The star IK Boo (= GSC 02013-00288,
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 × 10
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.
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
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.
The coordinates of IK Boo and the comparison stars 2MASS Catalogue, (Cutri [5]): yCat 2246C. 2MASS Catalogue, (Cutri [5]): yCat 2246C. GSC 2.2 catalogue (STScI, 2001). GSC 2.2 catalogue (STScI, 2001). GSC 2.2 catalogue (STScI, 2001). GSC 2.2 catalogue (STScI, 2001).Star name V IK Boo 14 +29° 29′ 07″.00 C1 N13323112930 14 +29° 29′ 51″.77 C2 N13323112929 14 +29° 29′ 50″.95
The magnitude of IK Boo and the comparison stars in different filters The Tycho catalogue (Hog+ 2000), [15]. The Tycho catalogue (Hog+ 2000), [15]. NOMAD Catalogue (Zacharias+2005), [28]. NOMAD Catalogue (Zacharias+2005), [28]. 2MASS Catalogue, (Cutri 2003), [5]. 2MASS Catalogue, (Cutri 2003), [5]. 2MASS Catalogue, (Cutri 2003), [5]. NOMAD Catalogue (Zacharias+2005), [28]. NOMAD Catalogue (Zacharias+2005), [28]. NOMAD Catalogue (Zacharias+2005), [28]. 2MASS Catalogue, (Cutri 2003), [5]. 2MASS Catalogue, (Cutri 2003), [5]. 2MASS Catalogue, (Cutri 2003), [5]. NOMAD Catalogue (Zacharias+2005), [28]. NOMAD Catalogue (Zacharias+2005), [28]. NOMAD Catalogue (Zacharias+2005), [28]. 2MASS Catalogue, (Cutri 2003), [5]. 2MASS Catalogue, (Cutri 2003), [5]. 2MASS Catalogue, (Cutri 2003), [5]. Star name mag.V mag.B mag.R mag.I mag.J mag.H mag.K V IK Boo 11.42 -11.76 12.37 10.78 10.69 10. 222 09.864 09.805 C1 N13323112930 15.82 15.61 15.03 - 14. 967 14.646 14. 525 C2 N13323112929 14.82 14. 96 14. 01 - 12.990 12. 400 12.284
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].
The observed light curves of IK Boo indicate typical short period (7
First, we have to determine the effective temperature of the primary star
To determine the effective temperature, we used the observed colour index (
To determine the mass ratio
Second, by using van Hamme’s [27] tables, the corresponding bolometric coefficient
The light curve fit parameters by PHOEBE for GSC 4405-00129Parameter Filter B Filter V Filter R Filter I 5190 5190 5190 5190 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 ( 0.648(±0.025) 0.673(±0.029) 0.660(±0.027) 0.648(±0.279) Inclination ( 63.2(±1.3) 61.9(±1.7) 62.0(±0.7) 63.2(±0.7) Albedo ( 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) 0.668(±0.0) 0.702(±0.057) 0.738(±0.023) 0.676(±0.016) 0.332(±0.0) 0.298(±0.057) 0.262(±0.064) 0.324(±0.016) 0.863(±0.046) 0.654(±0.023) 0.437(±0.037) 0.284(±0.052) 0.833(±0.047) 0.781(±0.130) 0.625(±0.130) 0.465(±0.196) Fill-out Factor -0.003 -0.003 -0.003 -0.003 Spots Pri. Sec. Pri. Sec. Pri. Sec. Pri. Sec. Latitude ( 80 75 90 80 90 75 60 50 Longitude ( 110 120 110 110 110 140 110 80 Radius ( 7 4 5 4 5 5 4 5.5 T 0.6 0.8 0.7 1.2 1.0 1.5 0.8 1.5
The fill-out factors of both components
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
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
Magnitude differences and minima depthes of IK BooFilter B= 445 nm -0.03 0.04 0.34 0.30 V= 550 nm -0.02 0.05 0.32 0.26 R= 560 nm -0.01 0.03 0.30 0.26 I= 800 nm -0.01 0.03 0.28 0.25
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]).
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 d
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.
