Period Variation Study and Light Curve Analysis of the Eclipsing Binary GSC 02013-00288

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Abstract

We analyzed the first set of complete CCD light curves of the W UMa type eclipsing binary IK Boo in the BVRI bands by using the PHOEBE code and deduced its first photometric parameters with, mass ratio q = 0.648 and orbital inclination i = 63o. We have applied a spotted model due to the light curves asymmetry. The system shows a distinct O’Connell effect. The best solution fit to the light curves suggested the influence of star spot(s) on both components. Such presence of star spot(s) is common among the RS CVn and W UMa chromospheric active late type stars.

We also present an analysis of mid–eclipse time measurements of IK Boo. The analysis indicates a period decrease rate dP/dt = −1.68 × 10−7d/yr, which can be interpreted in terms of mass transfer of rate 3.1 × 10−7M/yr, from the more massive to the less massive component.

Abstract

We analyzed the first set of complete CCD light curves of the W UMa type eclipsing binary IK Boo in the BVRI bands by using the PHOEBE code and deduced its first photometric parameters with, mass ratio q = 0.648 and orbital inclination i = 63o. We have applied a spotted model due to the light curves asymmetry. The system shows a distinct O’Connell effect. The best solution fit to the light curves suggested the influence of star spot(s) on both components. Such presence of star spot(s) is common among the RS CVn and W UMa chromospheric active late type stars.

We also present an analysis of mid–eclipse time measurements of IK Boo. The analysis indicates a period decrease rate dP/dt = −1.68 × 10−7d/yr, which can be interpreted in terms of mass transfer of rate 3.1 × 10−7M/yr, from the more massive to the less massive component.

1 Introduction

The star IK Boo (= GSC 02013-00288, magB=12.16, B-V=0.81, FONAC.Catalogue, Kislyuk+1999) was reported by Akerlof et al. [1] as a newly discovered eclipsing binary system. Unfiltered CCD light curve with SBIG ST-7 camera attached to the 0.15m starfire reflector in Wald, Switzerland, was obtained by Blättler during 6 nights between JD 2453382 (2005, Jan 12) and JD 2453517 (2005, May 27)(Figure 1). Blättler and Diethlem [3] reported the system to be an eclipsing W UMa type with a magnitude range 11.42-11.76 (<mag>=11.69).

Fig. 1
Fig. 1

The light curve of the binary IK Boo without filter given by Blättler in 2005.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

Hanna and Awadalla [11] in a poster paper have presented the first set of complete light curves in BVRI filters observed photometrically during a clear night on 2013, May 1-2. They made a preliminary study for its period variations giving two new linear and quadratic ephemerides and deduced a decrease in the orbital period by a rate of −1.976 × 107 day/year.

The aim of this study is to analyze these light curves to determine the physical and geometrical elements for the system, to show any morphological variation due to star spot(s) activity found and to study the period variability of the system with some more details.

2 Observations

The observations of the W UMa eclipsing binary IK Boo were carried out through an EEV CCD 42-40 camera of multi-color BVRI standard Johnson filters attached to the Newtonian focus (F=4.0) of the 74-inch reflector telescope of the Kottamia observatory in Egypt, during a clear photoelectric night on 2013, May 1-2 i.e., HJD 2456414.0 (Hanna and Awadalla [11]). The exposure times, ranged from 20 s to 90 s, depend on the observing sky conditions and the filter used. The CCD camera has a format 2048 x 2048 pixels with a scale of 0.308 per pixel that was cooled by liquid nitrogen down to about -122oC. The package of C-Muniwin, was used to reduce the CCD images.

The name and the coordinates of the variable star IK Boo (V), the comparison (C1), and the check (C2) stars are listed in Table 1, and their identification chart is shown in Figure 2. Also their magnitudes in different filters are presented in Table 2.

Table 1

The coordinates of IK Boo and the comparison stars

Star nameα2000α2000
VIK Boo14h 08m 46s.2701+29° 29′ 07″.001
C1N1332311293014h 08m 47s.9852+29° 29′ 51″.772
C2N1332311292914h 08m 47s.4802+29° 29 50.952

Table 2

The magnitude of IK Boo and the comparison stars in different filters

 Star namemag.Vmag.Bmag.Rmag.Imag.Jmag.Hmag.K
VIK Boo11.42 -11.76112.37110.78210.69210. 222309.864309.8053
C1N1332311293015.82215.61215.032-14. 967314.646314. 5253
C2N1332311292914.82214. 96214. 012-12.990312. 400312.2843

Fig. 2
Fig. 2

One of the CCD images of IK Boo (V), obtained using the 74 inch Telescope of the Kottamia observatory in Egypt. C1&C2 are the comparison and check stars, respectively. North is up and East is to the left.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

A total of 71 observations in B, 86 observations in V, 89 in R and 89 in I filters, were obtained and listed in Table 7, where Δ (BVRI) denote magnitude differences in the sense, variable minus comparison. The light curves in different filters with the calculated corresponding phases are plotted in Figure 3. The phases have been calculated from ephemeris given by Hanna and Awadalla [11].

Fig. 3
Fig. 3

The best match between the synthetic light curves and the observed light curves of binary IK Boo. The rectangle shows a hump like distortion in all the LCs.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

3 Light curve analysis

The observed light curves of IK Boo indicate typical short period (7h.27) W UMa eclipsing binary with narrow minima and broad maxima. To find the geometrical and physical parameters for the system, we proceed to solve the light curves simultaneously using the software PHOEBE (Prša and Zwitter [19]).

