1 Introduction

Cool Spot and Flare Activities of a RS CVn Binary KIC 7885570

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{Titlepage}\Title

Cool Spot and Flare Activities of a RS CVn Binary KIC 7885570 \AuthorM. Kunt and H. A. Dal Department of Astronomy and Space Sciences, University of Ege, Bornova,
35100  İzmir, Turkey e-mail: ali.dal@ege.edu.tr

\Received

Received May 10, 2016

\Abstract

We present here the results on the physical nature a RS CVn binary KIC 7885570 and its chromospheric activity based on the Kepler Mission data. Assuming the primary component temperature, 6530 K, the temperature of the secondary component was found to be 57324 K. The mass ratio of the components () was found to be 0.430.01, while the inclination () of the system 80.560.01. Additionally, the data were separated into 35 subsets to model the sinusoidal variation due to the rotational modulation, using the SPOTMODEL program, as the light curve analysis indicated the chromospherically active secondary component. It was found that there are generally two spotted areas, whose radii, longitudes and latitudes are rapidly changing, located around the latitudes of and on the active component. Moreover, 113 flares were detected and their parameters were computed from the available data. The One Phase Exponential Association function model was derived from the parameters of these flares. Using the regression calculations, the Plateau value was found to be 1.98150.1177, while the half-life value was computed as 3977.2 s. In addition, the flare frequency () - the flare number per hour, was estimated to be 0.00362 , while flare frequency () - the flare-equivalent duration emitted per hour, was computed as 0.00001. Finally, the times of eclipses were computed for 278 minima of the light curves, whose analysis indicated that the chromosphere activity nature of the system causes some effects on these minima times. Comparing the chromospheric activity patterns with the analogues of the secondary component, it is seen that the magnetic activity level is remarkably low. However, it is still at the expected level according to the B-V color index of 0.643 mag for the secondary component.

techniques: photometric – methods: data analysis – methods: statistical – binaries: eclipsing – stars: flare – stars: individual (KIC 7885570)

1 Introduction

About sixty five percent of stars in our Galaxy are red dwarfs. Some of them exhibit stellar spot activity or flare activity (as in the case of UV Cet stars), or both. Seventy-five percent of red dwarfs show flare activity (Rodonó 1986). It is well established that UV Cet objects are young stars on the main-sequence (Poveda et al. 1996), belonging to open clusters or associations. Strong flare activity is present in the majority of young cluster members (Mirzoyan 1990, Pigatto 1990) but the fraction of active stars decreases with the cluster age. The phenomenon can be understood as a result of decreasing of star rotation velocity with time - Skumanich’s law (Skumanich 1972, Pettersen 1991, Stauffer 1991, Marcy and Chen 1992). The flare activity is related to the strength of magnetic field, which increase with rotation velocity for red dwarfs. Because the flare activity is the main source of mass loss in cool main sequence stars, the mass loss rate can be very high for stars on the Zero Age Main Sequence. In the case of UV Cet type stars, it is about due to flare like events (Gershberg 2005), while it is only for the Sun. This suggests that also the angular momentum loss rate is the highest at the early stages of star evolution (also in the pre-main sequence stage according to Marcy and Chen 1992).

On the other hand the mechanism of heating of the stellar corona by the flare activity and causing mass loss is not fully understood. The highest energy detected from two-ribbon flares, which are the most powerful flares occurring on the Sun, is about - erg (Gershberg 2005, Benz 2008). This level is generally observed in the case of RS CVn type active binaries too (Haisch et al. 1991). However, the observed flare energies vary from erg to erg in the case of UV Cet type stars of spectral type dMe (Haisch et al. 1991, Gershberg 2005). In addition, some stars of young clusters such as the Pleiades cluster and Orion association exhibit some powerful flare events with erg (Gershberg and Shakhovskaya 1983).

There are some remarkable differences between the different types of stars, such as between the Sun itself and UV Cet relevant to the flare energy and the mass loss rate. Nonetheless, most of flare events occurring on a star of the spectral type dMe can be explained by the classical theory of solar flares, in which the main energy source is magnetic reconnection (Gershberg 2005, Hudson and Khan 1996). However, the classical theory of solar flare cannot explain all the flares detected from the UV Cet type stars, which is its shortcoming. Comparison of flare events occurring on different types of stars may improve the observational basis of the theoretical models.

For this purpose, we analyzed the light variations caused by both the rotational modulation due to the stellar cool spots and also the flare events detected in the observation of KIC 7885570, which is an eclipsing binary. Being a binary, KIC 7885570 has some different status as compared to a single UV Cet star. Analyzing the light curve of the system, we find the physical parameters of the components and orbital elements. Then, we analyze the out-of-eclipse variations to find the parameters of the chromospheric activity patterns.

KIC 7885570 (V=11.68 mag) is classified as an eclipsing binary of Algol type. There is no complete light curve or chromospheric activity data for the system listed in the Tycho Input Catalogue by Egret et al. (1992). The 2MASS All-Sky Survey Catalog gives J=10.461 mag, H=10.140 mag, K=10.055 mag (Cutri et al. 2003) for the system listed as 2MASS J19195369+4339137. The binary was observed during the Kepler Mission for a long time with high time resolution (Borucki et al. 2010, Koch et al. 2010, Caldwell et al. 2010). There are several estimates of the temperature of the system and its components. For the ratio of the components radii equal to 3.41 and system inclination .44, Coughlin et al. (2011) found the temperature of the system equal to 5398 K. From the initial analysis of data taken during the Kepler Mission, Slawson et al. (2011) and Prša et al. (2011) found the color excess E(B-V)=0.034 mag, and the temperature ratio of 0.763. Using the all available data, Pinsonneault et al. (2012) found metallicity dex, and the temperature of the primary in the range 5633-5682 K. Huber et al. (2014) derived the temperature of the system in the range 5590-5587 K. Their computed mass and radius of the primary are: and . Using the data taken by both the 2MASS All-Sky Survey and the Kepler Mission, Armstrong et al. (2014) obtained the temperatures of the components equal to 8254 K and 8233 K, respectively. The orbital period of the system is 1.729348 d (Watson 2006).