Time of Minima Ref.: Diethelm [6], Diethelm [7], Nelson [24], Diethelm [8], Nelson [25], Hübscher and Lehmann [13], Hanna and Awadalla [11], Hübscher and Lehmann (2015) [14].HJD (Min. I) (+2400000) Error Filter E (O—C)1 (O—C)2 Ref. 53382.62340 0.0008 C 0 -0.0030 0.0010 [1] 53445.37260 0.0010 C 207 0.0006 -0.0008 [1] 53445.52540 0.0017 C 207.5 0.0018 -0.0008 [1] 53463.41320 0.0008 C 266.5 0.0056 -0.0007 [1] 53502.35840 0.0004 C 395 0.0000 -0.0005 [1] 53502.51280 0.0007 C 395.5 0.0028 -0.0005 [1] 53515.39060 0.0019 C 438 -0.0019 -0.0005 [1] 53515.54440 0.0006 C 438.5 0.0003 -0.0005 [1] 53517.36600 0.0019 C 444.5 0.0032 -0.0005 [1] 53517.51570 0.0011 C 445 0.0013 -0.0005 [1] 53936.41790 0.0017 R 1827 -0.0069 -0.0014 [2] 54174.36990 0.0007 C 2612 -0.0033 -0.0026 [2] 54174.52030 0.0008 C 2612.5 -0.0045 -0.0026 [2] 54619.80250 0.0002 R 4081.5 -0.0041 -0.0050 [3] 55015.37130 0.0010 C 5386.5 -0.0056 -0.0074 [4] 55015.52210 0.0008 C 5387 -0.0064 -0.0074 [4] 55937.00040 0.0002 C 8427 -0.0098 -0.0139 [5] 56069.46040 0.0020 I 8864 -0.0128 -0.0155 [6] 56414.40227 0.0030 B 10002 -0.0204 -0.0178 [7] 56414.40278 0.0030 V 10002 -0.0199 -0.0178 [7] 56414.40288 0.0026 R 10002 -0.0198 -0.0178 [7] 56414.40333 0.0024 I 10002 -0.0193 -0.0178 [7] 56414.55457 0.0031 B 10002.5 -0.0196 -0.0178 [7] 56414.55517 0.0029 V 10002.5 -0.0190 -0.0178 [7] 56414.55656 0.0025 R 10002.5 -0.0176 -0.0178 [7] 56414.55567 0.0026 I 10002.5 -0.0185 -0.0178 [7] 56747.38050 0.0006 -I 11100.5 -0.0184 -0.0208 [8] 56747.53230 0.0023 -I 11101 -0.0181 -0.0208 [8]
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:
with standard deviation (SD) =0.0025 day, correlation coefficient (r)=0.9609, and residual sum of squares = 1.68 × 10
with SD=0.0025 day, r=0.9636, and residual sum of squares = 1.57 × 10
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]:
where,
Eliminating the effect of mass transfer which is represented by the parabolic term of equation 2, we obtain the (
The present (
the values Δ
Four linear fit sections, intervals, and the rates of change of the period of IK Boo Interval (in Cycles) 0.0 to 1827 1827.0 to 8427.0 8427.5 to 10002.5 10002.5 to 11101 Interval (in JD:2400000+) 53382.62340 to 53936.41790 to 55937.00040 to 56414.55567 to 53936.41790 55937.00040 56414.55567 56747.5323 Epoch 53382.6287 53382.6211 53382.6560 53382.5923 Period (days) 0.3031159 0.3031206 0.3031182 0.3031219 SD, Stand. Div., 0.0028 0.0014 0.0018 0.0002 0.4864 0.8797 0.5627 0.9979 Res. sum of sq.(× 10—5) 6.96 0.829 2.93 0.003 Δ 0.0023 -0.0053 0.0296 -0.0341 Δ -3.092 1.558 -0.820 2.919 Δ -1.021 0.514 -0.271 0.963 Δ -1.693 0.236 -0.521 2.657
BVRI-Observations of IK BooHJD. HJD. HJD. HJD. (+2450000) Δ (+2450000) Δ (+2400000) Δ (+2450000) Δ 6414.30566 -4.02437 6414.30666 -3.64348 6414.30407 -3.35437 6414.30457 -3.17065 6414.30866 -4.00268 6414.31257 -3.65419 6414.30728 -3.37802 6414.30777 -3.17864 6414.31160 -3.96709 6414.31552 -3.65237 6414.31020 -3.38707 6414.31069 -3.20317 6414.32347 -4.01359 6414.31843 -3.66495 6414.31317 -3.38786 6414.31368 -3.18568 6414.32640 -3.99298 6414.32442 -3.66115 6414.31611 -3.39329 6414.31659 -3.21114 6414.33537 -3.99183 6414.32736 -3.66618 6414.31904 -3.39744 6414.31951 -3.19473 6414.33832 -3.93605 6414.33032 -3.67598 6414.32205 -3.39774 6414.32252 -3.17867 6414.34428 -3.95282 6414.33334 -3.63581 