First, we have to determine the effective temperature of the primary star T1, and the mass ratio q since there is no information about the mass ratio of the system in previous literature till now.

To determine the effective temperature, we used the observed colour index (B −V )o = 0.81 from FONAK catalogue (Kislyuk, 1999) and the colour excess E(BV) = 0.016 from the All Sky Imaging Survey AIS (Bianchi et al. [2]). Hence, the intrinsic colour index equals 0.794. Then, using tables of Cox [4] for the main sequence stars, a surface temperature 5190K was obtained for the primary component of IK Boo.

To determine the mass ratio q we have applied an extensive q-search procedure. We searched for solutions with mass ratios from 0.1 to 1.7. The relation between the resulted sum Σ of the weight square deviation (OC)2 and q is shown in Figure 4. The q-search of PHOEBE converged and resulted acceptable photometric solution for a contact configuration at about qph ≃ 0.657.

Fig. 4
Fig. 4

Relation between Σ and q.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

Second, by using van Hamme’s [27] tables, the corresponding bolometric coefficient x1 and x2 were interpolated and found. Also, by following Lucy [17] and Rucinski [26], the gravity darkening exponent g1 = g2 = 0.32 and the bolometric albedo A1 = A2 = 0.5 were assumed for both components with a convective envelope. With the assumed initial parameters we continued the programme process, by using the "over contact mode" based on the shape of the light curves, till the solution converged. Finally, the solution with the standard errors obtained is tabulated for each filter in Table 3. The theoretical light curves are computed with the obtained parameters and plotted in Figure 3 as solid lines.

Table 3

The light curve fit parameters by PHOEBE for GSC 4405-00129

ParameterFilter BFilter VFilter RFilter I
T1(K)5190519051905190
T2(K)5000(±189)5000(±128)5000(±128)5000(±261)
Surface potential (Ω)3.20(±0.05)3.20(±0.04)3.20(±0.04)3.20(±0.05)
Mass ratio (qph = M2/M1)0.648(±0.025)0.673(±0.029)0.660(±0.027)0.648(±0.279)
Inclination (i)63.2(±1.3)61.9(±1.7)62.0(±0.7)63.2(±0.7)
Albedo (A2), (A2)0.50(±0.13)0.50(±0.13)0.50(±0.13)0.50(±0.13)
Gravity darkening Coef. (g)0.32±(0.04)0.32±(0.04)0.32±(0.04)0.32±(0.04)
l1 = L1/(L1 + L2)0.668(±0.0)0.702(±0.057)0.738(±0.023)0.676(±0.016)
l2 = L2/(L1 + L2)0.332(±0.0)0.298(±0.057)0.262(±0.064)0.324(±0.016)
x10.863(±0.046)0.654(±0.023)0.437(±0.037)0.284(±0.052)
x20.833(±0.047)0.781(±0.130)0.625(±0.130)0.465(±0.196)
Fill-out Factor f-0.003-0.003-0.003-0.003
SpotsPri.Sec.Pri.Sec.Pri.Sec.Pri.Sec.
Latitude (o)8075908090756050
Longitude (o)11012011011011014011080
Radius (o)74545545.5
T0.60.80.71.21.01.50.81.5

4 Light curve study

The fill-out factors of both components f1 = f2 ≃ −0.003, as obtained and listed in Table 3, imply that IK Boo is a contact binary system according to Lucy and Wilson [18]. The Roche lobe configuration of IK Boo is illustrated in Figure 5.

Fig. 5
Fig. 5

Roche lobe configuration of IK Boo.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

Rucinski [23] has discussed the properties of W UMa-type systems in terms of their division into A- and W-types. He reported that for q nearer to the upper limit of the range 0.145 < q < 0.88, later spectral type G-K, for shallow envelopes Roche lobe configuration denoted by the fill-out factor f and for high colour index B − V ≥ 0.54; the system can be classified as W-type contact binary system. For IK Boo, the results show a q value 0.65, late spectral type K0 + K1.5 (corresponding to the obtained low temperatures T1 = 5190,T2 = 5000K), the Roche geometry configuration (Figure 5) where the fill out factor f = −0.003, and the colour index B −V = 0.796 > 0.54. Hence, one can deduce that IK Boo is likely to be of W-type W UMa system.

To follow the light curve variation for IK Boo, we measured the light curve levels at maxima and minima directly from Figure 3. Table 4 shows the magnitude difference between both maxima Dmax. (O’Connell effect) and both minima Dmin.; and the depths of the primary (Ap) and secondary (As) minima for the observed light curves in all bands (BVRI). Table 4 and Figure 3 show that the primary and secondary minima are deeper (Ap&As) in short wavelength and decreased with increasing the wave length, while the depth difference in minima is larger in V-band.

Table 4

Magnitude differences and minima depthes of IK Boo

FilterDmax.Dmin.ApAs
maxp — maxsminp — minsminp — maxpmins — maxp
B= 445 nm-0.030.040.340.30
V= 550 nm-0.020.050.320.26
R= 560 nm-0.010.030.300.26
I= 800 nm-0.010.030.280.25

Some of interesting in all light curves of IK Boo is the existence of a hump like distortion waves between phase 0.75 and 0.90 (Figure 3). This phenomenon displays when the primary goes free from the secondary and it has been recorded for the RS CVn binary systems as flare-like episodes (Zeilik, et al., [29]).

