
heat transportation in the envelopes, the values of gravity
brightening exponents for the systems were set as
g1 g 2 0.32 [16] and bolometric albedo A1 and A2
were set at the values suggested for convective and radiative atmospheres by [17]. The adopted adjustable parameters were: the effective temperature of secondary
component T2 , orbital radius, the orbital inclination i,
the fill-out factor, and the monochromatic luminosity of
the primary star L1 . Since no spectroscopic observations
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J. A. OBU, P. N. OKEKE
are available for these systems, we used the q-search
method to constrain the most important parameter, the
mass ratio q m2 m1 . In order to find the best value
of the mass ratio, we executed the code for various assumed values of mass ratio, while keeping in mind that
surface potential 1 2 also changes with respect
to the mass ratio.
6. Results
The results obtained from the photometric analysis of
each binary system are shown in Table 2, while the light
curves, 3-D model and surface outline of the binary systems are given in Table 3. The results of each of the systems are presented below.
127
6.1. ASAS 110609-2045.3
The photometric magnitude data for ASAS 110,609 −
2045.3 used for this study were those obtained between
30th September 2000 and 23rd July 2008. As evidenced
from its light curve (Table 3) we infer that the system is
a near-contact binary star of the W Uma type comprising
two main sequence stars. In addition, that the nature of
the primary eclipse is an occultation, while that of the
secondary is a transit. The computed value of the angle
of inclination of the system is 80˚ ± 1 to the line of sight.
We also established that ASAS 110609 − 2045.3 has a
mass ratio of about 0.5, a value that is consistent with
other W Uma-type binaries such as RW Com and BD +
07˚ 3142 [18]. The system showed evidence of a third
Table 3. The light curves, 3-D model and surface outline of the binary systems under study. In the light curve, the solid lines
are the synthetic curve while the dots trace the observed curve.
Light curve
3-D model
Surface outline
ASAS
110609 − 2045.3
ASAS
105331 − 7424.7
ASAS
130057 + 2120.3
Copyright © 2013 SciRes.
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128
J. A. OBU, P. N. OKEKE
light with a third light factor of about 0.5. Using the calibration scheme of [13] the deduced effective temperature
of ASAS 110,609 − 2045.3 is in the range of 5800 K 6200 K, making it a G2V-F7V system. The period was
established to be 0.2933 ± 0.0130 days. With this period,
the linear ephemeris equation for ASAS 110,609 −
2045.3 was determined to be:
Min I Hel. 2451871.85617 0.2933E 0.0130
(9)
where E corresponds to the cycle number.
6.2. ASAS 105331 − 7424.7
The photometric data for ASAS 105331 − 7424.7 obtained from 22nd November, 2000 to 28th October, 2008
were used in the analysis of the system. The eclipse is
inferred to be total as evidenced by the high value of the
inclination of the system (about 86˚ ± 2) to the line of
sight. We infer from the almost V-shape of the light
curve eclipse depth and the 3-D model (Table 1) that
ASAS 105,331 − 7424.7 is an over-contact binary star of
the W Uma type comprising two main sequence stars.
This is consistent with the light curves of other W Umas,
such as QX and XY Leonis [19]. During the solution
seeking procedure, a third light factor of only 0.1 was
established. In the modelling procedure, no evidence of
spots or discs was inferred for either component. The
photometric mass ratio was determined to be about 0.9,
consistent with the computed values of other W Umatype binaries having similar characteristics such as CV
Vel [19] and V236 [20]. The effective temperature was
computed to be in the range 5200 K - 5300 K, making it
a K2V-K0V system. The deduced period of ASAS
105331 − 7424.7 was 0.4825 ± 0.0002, which is consistent with the measured periods of other close binaries
such as QX and RW Com [18]. Thus, the derived linear
ephemeris equation for ASAS 110609 − 2045.3 is given
by:
Min I Hel. 2451871.85617 0.4825E 0.0002 (10)
where E corresponds to the cycle number.