There are only a few studies in which the out-of-eclipse variations are analyzed, e.g., Pigulski et al. (2009). The chromospheric activity was studied by Debosscher et al. (2011), and there is only one study about the flare activity observed in the system (Balona 2015).

2 Data and Analyses

The Kepler Mission has monitored more than 150 000 targets (Borucki et al. 2010, Koch et al. 2010, Caldwell et al. 2010). The quality of these observations is the highest ever reached in photometry (Jenkins et al. 2010ab). The search for extra-solar planets was the main purpose of the Kepler Mission, but many variable stars such as new eclipsing binaries or pulsating stars have also been discovered (Slawson et al. 2011, Matijevič et al. 2012). Some of them exhibit chromospheric activity (Balona 2015).

\FigCap

All the light curves of KIC 7885570 obtained from the available short cadence data in the Kepler Mission Database.

In this study, we use the detrended short cadence data to analyze flare activity. The data used in this study were obtained during the Kepler Mission (Slawson et al. 2011, Matijevič et al. 2012). The phases are computed using the ephemeris taken from the Kepler Mission database. The resulting light curves are shown in Fig. 1. As can be seen in Fig. 1, there are three dominant variations of the light curve: the eclipses, the sinusoidal variation due to rotational modulation, and the short term flare events. After determining the physical parameters of the components with the light curve analysis, we analyze both the flare and the sinusoidal variations. In the last step, we analyze period variation of the system, using the (O-C) data obtained from the epochs of minima.

2.1 Light Curve Analysis

KIC 7885570 was observed during the Kepler Mission for d covering over 750 orbital cycles. It can be seen (Fig. 1) that beside eclipses there are two other out-of-eclipse variations, when the light curves are examined cycle by cycle. One of them is an instant-short term variation, while the other one is a strong sinusoidal variation, which varies from one cycle to another. Because of this, each light curve was examined to find the importance of these two variations. We found that there is little sinusoidal light variation effect and no flare variation in the light curve obtained from the data acquired between HJD 2455691.85632 and 2455693.58508. Therefore, the binary system modelling was done with these detrended short cadence data, using the PHOEBE V.0.32 software (Prša and Zwitter 2005), which employs in the 2003 version of the Wilson Devinney Code (Wilson and Devinney 1971, Wilson 1990).

We have tried to analyze the light curve under the following assumptions regarding the evolutionary status of the binary: detached system mode (Mod2), semidetached system with the primary component filling its Roche-Lobe mode (Mod4), and semi-detached system with the secondary component filling its Roche-Lobe mode (Mod5). Our attempts showed that the system is detached, while both semidetached models were rejected.

\FigCap

The observed (filled circles) and synthetic (red smooth line) light curves obtained from the averaged short cadence data taken from JD 24 55691.85632 and 24 55693.58508.

We determine the temperature of the primary component from the photometry of the system, using the values , , listed by Cutri et al. (2003) in the 2MASS All-Sky Survey Catalog. The derived de-reddened colors ( and ( give the temperature 6530 K with the calibrations of Tokunaga (2000). Thus, we fix the temperature of the primary at 6530 K, while the secondary temperature remains an adjustable parameter.

Parameter Value
0.4340.001
() 80.560.01
6530 (Fixed)
57324
3.79700.0018
5.70650.0040
0.94650.0015
0.32, 0.32 (Fixed)
0.50, 0.50 (Fixed)
0.680, 0.696 (Fixed)
0.636, 0.671 (Fixed)
0.30320.0002
0.09830.0001
1.3090.002
3.14160.0001
0.9950.0002
0.650.01
Table 1: The physical parameters of components obtained from the Kepler light curve analysis.

We use fixed values for the albedos ( and ) and the gravity darkening coefficients ( and ) of the components as for stars with the convective envelopes (Lucy 1967, Rucinski 1969). Also the non-linear limb-darkening coefficients ( and ) are fixed (van Hamme 1993). The other parameters (the dimensionless potentials and , the fractional luminosity of the primary, the inclination i of the system, the mass ratio , and the semi-major axis ) are all treated as the adjustable free parameters. The best fit (minimum sum of weighted squared residuals =0.00697) is found for the mass ratio value of .

Although the cycles which have been chosen for analysis, are little affected by the out-of-eclipse variations, the sinusoidal variation due to the rotational modulation was still seen in the analyzed light curve. Because of this, the out-of-eclipse variation was modeled with the stellar cool spots located on the secondary component.

We assumed that the secondary component was a spotted star for two reasons. The rapid variations in spot positions and sizes in our models (Section 2.3), which is generally seen in the spectral types K and M in the case of the young main sequence stars, point toward the cooler component of the system. In addition, the observed flare activity, characteristic for the stars of the spectral type M can be related to the secondary component.