5 Period variation study

The first light elements was obtained by Blättler and Diethelm [3] by performing a linear regression to 10 times of minima obtained from ROTSE1 data. Later, Hanna and Awadalla [11] collected all the available time of minima together with their observed minima times and deduced two linear and quadratic ephemerides by constructing the O-C diagram. They have deduced a decrease in the orbital period of IK Boo by a rate dP/dt= −1.979 × 107 day/year. In this section we aimed to re-visit the period variation study of this system in some more details.

In order to study the period variation of IK Boo, we used all the minima times used in Hanna and Awadalla [11] together with two new minima observed recently by Hübscher and Lehmann [14]. They are all listed in Table 5.

Table 5

Time of Minima

HJD (Min. I) (+2400000)ErrorFilterE(O—C)1(O—C)2Ref.
53382.623400.0008C0-0.00300.0010[1]
53445.372600.0010C2070.0006-0.0008[1]
53445.525400.0017C207.50.0018-0.0008[1]
53463.413200.0008C266.50.0056-0.0007[1]
53502.358400.0004C3950.0000-0.0005[1]
53502.512800.0007C395.50.0028-0.0005[1]
53515.390600.0019C438-0.0019-0.0005[1]
53515.544400.0006C438.50.0003-0.0005[1]
53517.366000.0019C444.50.0032-0.0005[1]
53517.515700.0011C4450.0013-0.0005[1]
53936.417900.0017R1827-0.0069-0.0014[2]
54174.369900.0007C2612-0.0033-0.0026[2]
54174.520300.0008C2612.5-0.0045-0.0026[2]
54619.802500.0002R4081.5-0.0041-0.0050[3]
55015.371300.0010C5386.5-0.0056-0.0074[4]
55015.522100.0008C5387-0.0064-0.0074[4]
55937.000400.0002C8427-0.0098-0.0139[5]
56069.460400.0020I8864-0.0128-0.0155[6]
56414.402270.0030B10002-0.0204-0.0178[7]
56414.402780.0030V10002-0.0199-0.0178[7]
56414.402880.0026R10002-0.0198-0.0178[7]
56414.403330.0024I10002-0.0193-0.0178[7]
56414.554570.0031B10002.5-0.0196-0.0178[7]
56414.555170.0029V10002.5-0.0190-0.0178[7]
56414.556560.0025R10002.5-0.0176-0.0178[7]
56414.555670.0026I10002.5-0.0185-0.0178[7]
56747.380500.0006-I11100.5-0.0184-0.0208[8]
56747.532300.0023-I11101-0.0181-0.0208[8]
Ref.: Diethelm [6], Diethelm [7], Nelson [24], Diethelm [8], Nelson [25], Hübscher and Lehmann [13], Hanna and Awadalla [11], Hübscher and Lehmann (2015) [14].

We have constructed the O-C diagram as seen in the Figure 7 by using the light elements of Blättler and Diethelm [3]. Then, by using the linear and quadratic least squares methods, we obtained the following new linear and quadratic ephemerides:

Fig. 7
Fig. 7

O-C diagram of IK Boo. Error bars due to minima times determination.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

HJD(MinI)=2453382d.62805+0d.303117067E,

with standard deviation (SD) =0.0025 day, correlation coefficient (r)=0.9609, and residual sum of squares = 1.68 × 104; and

HJD(MinI)=2453382d.62741+0d.303118999E6.96×1011E2,

with SD=0.0025 day, r=0.9636, and residual sum of squares = 1.57 × 104 associated with the period decrease rate dP/dt = −1.39 × 1010d/cycle(= −1.68 × 10−7d/yr). Such period decrease rate is usually interpreted to be due to a transfer of matter from the more massive to the less massive component.

If the period decrease is caused by conservative mass transfer, then one can calculate the mass transfer between the binary components. On using the formula derived by Kreiner & Ziolkowski [16]:

dMdt=Mtq3P(q21)dPdt,

where, Mt = M1 + M2 and q = M2/M1, and by adopting the value 0.91 M for M1 by using Harmanec’s [12] table for main sequence stars where T1 = 5190 K, consequently M2= 0.59 M, where qph = 0.648 (Table 3). Hence, we have obtained the rate of mass transfer dP/dt (= 3.1 × 107 M/yr) from the more massive to the less massive star.

Eliminating the effect of mass transfer which is represented by the parabolic term of equation 2, we obtain the (O −C)2 residual plot (Figure 8), which shows a significant orbital period variation. The dashed curve on Figure 8 represents the 4th order polynomial fit to all the data (without the last two points since they have a severe upward bind) with SD = 0.002 and r = 0.612. We have performed such polynomial fit just to show the sine like variation which is usually interpreted to be due to the presence of a third body orbiting the binary or the effect of magnetic activity cycling as a result of star spot(s) activity. However, at present we cannot able to distinguish between the two possibilities due to that, the data available represents only one cycle. One cycle cannot confirm the third body hypothesis without either spectroscopic evidence or a presence of another cycle equals in duration to the first cycle. Strictly periodic sine variation behavior concerning the O −C diagram shape is an essential property to prove the LITE due to the presence of a third body. Hence, More photoelectric and spectroscopic observations are indeed required to decide among the two possibilities that causing the sine variation.

