Volume 2015, Issue 1 590673
Research Article
Open Access

An Extensive Photometric Investigation of the W UMa System DK Cyg

M. M. Elkhateeb

M. M. Elkhateeb

Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo 11421, Egypt nriag.sci.eg

Physics Department, College of Science, Northern Border University, Arar 1321, Saudi Arabia nbu.edu.sa

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M. I. Nouh

Corresponding Author

M. I. Nouh

Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo 11421, Egypt nriag.sci.eg

Physics Department, College of Science, Northern Border University, Arar 1321, Saudi Arabia nbu.edu.sa

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E. Elkholy

E. Elkholy

Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo 11421, Egypt nriag.sci.eg

Physics Department, College of Science, Northern Border University, Arar 1321, Saudi Arabia nbu.edu.sa

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B. Korany

B. Korany

Astronomy Department, National Research Institute of Astronomy and Geophysics, Helwan, Cairo 11421, Egypt nriag.sci.eg

Physics Department, Faculty of Applied Science, Umm Al-Qura University, Makkah 715, Saudi Arabia uqu.edu.sa

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First published: 15 January 2015
Academic Editor: Theodor Pribulla

Abstract

DK Cyg (P = 0.4707) is a contact binary system that undergoes complete eclipses. All the published photoelectric data have been collected and utilized to reexamine and update the period behavior of the system. A significant period increase with rate of 12.590 × 10−11 days/cycle was calculated. New period and ephemeris have been calculated for the system. A long term photometric solution study was performed and a light curve elements were calculated. We investigated the evolutionary status of the system using theoretical evolutionary models.

1. Introduction

The eclipsing binary DK Cyg (BD +330 4304, 10.37–10.93 mv) is a well known contact binary system with a period of about 0.4707 days. It was discovered as variable star earlier by Guthnick and Prager [1], so their epoch of intensive observations is very long. The earliest photographic light curve classified the system as a W Ursae Majoris type. Rucinski and Lu [2] carried out the first spectroscopic observations and estimated the mass ratio as q = 0.325 and classified the system as an A-subtype contact system with spectral type of A8V. Visual light curves were published by Piotrowski [3] and Tsesevitch [4] from Klepikova’s observations.

First photoelectric observations for the system were carried out by Hinderer [5], while Binnendijk [6] observed the system photoelectrically in B- and V-bands and derived least squares orbital solution. The system DK Cyg was classified in the General Catalogue of Variable Stars as A7V [7], while Binnendijk [6] adopted it as A2. Mochnacki and Doughty [8] showed that the color index of the system judged its spectral type and found that the spectral type of the system is more likely to be about F0 to F2. Because the system DK Cyg is a summer object in the Northern hemisphere with 11.5-hour period and short durations of night, it is bound to remain ill-observed [9]. Only four complete light curves by Binnendijk [6], Paparo et al. [10], Awadalla [9], and Baran et al. [11] are published. Photoelectric observations and new times of minima have been carried out by many authors: Borkovits et al. [12], Sarounová and Wolf [13], Drozdz and Ogloza [14], Hübscher et al. [15], Dogru et al. [16], Hubscher et al. [17], Hubscher et al. [18], Erkan et al. [19], Diethelm [20], Dogru et al. [21], Simmons [22], Diethelm [23], and Diethelm [24].

In the present paper we are going to perform comprehensive photometric study for the system DK Cyg. The structures of the paper are as follows: Section 2 deals with the period change, Section 3 is devoted to the light curve modeling, and Section 4 presents the discussion and conclusion reached.

2. Period Change

Although the period variation of contact binary systems of the W UMa-type is a controversial issue of binary star astrophysics, the cause of the variations (long as well as short term) is still a mystery for a discussion of possible physical mechanisms [25]. Magnetic activity cycle is one of the main mechanisms that caused a period variation together with the mass exchange between the components of each system. Kaszas et al. [26] stated that the long term period variation may be interpreted by a perturbation of the third companion or surface activity of the system components.

Observations by Binnendijk [6] showed a change of the secondary minimum depth and a new linear light element was derived. Period study by Paparo et al. [10] showed that the orbital period of the system DK Cyg increases and the first parabolic light elements were calculated, which confirmed the light curve variability. Kiss et al. [25] updated the linear ephemeris of DK Cyg, while Awadalla [9] recalculated a new quadratic element for the system and confirmed the light curve variability suggested by Paparo et al. [10]. Wolf et al. [27] used a set of 101 published times of minimum covering the interval between 1926 and 2000 in order to update the quadratic element calculated by Awadalla [9]. They showed that the period increases by the rate 11.5 × 10−11 days/cycle. Borkovits et al. [28] follow the period behavior of the system using set of published minima from HJD 2424760 to HJD 2453302.