2.2 Orbital Period Variation

The times of minima were computed without any extra corrections on the available short cadence detrended data of the system from the Kepler Mission Database (Slawson et al. 2011, Matijevič et al. 2012). For all times of minima, the differences between observations and calculations were computed to determine the residuals , using the ephemeris from the Kepler’s database:

(1)

Some times of minima have very large error. In such cases we examined the light curves to find the sources of errors. It was generally noticed that there is a flare activity in these minima. Therefore, these times were removed from analysis. Finally, 278 times of minima were obtained from the observations during the Kepler Mission. Using the regression calculations, a linear correction was applied to the differences, and the residuals were obtained. After the linear correction on , a new ephemerides was calculated:

(2)
HJD Type HJD Type
(+24 00000) (day) day) (+24 00000) (day) (day)
55002.74831 27.5 II 0.03312 0.02709 55709.15823 436.0 I 0.00904 0.00306
55003.58186 28.0 I 0.00199 -0.00403 55710.00022 436.5 II -0.01364 -0.01962
55004.47610 28.5 II 0.03157 0.02554 55710.88801 437.0 I 0.00947 0.00350
55005.31987 29.0 I 0.01067 0.00464 55711.72532 437.5 II -0.01788 -0.02385
55006.20539 29.5 II 0.03153 0.02550 55712.61874 438.0 I 0.01087 0.00490
55007.05237 30.0 I 0.01383 0.00781 55713.45374 438.5 II -0.01880 -0.02477
55007.93612 30.5 II 0.03292 0.02689 55714.34884 439.0 I 0.01164 0.00566
55008.78460 31.0 I 0.01673 0.01071 55715.18194 439.5 II -0.01994 -0.02591
55009.66647 31.5 II 0.03393 0.02791 55716.07582 440.0 I 0.00928 0.00330
55010.50355 32.0 I 0.00634 0.00031 55716.90651 440.5 II -0.02470 -0.03067
55011.39547 32.5 II 0.03360 0.02757 55717.80126 441.0 I 0.00539 -0.00059
55012.22844 33.0 I 0.00190 -0.00413 55718.63570 441.5 II -0.02485 -0.03082
55013.12529 33.5 II 0.03408 0.02805 55719.52550 442.0 I 0.00028 -0.00569
55013.95732 34.0 I 0.00144 -0.00459 55720.36601 442.5 II -0.02387 -0.02985
55017.41845 36.0 I 0.00390 -0.00213 55721.25173 443.0 I -0.00282 -0.00880
55018.31187 36.5 II 0.03264 0.02662 55722.09823 443.5 II -0.02099 -0.02697
55019.14443 37.0 I 0.00053 -0.00549 55722.98395 444.0 I 0.00006 -0.00591
55020.04161 37.5 II 0.03306 0.02703 55723.82738 444.5 II -0.02118 -0.02715
55020.87099 38.0 I -0.00223 -0.00826 55724.72649 445.0 I 0.01326 0.00729
55021.77136 38.5 II 0.03347 0.02744 55725.55810 445.5 II -0.01980 -0.02577
55022.59450 39.0 I -0.00806 -0.01409 55726.45704 446.0 I 0.01448 0.00850
55023.49980 39.5 II 0.03256 0.02654 55727.31526 446.5 II 0.00803 0.00205
55024.31873 40.0 I -0.01317 -0.01920 55728.18804 447.0 I 0.01614 0.01017
55025.23112 40.5 II 0.03455 0.02853 55729.04112 447.5 II 0.00455 -0.00142
55026.04988 41.0 I -0.01136 -0.01738 55729.89719 448.0 I -0.00405 -0.01002
55026.95824 41.5 II 0.03234 0.02631 55730.77515 448.5 II 0.00925 0.00327
55027.78314 42.0 I -0.00743 -0.01346 55731.64613 449.0 I 0.01556 0.00958
55028.68842 42.5 II 0.03318 0.02716 55732.50781 449.5 II 0.01258 0.00660
55029.51503 43.0 I -0.00488 -0.01090 55733.37569 450.0 I 0.01578 0.00980
55030.41801 43.5 II 0.03343 0.02740 55734.23993 450.5 II 0.01535 0.00938
55031.24825 44.0 I -0.00100 -0.00702 55735.10168 451.0 I 0.01244 0.00647
55032.14242 44.5 II 0.02850 0.02248 55735.97329 451.5 II 0.01938 0.01340
55032.98297 45.0 I 0.00438 -0.00164 55736.82920 452.0 I 0.01062 0.00465
55156.65457 116.5 II 0.02842 0.02240 55737.70137 452.5 II 0.01812 0.01215
55157.49406 117.0 I 0.00324 -0.00278 55738.55748 453.0 I 0.00956 0.00359
55158.38133 117.5 II 0.02584 0.01982 56207.20342 724.0 I 0.00528 -0.00066
55159.22536 118.0 I 0.00521 -0.00081 56208.06640 724.5 II 0.00360 -0.00234
55160.10822 118.5 II 0.02340 0.01738 56208.93428 725.0 I 0.00681 0.00087
55160.95645 119.0 I 0.00696 0.00094 56209.79395 725.5 II 0.00181 -0.00413