6.3. ASAS 130,057 + 2120.3
Observational data for ASAS 130057 + 2120.3 obtained
from the 12th January 2003 to 27th July 2009 were used
in the analysis of the system. The results from the analysis of its light curve indicate that ASAS 130057 + 2120.3
is W Uma binary having a mass ratio of about 0.6 in a
state of marginal contact. This shallow degree of contact
is consistent with other eclipsing pairs such as XY Leo
[19]. The light curve variations is slightly above 0.1 mag
indicating a low orbital inclination, deduced in this study
to be 55˚ ± 1 to the line of sight. The effective temperature of this system was established to be in the range of
Copyright © 2013 SciRes.
6200 K - 6500 K, making it a F7-F5 stellar system,
which is consistent with spectral range of other W Uma
type binaries. The system showed evidence of third light,
with a third light factor of 0.6, however, the presence of
spots or discs could not be established for either component.
The deduced period of ASAS 130,057 + 2120.3 was
0.8930 ± 0.0014 days; so that its derived linear ephemeris equation is given by:
Min I Hel. 2451871.8561 0.8930 E 0.0014
(11)
where E corresponds to the cycle number.
7. Discussion
An inspection of the observed data curve for the three
binary systems reveals scattered phase points, with the
primary and secondary minima not coinciding with the
zero and 0.5 phase points as expected. This strongly
suggests that the period of these systems might actually
be varying over the time span of the observational data
used. In addition, our study shows that all the systems
have a mass ratio greater than 0.4 and so, they should
have a trend of increasing period i.e. the systems should
evolve towards a semi-detached configuration [21]. This
might be especially true for ASAS 130057 + 2120.3
which from its light curve can be inferred to be in a state
of marginal contact because of its evolution from a contact state to a semi-detached one according to the thermal
relaxation oscillation (TRO) model.
Furthermore, in performing the light curve solutionseeking procedure we assumed that there were no spots
or disks on the surfaces of the components of the binaries,
and as evidenced from the symmetrical shape of the light
curve, the systems do not exhibit any significant O’Connell effect. However, it is important to note here that the
case of these binaries in this regard is an exception, since
most of the light curves of W Uma-type systems, e.g.
V523 Cas [22-24] show asymmetries and irregularities
usually interpreted by invoking cool (and/or hot) spots on
the surfaces of the two components. Also, the scattered
phase points in the observed light curves of the three
systems (coupled with their respective third light factor)
further suggests the likely presence of a third body, such
as an exoplanet or another star altogether, in the neighbourhood of these systems, thus making them a triple
system.
Conclusions and Recommendations for Further
Work
We have carried out a photometric study of three previously unstudied eclipsing binary stars using data from the
ASAS catalogue, namely: ASAS 110609 − 2045.3,
ASAS 105331 − 7424.7, and ASAS 130057 + 2120.3.
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J. A. OBU, P. N. OKEKE
Preliminary result of our study reveals that ASAS
110,609 − 2045.3 a near-contact binary star of the W
Uma type comprising two main sequence stars, and that
the nature of the primary eclipse is an occultation, while
that of the secondary is a transit. The computed value of
the angle of inclination of the system is 80˚ ± 1 to the
line of sight. We also established that it has a mass ratio
of about 0.5, a value that is consistent with other W
Uma-type binaries. The modelling also suggests that the
system has a third light factor of about 0.5. Its deduced
effective temperature is in the range of 5800 K - 6200 K,
making it a G2V-F7V spectral system. The period was
established to be 0.2933 ± 0.0130 days. The photometric
analysis of ASAS 105331 − 7424.7 that ASAS 105331 −
7424.7 is an over-contact binary star of the W Uma type
comprising two main sequence stars. The eclipse is inferred to be total as evidenced by the high value of the
inclination of the system (about 86˚ ± 2) to the line of
sight. During the solution seeking procedure, only a third
light factor of just 0.1 was established, and the photometric mass ratio was determined to be about 0.9, consistent
with the computed values of other W Uma-type binaries
having similar characteristics such as CV Vel and V236.
