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

N.S. Awadalla
N.S. Awadalla
, 
M.A. Hanna
M.A. Hanna
, 
M.N. Ismail
M.N. Ismail
, 
I.A. Hassan
I.A. Hassan
 and 
M.A. Elkhamisy
M.A. Elkhamisy
   | Aug 01, 2016
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Published Online: Aug 01, 2016
Page range: 321 - 334
Received: Apr 07, 2016
Accepted: Aug 01, 2016
DOI: https://doi.org/10.21042/AMNS.2016.2.00027
Keywords
© 2016 N.S. Awadalla, M.A. Hanna, M.N. Ismail, I.A. Hassan, M.A. Elkhamisy, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

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

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.
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.

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.
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.

Fig. 4

Relation between Σ and q.
Relation between Σ and q.

Fig. 5

Roche lobe configuration of IK Boo.
Roche lobe configuration of IK Boo.

Fig. 7

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

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.
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.

Fig. 9

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

Fig. 6

A schematic spots modelling for IK Boo.
A schematic spots modelling for IK Boo.

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

 Star namemag.Vmag.Bmag.Rmag.Imag.Jmag.Hmag.K
VIK Boo11.42 -11.76

The Tycho catalogue (Hog+ 2000), [15].

12.37

The Tycho catalogue (Hog+ 2000), [15].

10.78

NOMAD Catalogue (Zacharias+2005), [28].

10.69

NOMAD Catalogue (Zacharias+2005), [28].

10. 222

2MASS Catalogue, (Cutri 2003), [5].

09.864

2MASS Catalogue, (Cutri 2003), [5].

09.805

2MASS Catalogue, (Cutri 2003), [5].

C1N1332311293015.82

NOMAD Catalogue (Zacharias+2005), [28].

15.61

NOMAD Catalogue (Zacharias+2005), [28].

15.03

NOMAD Catalogue (Zacharias+2005), [28].

-14. 967

2MASS Catalogue, (Cutri 2003), [5].

14.646

2MASS Catalogue, (Cutri 2003), [5].

14. 525

2MASS Catalogue, (Cutri 2003), [5].

C2N1332311292914.82

NOMAD Catalogue (Zacharias+2005), [28].

14. 96

NOMAD Catalogue (Zacharias+2005), [28].

14. 01

NOMAD Catalogue (Zacharias+2005), [28].

-12.990

2MASS Catalogue, (Cutri 2003), [5].

12. 400

2MASS Catalogue, (Cutri 2003), [5].

12.284

2MASS Catalogue, (Cutri 2003), [5].

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

The coordinates of IK Boo and the comparison stars

Star nameα2000α2000
VIK Boo14h 08m 46s.270

2MASS Catalogue, (Cutri [5]): yCat 2246C.

+29° 29′ 07″.00

2MASS Catalogue, (Cutri [5]): yCat 2246C.

C1N1332311293014h 08m 47s.985

GSC 2.2 catalogue (STScI, 2001).

+29° 29′ 51″.77

GSC 2.2 catalogue (STScI, 2001).

C2N1332311292914h 08m 47s.480

GSC 2.2 catalogue (STScI, 2001).

+29° 29′ 50″.95

GSC 2.2 catalogue (STScI, 2001).

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

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

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
ΔP/ΔE (d/cycle) (× 10—9)-1.6930.236-0.5212.657

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]
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