55161.83169 119.5 II 0.01752 0.01151 56210.66441 726.0 I 0.00760 0.00166
55162.68856 120.0 I 0.00973 0.00371 56211.52180 726.5 II 0.00033 -0.00561
55163.57005 120.5 II 0.02655 0.02053 56212.39378 727.0 I 0.00763 0.00169
55164.42028 121.0 I 0.01211 0.00610 56213.25015 727.5 II -0.00066 -0.00660
55165.29540 121.5 II 0.02257 0.01655 56214.12327 728.0 I 0.00779 0.00185
55166.15248 122.0 I 0.01498 0.00896 56214.97698 728.5 II -0.00317 -0.00911
55167.02427 122.5 II 0.02210 0.01608 56215.85460 729.0 I 0.00978 0.00384
55167.88375 123.0 I 0.01691 0.01089 56216.71199 729.5 II 0.00250 -0.00344
55168.73920 123.5 II 0.00769 0.00168 56217.58431 730.0 I 0.01016 0.00422
55169.61796 124.0 I 0.02179 0.01577 56218.42239 730.5 II -0.01644 -0.02238
55170.47215 124.5 II 0.01131 0.00529 56219.31582 731.0 I 0.01233 0.00639
55171.34619 125.0 I 0.02068 0.01467 56220.16941 731.5 II 0.00125 -0.00470
Table 2: Minima times and and residuals.
HJD Type HJD Type
(+24 00000) (day) day) (+24 00000) (day) (day)
55172.19796 125.5 II 0.00778 0.00176 56221.04827 732.0 I 0.01544 0.00951
55173.07251 126.0 I 0.01766 0.01164 56221.87832 732.5 II -0.01918 -0.02511
55173.90390 126.5 II -0.01561 -0.02163 56222.77777 733.0 I 0.01561 0.00967
55174.78336 127.0 I -0.00083 -0.00684 56223.60781 733.5 II -0.01902 -0.02496
55175.63188 127.5 II -0.01698 -0.02299 56224.50777 734.0 I 0.01627 0.01033
55176.50959 128.0 I -0.00394 -0.00995 56225.36065 734.5 II 0.00448 -0.00146
55177.36850 128.5 II -0.00969 -0.01571 56226.24004 735.0 I 0.01920 0.01326
55178.24244 129.0 I -0.00042 -0.00644 56227.06474 735.5 II -0.02077 -0.02671
55179.09370 129.5 II -0.01382 -0.01984 56227.96495 736.0 I 0.01478 0.00884
55179.97302 130.0 I 0.00082 -0.00519 56228.79864 736.5 II -0.01620 -0.02214
55180.82075 130.5 II -0.01611 -0.02213 56229.69068 737.0 I 0.01117 0.00523
55181.70384 131.0 I 0.00231 -0.00370 56230.54659 737.5 II 0.00241 -0.00353
55641.70747 397.0 I 0.00240 -0.00358 56231.42025 738.0 I 0.01141 0.00547
55642.57236 397.5 II 0.00263 -0.00335 56232.27571 738.5 II 0.00219 -0.00375
55643.43782 398.0 I 0.00341 -0.00257 56233.15045 739.0 I 0.01226 0.00632
55644.29863 398.5 II -0.00045 -0.00643 56234.00055 739.5 II -0.00231 -0.00824
55645.16605 399.0 I 0.00231 -0.00367 56234.88070 740.0 I 0.01318 0.00724
55646.02671 399.5 II -0.00170 -0.00768 56235.73364 740.5 II 0.00145 -0.00448
55646.89499 400.0 I 0.00191 -0.00407 56236.60967 741.0 I 0.01281 0.00688
55647.74968 400.5 II -0.00806 -0.01404 56238.34052 742.0 I 0.01432 0.00839
55648.62390 401.0 I 0.00149 -0.00449 56239.20686 742.5 II 0.01600 0.01006
55649.47771 401.5 II -0.00937 -0.01535 56240.07108 743.0 I 0.01555 0.00961
55650.35173 402.0 I -0.00003 -0.00601 56240.94101 743.5 II 0.02081 0.01487
55651.20608 402.5 II -0.01034 -0.01632 56241.80224 744.0 I 0.01737 0.01144
55652.07997 403.0 I -0.00112 -0.00710 56242.63717 744.5 II -0.01236 -0.01830
55652.92512 403.5 II -0.02064 -0.02662 56243.52947 745.0 I 0.01526 0.00933
55653.80259 404.0 I -0.00783 -0.01381 56244.40009 745.5 II 0.02122 0.01528
55654.65464 404.5 II -0.02045 -0.02643 56245.25853 746.0 I 0.01499 0.00906
55655.53157 405.0 I -0.00819 -0.01417 56252.17055 750.0 I 0.00966 0.00372
55656.38573 405.5 II -0.01870 -0.02468 56253.04765 750.5 II 0.02209 0.01616
55657.26225 406.0 I -0.00685 -0.01283 56253.89969 751.0 I 0.00947 0.00353
55658.11684 406.5 II -0.01693 -0.02291 56254.77715 751.5 II 0.02226 0.01633
55658.99140 407.0 I -0.00703 -0.01301 56255.62895 752.0 I 0.00939 0.00345
55659.84350 407.5 II -0.01960 -0.02558 56256.50576 752.5 II 0.02153 0.01560
55660.72121 408.0 I -0.00657 -0.01254 56257.35942 753.0 I 0.01053 0.00459
55661.57713 408.5 II -0.01530 -0.02128 56258.23514 753.5 II 0.02157 0.01563
55662.45300 409.0 I -0.00411 -0.01009 56259.08870 754.0 I 0.01047 0.00453
55663.32383 409.5 II 0.00205 -0.00393 56259.96721 754.5 II 0.02430 0.01837