6414.32502 -3.38880 6414.32551 -3.19801 6414.34723 -3.91849 6414.33632 -3.61634 6414.32796 -3.40047 6414.32845 -3.19543 6414.35021 -3.93183 6414.33928 -3.59945 6414.33095 -3.39098 6414.33145 -3.16099 6414.35986 -3.93855 6414.34228 -3.61216 6414.33394 -3.34611 6414.33448 -3.15799 6414.36581 -3.87267 6414.34525 -3.59620 6414.33691 -3.35521 6414.33741 -3.16171 6414.37177 -3.83452 6414.34821 -3.59440 6414.33990 -3.34370 6414.34037 -3.15892 6414.38969 -3.74906 6414.35118 -3.59982 6414.34287 -3.34502 6414.34336 -3.16052 6414.39263 -3.70469 6414.35785 -3.57566 6414.34584 -3.32106 6414.34633 -3.13863 6414.39843 -3.68975 6414.36677 -3.54375 6414.34882 -3.31500 6414.34929 -3.12770 6414.40134 -3.68329 6414.36972 -3.52042 6414.35178 -3.31286 6414.35227 -3.12886 6414.40422 -3.68512 6414.38528 -3.43963 6414.35846 -3.29993 6414.35894 -3.09889 6414.40718 -3.68969 6414.39061 -3.40603 6414.36146 -3.30848 6414.36196 -3.10811 6414.41015 -3.67348 6414.39355 -3.38488 6414.36443 -3.29425 6414.36491 -3.10956 6414.41310 -3.70936 6414.39647 -3.37200 6414.36738 -3.27644 6414.36786 -3.07826 6414.41602 -3.74467 6414.39936 -3.35017 6414.37034 -3.26982 6414.37082 -3.07792 6414.41890 -3.79969 6414.40517 -3.38035 6414.39122 -3.13334 6414.39170 -2.95536 6414.42182 -3.79328 6414.40810 -3.36956 6414.39414 -3.11726 6414.39462 -2.96251 6414.42475 -3.81160 6414.41108 -3.38878 6414.39706 -3.11711 6414.39753 -2.93136 6414.42765 -3.82808 6414.41405 -3.38428 6414.39994 -3.10736 6414.40044 -2.92693 6414.43344 -3.93091 6414.41696 -3.44406 6414.40286 -3.11168 6414.40333 -2.92091 6414.43640 -3.86038 6414.41985 -3.45141 6414.40576 -3.10990 6414.40624 -2.93063 6414.43932 -3.89629 6414.42275 -3.46115 6414.40872 -3.12317 6414.40919 -2.94535 6414.45500 -3.95317 6414.42567 -3.48664 6414.41169 -3.11540 6414.41218 -2.95074 6414.45802 -3.98208 6414.42859 -3.49959 6414.41464 -3.13684 6414.41512 -2.95194 6414.46108 -3.97359 6414.43148 -3.50941 6414.41755 -3.15000 6414.41801 -2.98455 6414.46404 -3.97184 6414.43437 -3.53880 6414.42045 -3.17722 6414.42093 -2.99608 6414.46694 -3.99016 6414.43733 -3.54508 6414.42333 -3.20088 6414.42385 -3.02218 6414.46988 -3.99485 6414.44029 -3.56637 6414.42625 -3.22437 6414.42677 -3.03106 6414.47281 -3.99293 6414.45078 -3.59509 6414.42918 -3.22879 6414.42966 -3.06942 6414.47575 -3.99235 6414.45206 -3.61690 6414.43208 -3.26235 6414.43255 -3.06939 6414.47882 -4.01102 6414.45596 -3.61215 6414.43498 -3.27926 6414.43545 -3.10065 6414.48179 -4.01246 6414.45897 -3.63415 6414.43792 -3.29056 6414.43840 -3.11625 6414.48479 -4.01953 6414.46201 -3.63551 6414.44088 -3.30604 6414.44140 -3.12359 6414.48773 -4.03093 6414.46498 -3.65469 6414.45657 -3.35315 6414.45705 -3.15426 6414.49068 -4.02132 6414.46789 -3.65648 6414.45959 -3.36862 6414.46009 -3.16861 6414.49359 -4.00925 6414.47083 -3.63990 6414.46265 -3.37594 6414.46313 -3.16521 6414.49657 -3.99700 6414.47375 -3.67385 6414.46557 -3.37822 6414.46606 -3.18349 6414.49951 -4.00102 6414.47670 -3.67419 6414.46847 -3.39283 6414.46899 -3.18361 6414.50250 -3.97494 6414.47978 -3.69023 6414.47144 -3.38820 6414.47192 -3.19292 6414.50553 -3.97492 6414.48278 -3.69096 6414.47435 -3.40975 6414.47485 -3.22558 6414.50846 -3.97438 6414.48574 -3.68139 6414.47735 -3.40449 6414.47782 -3.19679 6414.51142 -3.93653 6414.48869 -3.67834 6414.48038 -3.39648 6414.48087 -3.20110 6414.51438 -3.92664 6414.49162 -3.66740 6414.48337 -3.39940 6414.48388 -3.19757 6414.51778 -3.89895 6414.49455 -3.66660 6414.48634 -3.40047 6414.48683 -3.19487 6414.52075 -3.91008 6414.49751 -3.63948 6414.48928 -3.38499 6414.48978 -3.18485 6414.52368 -3.89689 6414.50047 -3.64840 6414.49222 -3.40091 6414.49270 -3.19890 6414.52666 -3.86159 6414.50345 -3.64957 6414.49517 -3.37656 6414.49567 -3.17769 6414.52966 -3.86647 6414.50648 -3.63621 6414.49812 -3.38720 6414.49861 -3.17667 6414.53269 -3.84928 6414.50944 -3.62274 6414.50108 -3.36690 6414.50155 -3.16169 6414.53578 -3.81341 6414.51238 -3.61398 6414.50409 -3.36006 6414.50457 -3.14524 6414.53881 -3.78881 6414.51532 -3.59513 6414.50707 -3.35208 6414.50757 -3.14997 6414.54182 -3.79060 6414.51873 -3.56983 6414.51005 -3.33744 6414.51052 -3.13050 6414.54771 -3.74313 6414.52169 -3.55700 6414.51299 -3.32362 6414.51347 -3.15082 6414.55067 -3.75169 6414.52463 -3.55548 6414.51593 -3.32372 6414.51642 -3.12454 6414.55363 -3.74839 6414.52760 -3.52624 6414.51934 -3.30017 6414.51985 -3.09640 6414.55657 -3.69175 6414.53061 -3.51531 6414.52230 -3.28860 6414.52279 -3.09629 6414.55953 -3.72178 6414.53363 -3.49757 6414.52524 -3.27041 6414.52575 -3.09083 6414.56258 -3.74201 6414.53672 -3.47249 6414.52824 -3.27677 6414.52872 -3.08256 6414.56561 -3.75830 6414.53977 -3.45351 6414.53124 -3.25651 6414.53174 -3.04411 6414.56858 -3.82962 6414.54278 -3.45826 6414.53428 -3.23939 6414.53477 -3.02405 6414.57150 -3.80046 6414.54573 -3.44013 6414.53736 -3.21856 6414.53785 -3.03043 6414.57743 -3.83625 6414.54866 -3.44010 6414.54041 -3.19800 6414.54088 -2.99843 6414.58323 -3.85780 6414.55161 -3.42833 6414.54337 -3.19318 6414.54385 -2.98659 6414.59233 -3.88628 6414.55457 -3.41750 6414.54633 -3.16064 6414.54681 -2.94536 6414.55755 -3.41686 6414.54926 -3.15239 6414.54977 -2.96036 6414.56046 -3.42375 6414.55221 -3.14553 6414.55273 -2.96942 6414.56352 -3.44078 6414.55517 -3.14976 6414.55567 -2.98336 6414.56656 -3.45854 6414.55814 -3.14249 6414.55863 -2.94095 6414.56953 -3.43661 6414.56110 -3.15709 6414.56161 -2.95867 6414.57247 -3.48379 6414.56416 -3.18986 6414.56463 -3.02289 6414.57542 -3.48103 6414.56716 -3.17518 6414.56766 -3.00127 6414.57840 -3.54157 6414.57013 -3.21859 6414.57061 -2.99313 6414.58418 -3.56333 6414.57307 -3.18574 6414.57355 -3.02348 6414.58715 -3.59460 6414.57603 -3.21754 6414.57653 -3.04310 6414.59019 -3.62027 6414.57900 -3.26195 6414.57951 -3.06134 6414.59328 -3.59783 6414.58478 -3.28646 6414.58527 -3.07382 6414.59633 -3.61881 6414.58778 -3.30990 6414.58826 -3.11400 6414.59935 -3.59469 6414.59086 -3.30683 6414.59135 -3.11844 6414.60233 -3.67044 6414.59390 -3.35342 6414.59439 -3.12964 6414.59697 -3.34156 6414.59745 -3.14733 6414.59995 -3.37410 6414.60045 -3.11837 6414.60292 -3.30471 6414.60341 -3.07985
results are shown in Figure 9, where we have plotted the difference between the real period
From the study of the color indices we can conclude that the system is of late spectral type (K0+K1.5).
The system was found to have mass ratio
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.
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]).
The study of the O-C diagram of IK Boo showed a long term orbital period modulation decrease of rate d
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 (
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?