Fig. 8
Fig. 8

Residuals of IK Boo from the quadratic ephemeris and their description by four linear ephemerides. The solid curve represents the 4th order polynomial fit with SD=0.002 and r = 0.632.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

The present (O −C)2 values in Figure 8, considering all the data, clearly suggest a non-continuous variation. Following Qian’s [20] method, three clear jumps have taken place in the period of IK Boo within a time interval of about 9 years between the middle of Jan 12, 2005 (or JD = 2453382.6234) and the end of Mar 31, 2014 (or JD = 2456747.5323). Between these jumps, the period is assumed to have undergone a steady decrease. Similar systems, such as Y Psc, BO Mon, Z Per, and UU And have been studied by Qian [21,22], AT Peg by Hanna [9], BB Peg by Hanna and Awadalla [10]. Using the least squares method, a linear function in each portion is used to obtain the best fit to the (O −C)2 values:

(OC)2=ΔT+ΔP×E;

the values ΔT and ΔP in each portion are listed in Table 6. The period at any cycle E has been computed with the following equation:

Table 6

Four linear fit sections, intervals, and the rates of change of the period of IK Boo

 to to t1t1 to t2t2 to t3t3 to t4
 E1E2E3E4
Interval (in Cycles)0.0 to 18271827.0 to 8427.08427.5 to 10002.510002.5 to 11101
Interval (in JD:2400000+)53382.62340 to53936.41790 to55937.00040 to56414.55567 to
53936.4179055937.0004056414.5556756747.5323
Epoch53382.628753382.621153382.656053382.5923
Period (days)0.30311590.30312060.30311820.3031219
SD, Stand. Div.,0.00280.00140.00180.0002
r Corr. Coef.0.48640.87970.56270.9979
Res. sum of sq.(× 10—5)6.960.8292.930.003
ΔT (day)0.0023-0.00530.0296-0.0341
ΔP (day) × 10—6-3.0921.558-0.8202.919
ΔP/P (× 10—5)-1.0210.514-0.2710.963
ΔPE (d/cycle) (× 10—9)-1.6930.236-0.5212.657