In this paper we studied the orbital period behavior of the system DK Cyg using the (OC) diagram based on more complete data set collected from the literatures and databases of BAV, AAVSO, and BBSAG observers. Part of our collected data set was given by Kreiner et al. [29]; unpublished Hipparcos observations and main part were downloaded from website (http://astro.sci.muni.cz/variables/ocgate/); Table 1 listed only those minima not listed on the mentioned websites. A total of 195 minima times were incorporated in our analysis covering about 86 years (66689 orbital revolutions) from 1927 to 2013. It is clear that our set of data added about 94 of new minima and increases the interval limit of the orbital period study about 13 years more than the data of Wolf et al. [27], which may give more accurate insight on the period behavior of the system. The different types of the collected minima (i.e., photographic, visual, photoelectric, and CCD) were weighted according to their type. The residual (OC)’s were computed using Binnendijk [6] ephemeris (1) and represented in Figure 1. No distinction has been made between primary and secondary minima:
()
It can be seen from the figure that the behavior of the orbital period of the system DK Cyg shows a parabolic distribution which is generally interpreted by the transfer of mass from one component to the other of binary. Reasonable linear least squares fit of the data available improved the light elements given in (1) to
()
The linear element yields a new period of P = 0d.47069206 days which is longer by 0.13 seconds with respect to the value given by Binnendijk [6]. Quadratic least squares fit gives
()
The rate of period increasing resulting from the quadratic elements (3) is dP/dE = 12.568 × 10−11 days/cycle or 9.746 × 10−8 days/year or 0.84 seconds/century. More future systematic and continuous photometric observations are needed to follow a continuous change in the orbital period of the system DK Cyg which may show a periodic behavior. The fourth column of Table 1 represents the quadratic residuals (OC)q calculated using the new element of (2) and represented in Figure 2. All published linear and quadratic elements together with that resulting from our calculations are listed in Table 2. It is noted from the table that the quadratic term resulting from our calculations has slightly higher value than that calculated by Awadalla [9], Wolf et al. [27], and Borkovits et al. [28]. This can be interpreted by the increasing of the set of minima in our study compared to the one they used (nearly double); also we covered an interval larger than the one they used.
Table 1. Times of minimum light for DK Cyg.
HJD Method E (OC) (OC)q References HJD Method E (OC) (OC)q References
2434179.4690 Vis −8116 0.00970 0.00971 1 2451749.4450 pe 29212 0.04885 −0.00370 3
2447758.4352 Pe 20733 0.02423 −0.00099 2 2451777.6740 ccd 29272 0.03642 −0.01636 5
2447790.4437 Pe 20801 0.02577 0.00037 2 2452163.6590 ccd 30092 0.05517 −0.00074 5
2447963.6620 Pe 21169 0.02995 0.00354 3 2452245.5592 ccd 30266 0.05521 −0.00137 5
2447963.8960 Pe 21169.5 0.02860 0.00220 3 2452253.5613 ccd 30283 0.05557 −0.00108 5
2448265.1380 Pe 21809.5 0.02865 0.00046 4 2452441.8384 ccd 30683 0.05645 −0.00176 5
2448265.1382 Pe 21809.5 0.02885 0.00066 4 2452512.4415 pe 30833 0.05597 −0.00284 7
2448272.1987 Pe 21824.5 0.02899 0.00076 4 2452525.6231 ccd 30861 0.05824 −0.00069 5
2448297.6160 Pe 21878.5 0.02900 0.00062 3 2452526.5644 ccd 30863 0.05816 −0.00078 5
2448302.7930 Pe 21889.5 0.02841 −0.00001 3 2452811.8062 ccd 31469 0.06148 0.00013 5
2448308.2078 Pe 21901 0.03027 0.00182 4 2453223.4286 ccd 32343.5 0.06500 −0.00006 8
2448308.2079 Pe 21901 0.03037 0.00192 4 2453228.3681 ccd 32354 0.06225 −0.00274 8
2448336.4491 Pe 21961 0.03013 0.00152 4 2453246.4950 ccd 32392.5 0.06756 0.00242 8
2449988.5840 ccd 25471 0.04120 0.00182 5 2453247.4346 ccd 32394.5 0.06578 0.00063 8
2450003.6456 ccd 25503 0.04070 0.00122 5 2453285.3260 ccd 32475 0.06659 0.00110 8
2450313.8240 ccd 26162 0.03403 −0.00765 5 2453286.2657 ccd 32477 0.06491 −0.00059 8
2450341.6130 ccd 26221 0.05229 0.01041 5 2453302.2672 ccd 32511 0.06293 −0.00271 8
2450397.6060 ccd 26340 0.03311 −0.00917 5 2454799.5505 ccd 35692 0.07959 0.00004 9
2450692.7400 ccd 26967 0.04414 −0.00030 5 2455043.8381 ccd 36211 0.07882 −0.00310 10
2451000.0990 pe 27620 0.04221 −0.00452 5 2455062.6680 ccd 36251 0.08107 −0.00105 11
2451095.6600 ccd 27823 0.05303 0.00557 5 2455088.5544 ccd 36306 0.07953 −0.00285 10
2451160.5980 ccd 27961 0.03573 −0.01222 5 2455810.6029 ccd 37840 0.08870 −0.00096 12
2451379.4820 pe 28426 0.04863 −0.00101 3
  • (1) Szafraniec [30]; (2) Hubscher et al. [31]; (3) Wolf et al. [27]; (4) Hipparcos observations (unpublished); (5) Baldwin and Samolyk [32]; (6) Kiss et al. [25]; (7) Borkovits et al. [33]; (8) Borkovits et al. [28]; (9) Gerner [34]; (10) Menzies [35]; (11) Samolyk [36]; (12) Simmons [22].
Table 2. The light elements of DK Cyg.
JD Period Quadratic term References
2437999.5838 0.470690550 Binnendijk [6]
2437999.5828 0.470690660 5.390 × 10−10 Paparo et al. [10]
2437999.5825 0.470690730 5.760 × 10−11 Awadalla [9]
2451000.0999 0.470692900 Kiss et al. [25]
2437999.5825 0.470690640 5.750 × 10−11 Wolf et al. [27]
2451000.1031 0.470693909 5.862 × 10−11 Borkovits et al. [28]
2437999.5961 0.470692060 Present work
2437999.5803 0.470690640 6.284 × 10−11 Present work
Details are in the caption following the image
Period behavior of DK Cyg.
Details are in the caption following the image
Calculated residuals from the quadratic ephemeris.