55664.18231 410.0 I -0.00413 -0.01011 56260.81578 755.0 I 0.00821 0.00228
55665.04958 410.5 II -0.00153 -0.00751 56261.69435 755.5 II 0.02212 0.01618
55665.91053 411.0 I -0.00525 -0.01123 56262.54418 756.0 I 0.00728 0.00134
55666.78703 411.5 II 0.00658 0.00060 56263.42314 756.5 II 0.02157 0.01563
55667.64249 412.0 I -0.00263 -0.00861 56264.27034 757.0 I 0.00410 -0.00184
55668.51667 412.5 II 0.00688 0.00090 56265.15334 757.5 II 0.02243 0.01649
55669.36772 413.0 I -0.00673 -0.01271 56265.99892 758.0 I 0.00334 -0.00260
55670.25048 413.5 II 0.01136 0.00538 56266.88216 758.5 II 0.02191 0.01597
55671.09659 414.0 I -0.00720 -0.01318 56267.72790 759.0 I 0.00299 -0.00295
55671.98282 414.5 II 0.01436 0.00838 56269.45838 760.0 I 0.00413 -0.00181
55672.82152 415.0 I -0.01161 -0.01759 56270.32895 760.5 II 0.01003 0.00410
55673.70902 415.5 II 0.01123 0.00525 56271.18755 761.0 I 0.00396 -0.00198
55674.55090 416.0 I -0.01157 -0.01755 56272.05794 761.5 II 0.00968 0.00375
Table 2: Continued From Previous Page.
HJD Type HJD Type
(+24 00000) (day) day) (+24 00000) (day) (day)
55675.43663 416.5 II 0.00950 0.00352 56272.91770 762.0 I 0.00477 -0.00116
55676.28279 417.0 I -0.00901 -0.01498 56273.78605 762.5 II 0.00846 0.00252
55677.16322 417.5 II 0.00675 0.00077 56274.64810 763.0 I 0.00584 -0.00010
55678.89492 418.5 II 0.00912 0.00314 56275.51604 763.5 II 0.00910 0.00317
55679.74916 419.0 I -0.00131 -0.00729 56276.37654 764.0 I 0.00495 -0.00099
55680.62492 419.5 II 0.00978 0.00380 56277.24773 764.5 II 0.01146 0.00552
55681.47994 420.0 I 0.00013 -0.00584 56278.10611 765.0 I 0.00518 -0.00076
55682.35009 420.5 II 0.00561 -0.00036 56278.97842 765.5 II 0.01282 0.00688
55683.20932 421.0 I 0.00017 -0.00581 56279.83831 766.0 I 0.00804 0.00210
55684.08012 421.5 II 0.00630 0.00033 56280.71650 766.5 II 0.02156 0.01563
55684.94104 422.0 I 0.00256 -0.00342 56281.57083 767.0 I 0.01122 0.00529
55685.81052 422.5 II 0.00737 0.00139 56282.44634 767.5 II 0.02206 0.01612
55686.67100 423.0 I 0.00319 -0.00279 56283.30063 768.0 I 0.01168 0.00574
55687.53104 423.5 II -0.00145 -0.00743 56284.17625 768.5 II 0.02264 0.01671
55688.39877 424.0 I 0.00162 -0.00436 56285.02861 769.0 I 0.01033 0.00439
55689.26303 424.5 II 0.00121 -0.00477 56285.90400 769.5 II 0.02104 0.01511
55690.12316 425.0 I -0.00333 -0.00931 56286.75468 770.0 I 0.00706 0.00113
55690.98790 425.5 II -0.00327 -0.00924 56287.63191 770.5 II 0.01962 0.01368
55691.84585 426.0 I -0.00998 -0.01595 56288.48294 771.0 I 0.00599 0.00005
55692.71187 426.5 II -0.00862 -0.01460 56289.36138 771.5 II 0.01976 0.01382
55693.57218 427.0 I -0.01299 -0.01896 56290.21326 772.0 I 0.00697 0.00103
55694.45862 427.5 II 0.00879 0.00281 56291.08996 772.5 II 0.01900 0.01307
55695.30483 428.0 I -0.00967 -0.01565 56291.94410 773.0 I 0.00847 0.00253
55696.16335 428.5 II -0.01582 -0.02180 56292.82090 773.5 II 0.02060 0.01467
55697.03614 429.0 I -0.00770 -0.01368 56293.67592 774.0 I 0.01095 0.00502
55697.89242 429.5 II -0.01609 -0.02207 56294.54272 774.5 II 0.01309 0.00715
55698.76872 430.0 I -0.00445 -0.01043 56295.40590 775.0 I 0.01160 0.00566
55699.61994 430.5 II -0.01790 -0.02388 56296.27452 775.5 II 0.01555 0.00962
55700.50753 431.0 I 0.00501 -0.00096 56297.13646 776.0 I 0.01282 0.00689
55701.35795 431.5 II -0.00923 -0.01521 56298.00600 776.5 II 0.01769 0.01176
55702.23928 432.0 I 0.00743 0.00145 56298.86704 777.0 I 0.01406 0.00813
55703.09170 432.5 II -0.00482 -0.01079 56299.73596 777.5 II 0.01831 0.01238
55703.97005 433.0 I 0.00887 0.00289 56300.59633 778.0 I 0.01402 0.00808
55704.82489 433.5 II -0.00096 -0.00694 56301.46651 778.5 II 0.01953 0.01359
55705.70050 434.0 I 0.00998 0.00400 56302.32643 779.0 I 0.01478 0.00885
55706.54829 434.5 II -0.00691 -0.01288 56303.19366 779.5 II 0.01734 0.01141
55708.27480 435.5 II -0.00972 -0.01570 56304.05716 780.0 I 0.01617 0.01024
Table 2: Continued From Previous Page.
\FigCap