Table 7

BVRI-Observations of IK Boo

HJD.HJD.HJD.HJD.
(+2450000)ΔB(+2450000)ΔV(+2400000)ΔR(+2450000)ΔI
6414.30566-4.024376414.30666-3.643486414.30407-3.354376414.30457-3.17065
6414.30866-4.002686414.31257-3.654196414.30728-3.378026414.30777-3.17864
6414.31160-3.967096414.31552-3.652376414.31020-3.387076414.31069-3.20317
6414.32347-4.013596414.31843-3.664956414.31317-3.387866414.31368-3.18568
6414.32640-3.992986414.32442-3.661156414.31611-3.393296414.31659-3.21114
6414.33537-3.991836414.32736-3.666186414.31904-3.397446414.31951-3.19473
6414.33832-3.936056414.33032-3.675986414.32205-3.397746414.32252-3.17867
6414.34428-3.952826414.33334-3.635816414.32502-3.388806414.32551-3.19801
6414.34723-3.918496414.33632-3.616346414.32796-3.400476414.32845-3.19543
6414.35021-3.931836414.33928-3.599456414.33095-3.390986414.33145-3.16099
6414.35986-3.938556414.34228-3.612166414.33394-3.346116414.33448-3.15799
6414.36581-3.872676414.34525-3.596206414.33691-3.355216414.33741-3.16171
6414.37177-3.834526414.34821-3.594406414.33990-3.343706414.34037-3.15892
6414.38969-3.749066414.35118-3.599826414.34287-3.345026414.34336-3.16052
6414.39263-3.704696414.35785-3.575666414.34584-3.321066414.34633-3.13863
6414.39843-3.689756414.36677-3.543756414.34882-3.315006414.34929-3.12770
6414.40134-3.683296414.36972-3.520426414.35178-3.312866414.35227-3.12886
6414.40422-3.685126414.38528-3.439636414.35846-3.299936414.35894-3.09889
6414.40718-3.689696414.39061-3.406036414.36146-3.308486414.36196-3.10811
6414.41015-3.673486414.39355-3.384886414.36443-3.294256414.36491-3.10956
6414.41310-3.709366414.39647-3.372006414.36738-3.276446414.36786-3.07826
6414.41602-3.744676414.39936-3.350176414.37034-3.269826414.37082-3.07792
6414.41890-3.799696414.40517-3.380356414.39122-3.133346414.39170-2.95536
6414.42182-3.793286414.40810-3.369566414.39414-3.117266414.39462-2.96251
6414.42475-3.811606414.41108-3.388786414.39706-3.117116414.39753-2.93136
6414.42765-3.828086414.41405-3.384286414.39994-3.107366414.40044-2.92693
6414.43344-3.930916414.41696-3.444066414.40286-3.111686414.40333-2.92091
6414.43640-3.860386414.41985-3.451416414.40576-3.109906414.40624-2.93063
6414.43932-3.896296414.42275-3.461156414.40872-3.123176414.40919-2.94535
6414.45500-3.953176414.42567-3.486646414.41169-3.115406414.41218-2.95074
6414.45802-3.982086414.42859-3.499596414.41464-3.136846414.41512-2.95194
6414.46108-3.973596414.43148-3.509416414.41755-3.150006414.41801-2.98455
6414.46404-3.971846414.43437-3.538806414.42045-3.177226414.42093-2.99608
6414.46694-3.990166414.43733-3.545086414.42333-3.200886414.42385-3.02218
6414.46988-3.994856414.44029-3.566376414.42625-3.224376414.42677-3.03106
6414.47281-3.992936414.45078-3.595096414.42918-3.228796414.42966-3.06942
6414.47575-3.992356414.45206-3.616906414.43208-3.262356414.43255-3.06939
6414.47882-4.011026414.45596-3.612156414.43498-3.279266414.43545-3.10065
6414.48179-4.012466414.45897-3.634156414.43792-3.290566414.43840-3.11625
6414.48479-4.019536414.46201-3.635516414.44088-3.306046414.44140-3.12359
6414.48773-4.030936414.46498-3.654696414.45657-3.353156414.45705-3.15426
6414.49068-4.021326414.46789-3.656486414.45959-3.368626414.46009-3.16861
6414.49359-4.009256414.47083-3.639906414.46265-3.375946414.46313-3.16521
6414.49657-3.997006414.47375-3.673856414.46557-3.378226414.46606-3.18349
6414.49951-4.001026414.47670-3.674196414.46847-3.392836414.46899-3.18361
6414.50250-3.974946414.47978-3.690236414.47144-3.388206414.47192-3.19292
6414.50553-3.974926414.48278-3.690966414.47435-3.409756414.47485-3.22558
6414.50846-3.974386414.48574-3.681396414.47735-3.404496414.47782-3.19679
6414.51142-3.936536414.48869-3.678346414.48038-3.396486414.48087-3.20110
6414.51438-3.926646414.49162-3.667406414.48337-3.399406414.48388-3.19757
6414.51778-3.898956414.49455-3.666606414.48634-3.400476414.48683-3.19487
6414.52075-3.910086414.49751-3.639486414.48928-3.384996414.48978-3.18485
6414.52368-3.896896414.50047-3.648406414.49222-3.400916414.49270-3.19890
6414.52666-3.861596414.50345-3.649576414.49517-3.376566414.49567-3.17769
6414.52966-3.866476414.50648-3.636216414.49812-3.387206414.49861-3.17667
6414.53269-3.849286414.50944-3.622746414.50108-3.366906414.50155-3.16169
6414.53578-3.813416414.51238-3.613986414.50409-3.360066414.50457-3.14524
6414.53881-3.788816414.51532-3.595136414.50707-3.352086414.50757-3.14997
6414.54182-3.790606414.51873-3.569836414.51005-3.337446414.51052-3.13050
6414.54771-3.743136414.52169-3.557006414.51299-3.323626414.51347-3.15082
6414.55067-3.751696414.52463-3.555486414.51593-3.323726414.51642-3.12454
6414.55363-3.748396414.52760-3.526246414.51934-3.300176414.51985-3.09640
6414.55657-3.691756414.53061-3.515316414.52230-3.288606414.52279-3.09629
6414.55953-3.721786414.53363-3.497576414.52524-3.270416414.52575-3.09083
6414.56258-3.742016414.53672-3.472496414.52824-3.276776414.52872-3.08256
6414.56561-3.758306414.53977-3.453516414.53124-3.256516414.53174-3.04411
6414.56858-3.829626414.54278-3.458266414.53428-3.239396414.53477-3.02405
6414.57150-3.800466414.54573-3.440136414.53736-3.218566414.53785-3.03043
6414.57743-3.836256414.54866-3.440106414.54041-3.198006414.54088-2.99843
6414.58323-3.857806414.55161-3.428336414.54337-3.193186414.54385-2.98659
6414.59233-3.886286414.55457-3.417506414.54633-3.160646414.54681-2.94536
6414.55755-3.416866414.54926-3.152396414.54977-2.96036
6414.56046-3.423756414.55221-3.145536414.55273-2.96942
6414.56352-3.440786414.55517-3.149766414.55567-2.98336
6414.56656-3.458546414.55814-3.142496414.55863-2.94095
6414.56953-3.436616414.56110-3.157096414.56161-2.95867
6414.57247-3.483796414.56416-3.189866414.56463-3.02289
6414.57542-3.481036414.56716-3.175186414.56766-3.00127
6414.57840-3.541576414.57013-3.218596414.57061-2.99313
6414.58418-3.563336414.57307-3.185746414.57355-3.02348
6414.58715-3.594606414.57603-3.217546414.57653-3.04310
6414.59019-3.620276414.57900-3.261956414.57951-3.06134
6414.59328-3.597836414.58478-3.286466414.58527-3.07382
6414.59633-3.618816414.58778-3.309906414.58826-3.11400
6414.59935-3.594696414.59086-3.306836414.59135-3.11844
6414.60233-3.670446414.59390-3.353426414.59439-3.12964
6414.59697-3.341566414.59745-3.14733
6414.59995-3.374106414.60045-3.11837
6414.60292-3.304716414.60341-3.07985

PRe(E)=PEph+ΔP+dPdE×E;

results are shown in Figure 9, where we have plotted the difference between the real period PRe(E) and the ephemeris period PEph (0d.303117067) - in units of 106 day- as a function of time.

Fig. 9
Fig. 9

Variations in the orbital period of IK Boo. Three jumps in the period are clearly visible.

Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

6 Conclusion

  1. From the study of the color indices we can conclude that the system is of late spectral type (K0+K1.5).
  2. The system was found to have mass ratio q = 0.648 approaching the upper limit of the range 0.145 < q < 0.88 which is a W-type property, (note, q < 0.54 for A-type, Rucinski, [23]). In addition, the shapes of the light curves appear to have a moderate activity (seen between phase 0.75 and 0.9 of Figure 3).
  3. The two spots were found on both components (Table 6, and Figure 6). The presence of star spots reveals the magnetic activity that characterizing the chromospheric activity in late W UMa and RS CVn stars.
    Fig. 6
    Fig. 6

    A schematic spots modelling for IK Boo.