3. Light Curve Modeling

Light curve modeling for the system DK Cyg by Mochnacki and Doughty [8] using Binnendijk [6] observations in V-band showed nonmatching between the theoretical curve and the observations. The photometric mass ratio calculated from their accepted model was qph = 0.33 ± 0.02, while the spectroscopic value estimated using radial velocity study by Rucinski and Lu [2] is qsp = 0.325 ± 0.04. Baran et al. [11] estimated an alternating model of spectroscopic and photometric data based on iterative solutions. Their model shows a better fit by introducing a cool spot on the surface of the more luminous component and adopted the third light as free parameter in the computations. On the other hand Rucinski and Lu [2] stated that they did not find any evidence for the existence of a third component in the system during their spectroscopic study. They refer the probability for the presence of a third star in the system to the (OC) diagram [29], which shows sinusoidal variation. This evidence is weak because only one cycle is covered up to date.

In the present work we used complete light curves published by Binnendijk [6], Paparo et al. [10], Awadalla [9], and Baran et al. [11] in V-band through a long term photometric solution study in order to estimate the physical parameters of the system and to follow its evolutionary status. The collected light curves showed a flat-bottom minima and O’Connell effect. Observations by Paparo et al. [10] and Awadalla [9] displayed some scattering specially at the two maxima of their light curves. Also the observed light curve by Awadalla [9] shows sudden increase in the light level at secondary minimum with respect to the other collected curves.

Photometric analysis for the studied light curves of the system DK Cyg was carried out using Mode 3 (overcontact) of WDint56a Package [43] based on the 2009 version of Wilson and Devinney (W-D) code with Kurucz model atmospheres [4446]. The observed light curves were analyzed using all individual observations. Appropriate gravity darkening and bolometric albedo exponents were assumed for the convective envelope. We adopted g1 = g2 = 0.32 [47] and A1 = A2 = 0.5 [48]. Bolometric limb darkening values are adopted using the table of van Hamme [49]. Temperature of the primary star was adopted according to Baran et al. [11] model (T1 = 7500°K).

The adjustable parameters are the mean temperature of the secondary component T2, orbital inclination i, and the potential of the two components Ω = Ω1 = Ω2, while the spectroscopic mass ratio (qsp = 0.306) by Baran et al. [11] was fixed for all calculated models together with the primary star’s temperature (T1).