The variation of the residuals obtained by the linear correction on . In the upper panel, filled black circles represent the residuals, while smooth red line represents a polynomial fit of the degree derived by the method of least squares. However, in the bottom panel, the residuals are plotted versus time (HJD) for the primary and secondary minima, separately. Here, the filled blue circles represent the primary minima, while the red ones represent the secondary minima.

Times of minima, epochs, minimum types, and residuals are listed in Table 2. A sample of the Table 2 is presented here, while full Table 2 is available from the Acta Astronomica Archive.

Variations of the residuals are shown in the upper panel of Fig. 3, while the residuals for the primary and secondary minima are plotted in the bottom panel. An interesting phenomenon can be seen in the bottom panel: the residuals of both the primary and the secondary minima vary synchronously, but in opposite directions. A similar phenomenon has been recently demonstrated for other chromospherically active systems by Tran et al. (2013) and Balaji et al. (2015).

2.3 Rotational Modulation and Stellar Spot Activity

The sinusoidal variations seen out of eclipses must be caused by the rotational modulation due to the cool stellar spots. After removing other variations from the data (eclipses and flares), the pre-whitened light curves have been obtained. If the sinusoidal variations phased with the orbital period are examined cycle by cycle, it can be seen that both the phases and brightness levels of maxima and minima are rapidly changing in a few cycle time scale. This indicates the rapid evolution of the magnetically active regions. Therefore, the whole pre-whitened light curves cannot be modeled as just one data set. For this reason, the whole data set was divided into several sub-data sets. From the beginning of the data, the variation in the pre-whitened light curves was inspected cycle by cycle. The new sub-data set was started, whenever the difference between the shapes of the two consecutive cycles became bigger than three times the standard deviation. Therefore, the consecutive cycle data, with almost the same phase distributions and brightness levels, were treated as one sub-data set. As a result, the whole data were split into 35 sub-data sets, each of them individually modeled.

\FigCap

Four examples from 35 models derived for the rotation modulations due to cool spots. In the left panels, the filled circles show the pre-whitened light curve, while the red lines represent the models derived by the SPOTMODEL. In the right panels, the spot distributions on the active component derived by the SPOTMODEL are shown as the 3D form.

Average HJD
(+24 50000) () () () () () ()
5004.03200 37.75 0.20 117.59 0.72 17.49 0.40 23.10 0.35 -15.71 0.01 35.65 0.06
5008.72031 12.41 0.09 111.25 0.06 11.66 0.06 26.47 0.03 -1.96 0.11 60.68 0.14
5012.68289 24.19 0.44 117.65 0.07 12.73 0.02 23.94 0.02 -2.57 0.08 54.01 0.09
5020.06827 28.53 0.60 118.08 0.15 14.61 0.04 22.69 0.05 -4.41 0.13 50.48 0.19
5023.47322 29.95 0.54 122.29 0.22 15.86 0.04 21.13 0.06 -5.66 0.13 47.10 0.20
5026.31184 34.42 0.81 125.32 0.41 15.74 0.07 20.76 0.10 -6.70 0.22 44.41 0.28
5029.93778 32.38 0.77 122.01 0.28 15.64 0.06 22.32 0.08 -5.92 0.17 40.24 0.23
5176.52260 35.05 0.41 101.44 0.08 17.00 0.05 28.87 0.04 0.51 0.04 -20.38 0.19
5180.78777 26.57 0.68 101.09 0.08 15.79 0.05 30.08 0.05 -0.73 0.07 -24.57 0.33
5642.56642 64.10 0.29 126.12 0.10 26.30 0.10 16.41 0.23 -7.17 0.05 -1.78 0.09
5649.31378 68.13 0.07 162.47 0.09 28.42 0.02 13.07 0.02 -14.58 0.05 -14.90 0.09
5655.91200 66.63 0.11 126.75 0.76 29.12 0.05 15.14 0.14 -19.46 0.04 -21.70 0.10
5659.18155 69.09 0.07 138.37 0.86 29.52 0.03 13.23 0.09 -24.51 0.05 -13.65 0.13
5663.14341 68.90 0.09 131.33 0.75 29.45 0.04 14.08 0.12 -24.29 0.06 -12.25 0.10
5668.95455 69.11 0.09 115.85 0.77 29.68 0.60 16.15 0.71 -20.43 0.41 -9.98 0.82
5672.69108 70.67 0.80 116.29 0.79 29.42 0.50 17.97 0.24 -15.36 0.85 11.51 0.20
5676.80771 68.02 0.11 121.31 0.81 28.22 0.53 18.75 0.16 -11.06 0.62 6.48 0.73
5683.96383 64.00 0.25 118.37 0.83 26.66 0.55 21.74 0.92 -7.21 0.28 2.70 0.39
5691.52471 45.64 0.67 104.96 0.33 20.78 0.17 20.09 0.15 -1.45 0.04 3.95 0.13
5709.48021 42.08 0.35 122.35 0.49 23.36 0.06 19.34 0.11 2.73 0.08 -26.06 0.23
5713.52167 43.58 0.48 114.78 0.56 23.53 0.11 20.52 0.18 -1.53 0.14 -41.00 0.57
5717.33918 55.79 0.16 129.53 0.75 26.74 0.06 16.70 0.14 -0.61 0.14 -44.82 0.33
5728.18173 69.85 0.02 238.41 0.77 32.34 0.01 10.64 0.35 8.08 0.03 -42.31 0.07
5731.62378 68.73 0.05 244.09 0.79 31.95 0.02 10.10 0.56 9.30 0.06 -32.14 0.07
6230.51567 42.81 0.32 263.64 0.09 18.78 0.08 55.91 0.06 7.74 0.03 -4.34 0.17
6234.02066 37.91 0.71 267.06 0.14 17.36 0.13 57.42 0.09 10.36 0.07 -2.25 0.68
6241.79821 39.10 0.50 263.76 0.13 19.08 0.11 50.20 0.11 11.77 0.07 59.75 0.17
6255.60165 43.95 0.40 256.65 0.11 20.47 0.11 50.28 0.12 9.34 0.12 67.98 0.60
6262.55028 43.82 0.38 257.77 0.10 19.74 0.09 51.03 0.10 3.16 0.09 54.90 0.49
6266.00699 49.31 0.37 256.93 0.15 20.62 0.12 49.19 0.14 0.87 0.12 48.35 0.58
6269.60959 33.21 0.90 263.26 0.06 15.36 0.12 53.27 0.09 5.05 0.12 76.36 0.21
6273.80010 34.16 0.58 264.27 0.02 14.35 0.07 55.23 0.04 2.75 0.07 86.96 0.73
6282.43076 47.03 0.83 262.77 0.13 16.01 0.20 56.30 0.11 8.59 0.14 54.49 0.95
6286.77790 49.15 0.69 264.95 0.12 16.91 0.20 56.35 0.12 13.13 0.11 59.14 0.38
6292.81678 65.78 0.31 250.68 0.40 27.28 0.15 42.52 0.40 11.81 0.12 46.35 0.22
Table 3: The parameters of the models derived by the SPOTMODEL program.