    Citation: Applied Mathematics and Nonlinear Sciences 1, 2; 10.21042/AMNS.2016.2.00027

  4. The schematic picture of the Roche lobe (Figure 5) showed moderate outer convective zone with common radiative envelope for both components which is a property of W-type W UMa systems (Rucinski, [23]).
  5. The study of the O-C diagram of IK Boo showed a long term orbital period modulation decrease of rate dP/dt = −1.68 × 107d/yr, that can be interpreted to be due to mass transfer from the more to the less massive component.
  6. The light curves solution showed presence of star spots on both components. Such magnetic activity is recommended to be the reason of the sine-like variation seen in the (O−C)2 diagram (Figure 8). However, one cannot dismiss a probable detection of a third body orbiting the system, which can be proved by a periodic behaviour of the O-C diagram. The presence of a third body has to be supported by more observed minima time of mid-eclipse, and/or spectroscopic observations.

Spectroscopic observations for the binary system IK Boo are strongly recommended in order to determine its physical parameters and to verify the obtained photometric results. Also, observing more minima times are needed to re-study the period variability in order to decide among, is the alternating change in its period cyclic or periodic?

Communicated by E.I. Abouelmagd

References

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    Akerlof C. Amrose S. Balsano R. Bloch J. et al.: (2000) ROTSE All-Sky Surveys for Variable Stars. I. Test Fields Astronomical Journal 119 1901.

    • Crossref
    • Export Citation
  • [2]

    Bianchi L. Herald J. Efremova B. Girardi L. Zabot A. Marigo P. Conti A. Shiao B.: (2011) GALEX catalogs of UV sources: statistical properties and sample science applications: hot white dwarfs in the Milky Way Astrophysics and Space Science 335 161.

    • Crossref
    • Export Citation
  • [3]

    Blättler E. and Diethelm R.: (2006) Observations of Variables Infomation Bulltine of Vaiable Stars No. 5699.

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    Cox A.N.: (2002) Book Review: Allen’s astrophysical quantities. - 4th ed.; New York: Springer.

    • Crossref
    • Export Citation
  • [5]

    Cutri R.M. Skrutskie M.F. van Dyk S. Beichman C.A. Carpenter J. M. Chester T. Cambresy L. Evans T. Fowler J. Gizis J. and 15 coauthors: (2003) “VizieR Online Data Catalog: 2MASS All-Sky Catalog of Point Sources (Cutri+2003)" yCat. 2246 0.

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    Diethelm R.: (2006) 165. List of Timings of Minima Eclipsing Binaries by BBSAG Observers Information Bulletin of Variable Stars Stars No. 5713.

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    Diethelm R.: (2007) 166. List of Timings of Minima Eclipsing Binaries by BBSAG Observers Information Bulletin of Variable Stars No. 5781.

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    Diethelm R.: (2010) 166. Timings of Minima of Eclipsing Binaries Information Bulletin of Variable Stars No. 5920.

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    Hanna M.A. (2012): Orbital period changes and possible stellar wind mass loss in the algol-type binary system AT Pegasi Journal of Astronomy and Geophysics 1 87.

    • Crossref
    • Export Citation
  • [10]

    Hanna M.A. and Awadalla N.S.: (2011) Orbital period variation and morphological light curve studies for the W UMa binary BB Pegasi Journal of Korean Astronomical Society 44 97.

    • Crossref
    • Export Citation
  • [11]

    Hanna M.A. and Awadalla N.S.: (2014) New CCD photoelectric observations of the contact binary GSC 02013-00288 Contributions of the Astronomical Observatory Skalnaté Pleso 43 440.

  • [12]

    Harmanec P.: (1988) Stellar masses and radii based on modern binary data BAICz 39 329.

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    Hübscher J. and Lehmann P.B.: (2013) BAV-Results of Observations - Photoelectric Minima of Selected Eclipsing Binaries and Maxima of Pulsating Stars Information Bulletin of Variable Stars No. 6070.

  • [14]

    Hübscher J. and Lehmann P.B.: (2015) BAV-Results of Observations - Photoelectric Minima of Selected Eclipsing Binaries and Maxima of Pulsating Stars Information Bulletin of Variable Stars No. 6149.

  • [15]

    Hog E. Fabricius C. Makarov V. V. Urban S. Corbin T. Wycoff G. Bastian U. Schwekendiek P. Wicenec A.: (2000) The Tycho-2 catalogue of the 2.5 million bcenterest stars Astronomy and Astrophysics 355 27.

  • [16]

    Kreiner J.M. and Ziolkowski J.: (1978) Period changes and evolutionary status of 18 Algol-Type Systems Acta Astronomica 28 497.

  • [17]

    Lucy L.B.: (1967) Gravity-Darkening for Stars with Convective Envelopes Zeitschrift für Astrophysik 65 89.

  • [18]

    Lucy L.B. and Wilson: (1979) Observational tests of theories of contact binaries Astrophysical Journal 231 502.

  • [19]

    Prša A. and Zwitter T.: (2005) A Computational Guide to Physics of Eclipsing Binaries. I. Demonstrations and Perspectives Astrophysical Journal 628 426.