We started modeling using as initial values the parameters of Baran et al. [11] solution based on cool spot on the luminous components and a third light as a free parameter. The used parameters show disagreement between the theoretical and observed light curves, except for Baran et al. observations. Regarding the conclusion of Rucinski and Lu [2], which stated a weak evidence of presence of a third component, we tried to construct a spotted model without the third light. We constructed a model including two spots; the first one is a cool spot located on surface of the more massive component, while the other is a hot spot located on the surface of the other component. The accepted model reveals good agreement between theoretical and observed light curves for all collected data. Table 3 lists the calculated parameters for the four light curves, while Figure 3 represented the theoretical light curves according to the accepted solution together with the reflected points in V-band. The ∑(OC) 2 values in Table 3 are indicative of comparisons in future studies, since the number of observations and the accuracy are not the same in the four light curves. Absolute physical parameters for each component of the system DK Cyg were calculated based on the results of the radial velocity data of Baran et al. [11] and our new photometric solution for each light curve. The calculated parameters are listed in Table 3. The results show that the primary component is more massive and hotter than the secondary component. A three-dimensional geometrical structure for the system DK Cyg is displayed in Figure 4 using the software Package Binary Maker 3.03 [50] based on the calculated parameters resulting from our models.

Table 3. Photometric solutions for DK Cyg.
Parameter Binnendijk [6] Paparo et al. [10] Awadalla [9] Baran et al. [11]
A 5500 5500 5500 5500
i (°) 80.59 ± 0.12 80.22 ± 0.21 80.83 ± 0.27 79.97 ± 0.06
g1 = g2 0.32 0.32 0.32 0.32
A1 = A2 0.5 0.5 0.5 0.5
q (M2/M1) 0.306* 0.306* 0.306* 0.306*
Ω1 = Ω2 2.4064 ± 0.002 2.4077 ± 0.005 2.3325 ± 0.004 2.3886 ± 0.001
Ωin 2.4794 2.4794 2.4794 2.4794
Ωout 2.2888 2.2888 2.2888 2.2888
T1 (°K) 7500* 7500* 7500* 7500*
T2 (°K) 6767 ± 4 6726 ± 7 6726 ± 9 6759 ± 2
  
r1 pole 0.4696 ± 0.0007 0.4694 ± 0.0013 0.4861 ± 0.0014 0.4735 ± 0.0003
r1 side 0.5091 ± 0.0010 0.5087 ± 0.0018 0.5328 ± 0.0021 0.5145 ± 0.0004
r1 back 0.5400 ± 0.0013 0.5395 ± 0.0024 0.5716 ± 0.0029 0.5471 ± 0.0005
r2 pole 0.2792 ± 0.0008 0.2789 ± 0.0014 0.2980 ± 0.0017 0.2835 ± 0.0003
r2 side 0.2932 ± 0.0010 0.2929 ± 0.0017 0.3166 ± 0.0022 0.2985 ± 0.0004
r2 back 0.3414 ± 0.0019 0.3407 ± 0.0034 0.3982 ± 0.0068 0.3522 ± 0.0008
  
Spot A of star 1
 Colatitude 130* 130* 130* 130*
 Longitude 180* 180* 180* 180*
 Spot radius 33.61 ± 0.230 30.74 ± 0.437 27.23 ± 1.14 35.014 ± 0.09
 Temp. factor 0.796 ± 0.003 0.840 ± 0.007 0.924 ± 0.01 0.819 ± 0.001
  
Spot A of star 2
 Colatitude 120* 120* 120* 120*
 Longitude 290* 290* 290* 290*
 Spot radius 32.99 ± 3.60 29.42 ± 1.34 33.08 ± 1.24 29.44 ± 1.20
 Temp. factor 1.01 ± 0.01 1.01 ± 0.01 1.17 ± 0.01 1.02 ± 0.002
  
∑(OC)2 0.0229 0.02909 0.02458 0.0453
  • *Not adjusted.
Details are in the caption following the image
Observed and synthetic light curves of Binndijik [6] (Bin), Paparo et al. [10] (Pap), Awadalla [9] (Awa), and Baran et al. [11] (Bar), for the system DK Cyg.
Details are in the caption following the image
Three-dimensional models of the components of DK Cyg.

4. Discussion and Conclusion

Studying of the period behavior of the system DK Cyg based on all available published times of minima, covering 86 yr of observations including 195 times of light minima, shows a continuous period increase with the rate dP/dE = 12.590 × 10−11 days/cycle or 9.763 × 10−8 days/year or 0.84 seconds/century. New linear and quadratic elements were calculated using all available published data and yield a new period of P = 0.47069203 days. A long term photometric study was performed using published observations by Binnendijk [6], Paparo et al. [10], Awadalla [9], and Baran et al. [11]. More systematic and continuous photometric observations for the system DK Cyg are needed to confirm a continuous change in the period and follow its light curve variation.