Using the SPOTMODEL program (Ribárik 2002, Ribárik et al. 2003), the subdata sets were modeled under some assumptions to derive the spot distribution on the stellar surface and to find their parameters such as the spot radius, latitude and especially longitude. To model any spot distribution on the stellar surface, the SPOTMODEL program needs two-band observations or spot temperature factor parameter. However, the available data taken from the Kepler Mission Database contain only monochromatic observations. At this point, considering the results obtained from the light curve analysis of the system and also the results found for other similar systems (Clausen et al. 2001, Thomas and Weiss 2008), it was assumed that this is the secondary component which exhibits chromospheric activity. According to the light curve analysis, there are two spotted areas on the secondary component. One spotted area or more than two do not give any acceptable fit to the observations.

We assumed that the spot temperature factor parameter should be in the range of 0.70-0.95 in the SPOTMODEL. Our tests indicated that the best solutions are obtained if the spot temperature factor was taken as for the primary spot (Spot 1), and as for the secondary one (Spot 2). Therefore, it was assumed that the spot temperature factors were constant parameters for all sub-data set, while the other parameters such as the longitudes (), latitudes () and radii of the spots (), were treated as the adjustable free parameters for each sub-data set separately.

Fig. 4 shows four models from our 35 models of photometric sub-data sets. Model fits and the distribution of cool spot on the 3D plot are presented. The spot parameters derived by SPOTMODEL are listed for all sub-data sets in Table 3. The average of the HJD interval for each sub-data set, spot latitudes (), radii of the spots () and spot longitudes () are listed there. As can be seen from Table 3, the spot parameters remain constant for several cycles and then change by several degrees when going from one cycle to another. This is a common phenomenon seen in the case of the chromospherically active young stars like FL Lyr (Yoldas and Dal 2016). It is well known that the chromospheric activity patterns can in general change rapidly in short time intervals (Gershberg 2005, Benz 2008). The variations of spot parameters vs. time are shown in Fig. 5. It should be noted here that if it was assumed that chromospherically active star is not the secondary component, but the primary one, there would be no astrophysically reasonable solution and distinctive changes in the values of spot latitudes (), radii of the spots () and spot longitudes (). This is because the surface temperatures of the both components are substantially different.

\FigCap

The variations of the free parameters found by the SPOTMODEL Program. The filled black circles represent the Spot 1 (), while filled red circles represent the Spot 2 () in the figure.

2.4 Flare Activity and the OPEA Model

To analyze the flare activity in KIC 7885570, we removed all other variations from light the curve. Observations between the phases 0.96-0.04 and 0.46-0.54 (related to the primary and secondary minima) were neglected. Also all observations with large error due to technical problems were removed from the data sets. As described in Section 2.3 the sinusoidal variation in the light curve has been fitted based on data out of eclipses and flares. The whole dataset can now be compared to the synthetic light curves obtained in this way in a search for short lasting intensity excess, i.e., flares. Three flare light curves and the synthetic light curves are shown in Fig. 6. Comparing the data with the model light curve, the flare rise times (), decay times (), the flare amplitudes () and finally the flare equivalent durations () were computed. The parameters of flares are listed in Table 4. A sample part of Table 4 is presented here, while full table is available from the Acta Astronomica Archive.

\FigCap

There flare light curve samples. In the figure, filled circles represent the observations, while the dotted lines represent the Fourier models.