The effective temperature was computed to be in the
range 5200 K - 5300 K, making it a K2V-K0V spectral
system. Its deduced period was 0.4825 ± 0.0002. For
ASAS 130,057 + 21220.3 the analysis of its light curve
indicates that it is a W Uma binary having a mass ratio of
about 0.6 in a state of marginal contact. This shallow
degree of contact is consistent with other eclipsing pairs
such as XY Leo. The light curve variations are slightly
above 0.1 mag indicating a low orbital inclination, deduced in this study to be 55˚ ± 1 to the line of sight. The
effective temperature of this system was established to be
in the range of 6200 K - 6500 K, making it a F7V-F5V
stellar system, which is consistent with spectral range of
other W Uma type binaries. The system showed evidence
of third light, with a third light factor of 0.6. The deduced
period of ASAS 130,057 + 2120.3 was 0.8930 ± 0.0014
days.
Since this was a first time photometric study of these
eclipsing binary stars, the solutions obtained here does
not give all the physical properties of the systems as will
be expected, and even those obtained here using the photometric technique might not be as precise as required. It
is therefore recommended that further photometric and
spectroscopic observations and modelling be undertaken
to know the possible period changes and constrain the
mass ratio and age of the component stars in these binary
systems. Astrometric observations would also be useful
to detect astrometric wobbles associated with a third body in the system. A combination of this technique and a
detection of radial velocity variations in the parent stars
(induced by the gravitational tug of the orbiting third
Copyright © 2013 SciRes.
129
body) will confirm or refute the presence of a third body
such as an exoplanet or third star in the system.
REFERENCES
[1]
H. A. Abt, “Normal and Abnormal Binary Frequencies,”
Annual Review of Astronomy and Astrophysics, Vol. 21,
1983, pp. 343-372.
doi:10.1146/annurev.aa.21.090183.002015
[2]
D. W. Latham, T. Mazeh, R. P. Stefanik, R. J. Davis, B.
W. Carney, G. Torres and J. B. Laird, “Spectroscopic Binaries in the Halo,” In: H. A. McAlister and W. I. Hartkopf, Eds., Complementary Approaches to Double and
Multiple Star Research, IAU Colloquium 135, ASP Conference Series, Vol. 32, 1992, pp. 158-161.
[3]
D. J. Pinfield, P. D. Dobbie, R. F. Jameson, I. A. Steele,
H. R. A. Jones and A. C. Katsiyannis, “Brown Dwarfs
and Low-Mass Stars in the Pleiades and Praesepe: Membership and Binarity,” Monthly Notices of the Royal Astronomical Society, Vol. 342, No. 4, 2003, pp. 1241-1259.
doi:10.1046/j.1365-8711.2003.06630.x
[4]
C. Maceroni, “Binaries as Astrophysical Laboratories: An
Overview,” In: C. Sterken and C. Aerts, Eds., Astrophysics of Variable Stars, ASP Conference Series, Vol. 349,
2006, pp. 41-53.
[5]
I. Ribas, “Binary Stars as Astrophysical Laboratories: Open
Questions,” In: C. Sterken and C. Aerts, Eds., Astrophysics of Variable Stars, ASP Conference Series, Vol. 349,
2006, pp. 55-70.
[6]
B. Paczynski, D. M. Szczygiel, B. Pilecki and G. Pojmanski, “Eclipsing Binaries in the All Sky Automated Survey
Catalogue,” Monthly Notices of the Royal Astronomical
Society, Vol. 368, No. 3, 2006, pp. 1311-1318.
doi:10.1111/j.1365-2966.2006.10223.x
[7]
R. E. Wilson and E. J. Divenney, “Realization of Accurate
Close-Binary Light Curves: Application to MR Cygni,”
The Astrophysical Journal, Vol. 166, 1971, pp. 605-619.
doi:10.1086/150986
[8]
T. Vanmunster, “Peranso 2.5: A Light Curve and Analysis Software User Manual,” 2008. CBABelgium.com
[9]
D. H. Bradstreet and D. P. Steelman, “Binary Maker 3: User
Manual,” Contact Software, Norristown, 2005.