One of the difficulties for W UMa binaries is to use stellar models of single stars to investigate the evolutionary status of these systems. However, using these theoretical models may give approximate view about the evolutionary status of the system.

We used the physical parameters listed in Table 4 to investigate the current evolutionary status of DK Cyg. In Figures 5 and 6, we plotted the components of DK Cygon on the mass-luminosity (M-L) and mass-radius (M-R) relations along with the evolutionary tracks computed by Girardi et al. [51] for both zero age main sequence stars (ZAMS) and terminal age main sequence stars (TAMS) with metallicity z = 0.019. As it is clear from the figures, the primary component of the system is located nearly on the ZAMS for both the M-L and M-R relations. The secondary component is above the TAMS track for M-L and the M-R relations. For the sake of comparison, we plotted sample of A-type contact binaries listed in Table 5. The components of DK Cyg have the same behavior of the selected A-type systems.

Table 4. Absolute physical parameters for DK Cyg.
Parameter Binnendijk [6] Paparo et al. [10] Awadalla [9] Baran et al. [11]
M1⊙ 1.7363 ± 0.0709 1.7358 ± 0.0709 1.7679 ± 0.0722 1.7438 ± 0.0712
M2⊙ 0.5313 ± 0.0217 0.5312 ± 0.0217 0.5410 ± 0.0221 0.5336 ± 0.0218
R1⊙ 1.7037 ± 0.0696 1.7029 ± 0.0695 1.7635 ± 0.0720 1.7178 ± 0.0701
R2⊙ 1.0129 ± 0.0414 1.0118 ± 0.0413 1.0811 ± 0.0441 1.0285 ± 0.0420
T1⊙ 1.2980 ± 0.0530 1.2980 ± 0.0530 1.2980 ± 0.0530 1.2980 ± 0.053
T2⊙ 1.1712 ± 0.0478 1.1641 ± 0.0475 1.1641 ± 0.0475 1.1698 ± 0.0478
M1_bol 2.4617 ± 0.1005 2.4627 ± 0.1005 2.3868 ± 0.0974 2.4438 ± 0.1000
M2_bol 4.0375 ± 0.1648 4.0662 ± 0.1660 3.9224 ± 0.1601 4.0094 ± 0.1637
L1⊙ 8.2285 ± 0.3359 8.2208 ± 0.3356 8.8163 ± 0.3600 8.3653 ± 0.3415
L2⊙ 1.9276 ± 0.0787 1.8772 ± 0.0766 2.1431 ± 0.0875 1.9780 ± 0.0808
  • Note: subscripts 1 and 2 mean primary and secondary component, respectively.
Table 5. Physical parameters of the five A-type contact binaries.
Star name Parameters References
M1(M) M2(M) R1(R) R2(R) L1(L) L2(L)
YY CrB 1.404 0.339 1.427 0.757 2.58 6.68 1
AW UMa 1.6 0.121 1.786 0.739 7.47 0.804 2
EQ Tau 1.214 0.541 1.136 0.787 1.31 0.6 3
RR Cen 1.82 0.38 2.1 1.05 8.89 2.2 4
V566 Oph 1.41 0.34 1.45 0.77 4.46 1.23 5
  • (1) Essam et al. [38], (2) Elkhateeb and Nouh [39], (3) Elkhateeb and Nouh [40], (4) Yang et al. [41], and (5) Degirmenci [42].
Details are in the caption following the image
The position of the components of DK Cyg on the mass-radius diagram. The filled symbols denote the primary component and the open symbols represent the secondary component. The star symbols denote the sample of the selected A-type systems listed in Table 5.
Details are in the caption following the image
The position of the components of DK Cyg on the mass-luminosity diagram. The filled symbols denote the primary component and the open symbols represent the secondary component. The star symbols denote the sample of the selected A-type systems listed in Table 5.

The mass-effective temperature relation (M-Teff) for intermediate and low mass stars [37] is displayed in Figure 7. The location of our mass and radius on the diagram revealed a good fit for the primary and poor fit for the secondary components. This gave the same behavior of the system on the mass-luminosity and mass-radius relations.

Details are in the caption following the image
Position of the components of DK Cyg on the empirical mass-Teff relation for low-intermediate mass stars by Malkov [37]. The filled symbols denote the primary component and the open symbols represent the secondary component.

Conflict of Interests

The authors declare that they have no conflict of interests regarding the publication of this paper.

Acknowledgments

This research has made use of NASA’s ADS and the available on-line material of the IBVS. The authors sincerely thank Dr. Bob Nelson, who allowed them to use his windows interface code WDwint56a, for his helpful discussions and advice.

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