    • Crossref
    • Export Citation
  • [20]

    Qian S. Orbital period changes and possible mass and angular momentum loss in two Algol-type binaries: RW Coronae Borealis and TU Herculis.: (2000a) Astronomical Jounal 119 901.

    • Crossref
    • Export Citation
  • [21]

    Qian S. Possible Mass and Angular Momentum Loss in Algol-Type Binaries. II. TT Delphini BO Monocerotis and Y Piscium: (2000c) Astronomical Jounal 119 3064.

    • Crossref
    • Export Citation
  • [22]

    Qian S. Possible Mass and Angular Momentum Loss in Algol-Type Binaries. IV. UU Andromedae and Z Persei: (2001b) Astronomical Jounal 122 1561.

    • Crossref
    • Export Citation
  • [23]

    Rucinski S.M.: (1973) The Photometric Proximity Effects in Close Binary Systems. VI. The Exact Solution for the Source Function in Monodirectional Illumination of the Grey Atmosphere Acta Astronomica 23 301.

  • [24]

    Nelson R.H.: (2009) CCD Minima for Selected Eclipsing Binaries in 2008 Information Bulletin of Variable Stars No. 5875.

  • [25]

    Nelson R.H.: (2013) CCD Minima for Selected Eclipsing Binaries in 2012 Information Bulletin of Variable Stars No. 6050.

  • [26]

    Rucinski S.M.: (1974) Binaries. II. A- and W-type Systems. The W UMa-type Systems as Contact Acta Astronomica 24 119.

  • [27]

    van Hamme W. (1993) New Llimb-darkening Coefficients for Modeling Binary Star Light Curves Astronomical Journal 106 2096.

    • Crossref
    • Export Citation
  • [28]

    Zacharias N. Monet D.G. Levine S.E. Urban S.E. Gaume R. Wycoff G.L.: (2004) "The Naval Observatory Merged Astrometric Dataset (NOMAD)" American Astronomical Society Meeting 205 4815.

  • [29]

    Zeilik M. Elston R. and Henson G.: (1983) The short-period eclipsing system XY UMa - 1982 UBV light curves and a flare-like event Astronomical Jounal 88 532.

    • Crossref
    • Export Citation

Footnotes

12MASS Catalogue, (Cutri [5]): yCat 2246C.
12MASS Catalogue, (Cutri [5]): yCat 2246C.
2GSC 2.2 catalogue (STScI, 2001).
2GSC 2.2 catalogue (STScI, 2001).
2GSC 2.2 catalogue (STScI, 2001).
2GSC 2.2 catalogue (STScI, 2001).
1The Tycho catalogue (Hog+ 2000), [15].
1The Tycho catalogue (Hog+ 2000), [15].
2NOMAD Catalogue (Zacharias+2005), [28].
2NOMAD Catalogue (Zacharias+2005), [28].
32MASS Catalogue, (Cutri 2003), [5].
32MASS Catalogue, (Cutri 2003), [5].
32MASS Catalogue, (Cutri 2003), [5].
2NOMAD Catalogue (Zacharias+2005), [28].
2NOMAD Catalogue (Zacharias+2005), [28].
2NOMAD Catalogue (Zacharias+2005), [28].
32MASS Catalogue, (Cutri 2003), [5].
32MASS Catalogue, (Cutri 2003), [5].
32MASS Catalogue, (Cutri 2003), [5].
2NOMAD Catalogue (Zacharias+2005), [28].
2NOMAD Catalogue (Zacharias+2005), [28].
2NOMAD Catalogue (Zacharias+2005), [28].
32MASS Catalogue, (Cutri 2003), [5].
32MASS Catalogue, (Cutri 2003), [5].
32MASS Catalogue, (Cutri 2003), [5].

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  • [1]

    Akerlof C. Amrose S. Balsano R. Bloch J. et al.: (2000) ROTSE All-Sky Surveys for Variable Stars. I. Test Fields Astronomical Journal 119 1901.

    • Crossref
    • Export Citation
  • [2]

    Bianchi L. Herald J. Efremova B. Girardi L. Zabot A. Marigo P. Conti A. Shiao B.: (2011) GALEX catalogs of UV sources: statistical properties and sample science applications: hot white dwarfs in the Milky Way Astrophysics and Space Science 335 161.

    • Crossref
    • Export Citation
  • [3]

    Blättler E. and Diethelm R.: (2006) Observations of Variables Infomation Bulltine of Vaiable Stars No. 5699.

  • [4]

    Cox A.N.: (2002) Book Review: Allen’s astrophysical quantities. - 4th ed.; New York: Springer.

    • Crossref
    • Export Citation
  • [5]

    Cutri R.M. Skrutskie M.F. van Dyk S. Beichman C.A. Carpenter J. M. Chester T. Cambresy L. Evans T. Fowler J. Gizis J. and 15 coauthors: (2003) “VizieR Online Data Catalog: 2MASS All-Sky Catalog of Point Sources (Cutri+2003)" yCat. 2246 0.

  • [6]

    Diethelm R.: (2006) 165. List of Timings of Minima Eclipsing Binaries by BBSAG Observers Information Bulletin of Variable Stars Stars No. 5713.

  • [7]

    Diethelm R.: (2007) 166. List of Timings of Minima Eclipsing Binaries by BBSAG Observers Information Bulletin of Variable Stars No. 5781.

  • [8]

    Diethelm R.: (2010) 166. Timings of Minima of Eclipsing Binaries Information Bulletin of Variable Stars No. 5920.