[10] G. Pojmanski, “The All Sky Automated Survey. Catalog
of Variable Stars I. 0h-6h Quarter of the Southern Hemisphere,” Acta Astronomica, Vol. 52, 2002, pp. 397-427.
[11] M. S. Bessell and J. M. Brett, “JHKLM Photometry: Standard Systems, Passbands, and Intrinsic Colors,” Publications of the Astronomical Society of the Pacific, Vol. 100,
1988, pp. 1134-1151. doi:10.1086/132281
[12] R. E. Wilson, “Eccentric Orbit Generalization and Simultaneous Solution of Binary Star Light and Velocity
Curves,” The Astrophysical Journal, Vol. 234, 1979, pp.
1054-1066. doi:10.1086/157588
[13] A. T. Tokunaga, “Effective Temperatures and Intrinsic
Colours for Main Sequence, Giant, and Supergiant Stars,”
In: A. N. Cox, Ed., Allen’s Astrophysical Quantities, 4th
Edition, Springer-Verlag, New York, 2000, pp. 143-149.
doi:10.1007/978-1-4612-1186-0_7
IJAA
130
J. A. OBU, P. N. OKEKE
[14] S. Ferraz-Mello, “Estimation of Periods from Unequally
Spaced Observations,” Astronomical Journal, Vol. 86,
1981, pp. 619-624. doi:10.1086/112924
Binary Stars,” Ph.D. Dissertation, Ege University, Izmir,
2006.
[15] W. van Hamme, “New Limb-Darkening Coefficients for
Modeling Binary Star Light Curves,” Astronomical Journal, Vol. 106, No. 5, 1993, pp. 2096-2117.
doi:10.1086/116788
[20] R. Y. Kiron, K. Sriram and R. Vivekananda, “Photometric
Parameters, Distance and Period-Colour Study of Contact Binary Stars in the Globular Cluster ω Centauri,”
Bulletin of the Astronomical Society of India, Vol. 39,
2011, pp. 247-257.
[16] L. B. Lucy, “The Light Curves of W Ursae Majoris Stars,”
Astrophysical Journal, Vol. 153, 1968, pp. 877-884.
doi:10.1086/149712
[21] Qian, “Possible Mass and Angular Loss in Algol-Type Binaries. V. RT Persei and TX Ursae Majoris,” Astronomical Journal, Vol. 122, 2001, pp. 2686-2691.
[17] S. M. Rucinski, “The Photometric Proximity Effects in
Close Binary Systems. I. The Distortion of the Components and the Related Effects in Early Type Binaries,”
Acta Astronomica, Vol. 19, 1969, pp. 125-153.
[22] R. G. Samec, D. R. Faulker and D. B. Williams, “The Physical Nature and Orbital Behavior of V523 Cassiopeiae,”
Astronomical Journal, Vol. 128, No. 6, 2004, pp. 29973004. doi:10.1086/426357
[18] G. Djuraševic, M. Yilmaz, Ö. Bastürk, T. Kiliçoglu, O.
Latkovic and S. Çaliskan, “Physical Parameters of Close
Binaries QX Andromedae, RW Comae Berenices, MR
Delphini, and BD + 07˚ 3142,” Astronomy and Astrophysics, Vol. 525, 2011.
doi:10.1051/0004-6361/201014895
[23] O. Latkovic, M. Zboril and G. Djurassevic, “Light Curve
Analysis of the Late Type Binary V523 Cassiopeiae” Serbian Astronomical Journal, Vol. 178, 2009, pp. 45-48.
doi:10.2298/SAJ0978045L
[19] K. Yakut, “An Observational Study of Unevolved Close
Copyright © 2013 SciRes.
[24] S. Zola, P. Niarchos, V. Manimamis and A. Dapergolas,
“A Photometric Study of BH Cas,” Astronomy & Astrophysics, Vol. 374, 2001, pp. 164-170.
IJAA