  • [9]

    Hanna M.A. (2012): Orbital period changes and possible stellar wind mass loss in the algol-type binary system AT Pegasi Journal of Astronomy and Geophysics 1 87.

    • Crossref
    • Export Citation
  • [10]

    Hanna M.A. and Awadalla N.S.: (2011) Orbital period variation and morphological light curve studies for the W UMa binary BB Pegasi Journal of Korean Astronomical Society 44 97.

    • Crossref
    • Export Citation
  • [11]

    Hanna M.A. and Awadalla N.S.: (2014) New CCD photoelectric observations of the contact binary GSC 02013-00288 Contributions of the Astronomical Observatory Skalnaté Pleso 43 440.

  • [12]

    Harmanec P.: (1988) Stellar masses and radii based on modern binary data BAICz 39 329.

  • [13]

    Hübscher J. and Lehmann P.B.: (2013) BAV-Results of Observations - Photoelectric Minima of Selected Eclipsing Binaries and Maxima of Pulsating Stars Information Bulletin of Variable Stars No. 6070.

  • [14]

    Hübscher J. and Lehmann P.B.: (2015) BAV-Results of Observations - Photoelectric Minima of Selected Eclipsing Binaries and Maxima of Pulsating Stars Information Bulletin of Variable Stars No. 6149.

  • [15]

    Hog E. Fabricius C. Makarov V. V. Urban S. Corbin T. Wycoff G. Bastian U. Schwekendiek P. Wicenec A.: (2000) The Tycho-2 catalogue of the 2.5 million bcenterest stars Astronomy and Astrophysics 355 27.

  • [16]

    Kreiner J.M. and Ziolkowski J.: (1978) Period changes and evolutionary status of 18 Algol-Type Systems Acta Astronomica 28 497.

  • [17]

    Lucy L.B.: (1967) Gravity-Darkening for Stars with Convective Envelopes Zeitschrift für Astrophysik 65 89.

  • [18]

    Lucy L.B. and Wilson: (1979) Observational tests of theories of contact binaries Astrophysical Journal 231 502.

  • [19]

    Prša A. and Zwitter T.: (2005) A Computational Guide to Physics of Eclipsing Binaries. I. Demonstrations and Perspectives Astrophysical Journal 628 426.

    • Crossref
    • Export Citation
  • [20]

    Qian S. Orbital period changes and possible mass and angular momentum loss in two Algol-type binaries: RW Coronae Borealis and TU Herculis.: (2000a) Astronomical Jounal 119 901.

    • Crossref
    • Export Citation
  • [21]

    Qian S. Possible Mass and Angular Momentum Loss in Algol-Type Binaries. II. TT Delphini BO Monocerotis and Y Piscium: (2000c) Astronomical Jounal 119 3064.

    • Crossref
    • Export Citation
  • [22]

    Qian S. Possible Mass and Angular Momentum Loss in Algol-Type Binaries. IV. UU Andromedae and Z Persei: (2001b) Astronomical Jounal 122 1561.

    • Crossref
    • Export Citation
  • [23]

    Rucinski S.M.: (1973) The Photometric Proximity Effects in Close Binary Systems. VI. The Exact Solution for the Source Function in Monodirectional Illumination of the Grey Atmosphere Acta Astronomica 23 301.

  • [24]

    Nelson R.H.: (2009) CCD Minima for Selected Eclipsing Binaries in 2008 Information Bulletin of Variable Stars No. 5875.

  • [25]

    Nelson R.H.: (2013) CCD Minima for Selected Eclipsing Binaries in 2012 Information Bulletin of Variable Stars No. 6050.

  • [26]

    Rucinski S.M.: (1974) Binaries. II. A- and W-type Systems. The W UMa-type Systems as Contact Acta Astronomica 24 119.

  • [27]

    van Hamme W. (1993) New Llimb-darkening Coefficients for Modeling Binary Star Light Curves Astronomical Journal 106 2096.

    • Crossref
    • Export Citation
  • [28]

    Zacharias N. Monet D.G. Levine S.E. Urban S.E. Gaume R. Wycoff G.L.: (2004) "The Naval Observatory Merged Astrometric Dataset (NOMAD)" American Astronomical Society Meeting 205 4815.

  • [29]

    Zeilik M. Elston R. and Henson G.: (1983) The short-period eclipsing system XY UMa - 1982 UBV light curves and a flare-like event Astronomical Jounal 88 532.

    • Crossref
    • Export Citation
Search
Journal information
Figures
  • View in gallery

    The light curve of the binary IK Boo without filter given by Blättler in 2005.

  • View in gallery

    One of the CCD images of IK Boo (V), obtained using the 74 inch Telescope of the Kottamia observatory in Egypt. C1&C2 are the comparison and check stars, respectively. North is up and East is to the left.

  • View in gallery

    The best match between the synthetic light curves and the observed light curves of binary IK Boo. The rectangle shows a hump like distortion in all the LCs.

  • View in gallery

    Relation between Σ and q.

  • View in gallery

    Roche lobe configuration of IK Boo.

  • View in gallery

    O-C diagram of IK Boo. Error bars due to minima times determination.

  • View in gallery

    Residuals of IK Boo from the quadratic ephemeris and their description by four linear ephemerides. The solid curve represents the 4th order polynomial fit with SD=0.002 and r = 0.632.

  • View in gallery

    Variations in the orbital period of IK Boo. Three jumps in the period are clearly visible.

  • View in gallery

    A schematic spots modelling for IK Boo.

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