Flare Time
(+24 00000) (s) (s) (s) (Intensity)
55002.897228 10.67513 1588.95475 5708.47565 0.00416
55002.980327 8.65908 353.09952 5119.96378 0.00511
55004.100798 27.57592 1059.30806 7297.42608 0.01108
55004.626635 11.30656 529.65360 6532.37568 0.00309
55008.327249 2.85669 1235.85091 2765.96122 0.00185
55010.620632 6.48999 411.96384 2942.49370 0.00626
55010.876057 32.90377 7768.21018 3825.25286 0.01408
55011.592611 7.65157 588.50842 5296.50230 0.00213
55018.732927 1.02885 235.40976 823.88966 0.00161
55018.749274 1.54401 588.49805 1471.24426 0.00154
55018.771751 0.35084 470.80138 470.79274 0.00108
55019.342539 97.19761 6179.22346 9121.71024 0.01868
55020.618979 2.49765 588.49632 1294.69018 0.00271
55021.104625 3.73807 1765.49933 1824.33859 0.00175
55022.103843 2.01406 117.69581 3119.02618 0.00123
55023.766481 1.69797 529.64755 2236.27910 0.00146
55025.866401 13.71493 1942.03699 2059.72416 0.00763
55027.306306 1.23595 1000.43770 1118.14992 0.00139
55027.502470 26.28887 1942.03440 9474.75014 0.00445
55030.133664 0.62521 235.39075 470.78928 0.00237
55030.577078 0.61956 176.54285 647.34941 0.00482
55030.586613 0.39579 176.55149 470.78928 0.00167
55032.270357 1.09919 765.04349 588.49286 0.00141
55032.281936 0.74200 411.94051 823.89139 0.00131
55175.292675 0.39886 176.54371 58.83667 0.00609
55176.697777 4.29154 1941.94627 1824.25651 0.00241
55178.366464 0.23733 117.69062 58.83667 0.00343
55179.853981 1.58539 353.07878 823.86634 0.00485
55181.170544 0.77598 176.53507 235.38989 0.01071
55182.059377 8.47162 411.94224 4236.97478 0.00688
55648.070187 3.38497 823.91040 1530.11549 0.00292
55649.839794 6.08832 706.21373 4119.54077 0.00446
55650.736178 18.74595 2412.87811 7532.88768 0.00502
55651.834181 128.60604 3825.29866 11652.46128 0.02497
55654.184807 14.47501 353.11248 8121.41510 0.00574
55656.132879 6.16941 823.90522 4237.27459 0.00387
55656.235732 78.13174 2824.84454 5590.84032 0.03034
55656.712533 10.75699 823.90522 4649.22893 0.00319
55657.663411 6.82572 1530.11290 4531.51498 0.00239
55658.317991 4.32212 1294.71610 2707.14010 0.00225
55659.549501 9.01695 2883.69763 2707.14960 0.00408
55660.458830 19.09031 941.61312 7768.32941 0.00512
55660.559639 2.94486 588.50928 2059.78291 0.00393
55661.459432 8.92595 2295.19786 3354.50074 0.00284
55662.095622 2.64608 353.10384 1706.67994 0.00341
55663.424538 0.36284 58.84963 117.70704 0.00545
55664.664224 25.26883 1059.32102 8297.99251 0.00573
55668.161911 3.95248 941.62349 3295.65888 0.00237
55668.803552 2.27129 1294.71178 1471.28573 0.00155
55670.835413 2.59642 1118.18189 1647.83462 0.00171
55671.519285 0.39148 294.25507 294.26458 0.00248
Table 4: The flare parameters computed from the available Short Cadence Data in the Kepler Mission database.
Flare Time
(+24 00000) (s) (s) (s) (Intensity)
55672.224954 2.66442 1471.27795 1942.09056 0.00145
55672.253562 0.43699 117.70790 588.51101 0.00121
55672.599585 4.95169 1294.72128 2766.00874 0.00255
55674.090617 2.90422 706.21027 2295.19613 0.00163
55675.313277 5.52057 529.66224 1647.83549 0.00435
55678.627062 12.28612 411.96384 5296.60685 0.00824
55679.507787 1.02091 411.95434 823.91818 0.00193
55682.625403 0.52162 235.39853 529.66224 0.00234
55685.970523 1.56884 588.51274 1647.82858 0.00143
55691.100934 11.86987 529.67174 4001.87779 0.00798
55693.982193 5.79558 1588.98845 2177.49168 0.00272
55694.948061 12.58234 353.10557 3236.81616 0.01100
55697.759842 7.42440 1412.42141 2589.46330 0.00377
55702.705658 146.22706 2118.64032 14771.65853 0.02786
55708.990607 1.48384 176.54803 941.62435 0.00235
55712.093912 11.57002 1530.12586 5590.85069 0.00426
55714.529692 12.60495 529.66138 3177.96480 0.00760
55716.528856 0.80430 529.66051 529.66051 0.00145
55717.573052 12.20767 823.90694 5943.95539 0.00380
55718.229677 1.02910 529.66915 765.04867 0.00137
55718.239213 0.29040 58.85741 588.51014 0.00118
55718.382253 5.66139 1118.16115 4119.56755 0.00253
55719.820832 0.28776 117.69840 294.25421 0.00297
55720.765580 0.60883 235.39680 529.65965 0.00319
55727.607674 3.16930 882.76954 1883.22192 0.00263
55730.895551 0.69733 235.40458 529.66656 0.00197
55731.353278 2.09393 882.76003 882.76867 0.00257
55731.761283 2.57682 1294.71955 1588.95648 0.00183
55731.780355 0.41303 58.85741 411.95088 0.00238
55732.360688 5.69604 1000.46707 2471.73293 0.00523
55732.392020 0.81147 235.39507 529.65792 0.00190
55736.629401 0.35955 235.41235 176.55494 0.00295
56231.120993 3.55548 765.00634 1706.54774 0.00338
56231.656332 1.99454 411.92150 1647.70243 0.00241
56235.156467 0.88557 470.76509 411.93878 0.00159
56240.815658 3.00616 1647.69120 588.47126 0.00321
56241.066300 12.79948 470.77286 4707.70272 0.00622
56241.562815 20.98885 647.30707 4236.93677 0.01036
56242.067504 0.84725 529.61818 764.99683 0.00114
56254.097596 1.81944 411.91978 1706.53306 0.00196
56255.127405 4.31030 294.23952 3001.15498 0.00212
56255.865707 4.12307 1176.91574 2236.15901 0.00253
56256.935700 8.94963 1294.62192 5001.92755 0.00407
56260.990914 4.99894 1412.31082 2648.08915 0.00453
56263.640357 6.43391 706.16016 4472.32147 0.00398
56265.358068 1.06821 235.37779 941.54659 0.00146
56265.415961 41.10177 4060.39392 7767.70128 0.00994
56266.119528 21.00597 1176.93302 6473.09750 0.00686
56267.019250 2.38824 706.14288 2236.16160 0.00196
56268.021135 1.38561 294.22310 1353.46810 0.00186
56270.590893 7.33015 706.16102 4178.08627 0.00404
Table 4: Continued From Previous Page.
Flare Time
(+24 00000) (s) (s) (s) (Intensity)
56272.542903 2.35347 411.92064 1412.30477 0.00216
56272.664818 92.02830 2942.31658 10651.19328 0.01879
56273.280525 2.69546 529.60954 2353.85395 0.00220
56274.777566 4.94307 588.46349 2295.00173 0.00274
56274.878368 11.65929 529.61904 3648.47155 0.00538
56281.847993 0.16988 117.69840 58.84445 0.00273
56285.207831 2.92960 588.46522 1883.08714 0.00313
56286.512809 9.49735 706.16448 5296.19386 0.00309
56288.216910 1.36715 294.24211 1118.07907 0.00223
56292.129807 4.13727 411.92410 2530.41322 0.00377
56293.043839 6.09957 588.45917 4119.27379 0.00205
Table 4: Continued From Previous Page.

In total, 113 flares were detected from the available observations in the Kepler Mission database. The flare equivalent durations of the flare events were computed using Eq.(3) (Gershberg 1972):

(3)

where is the flux of the star in the quiet state (computed using the models of Section 2.3).

Our analysis has shown that the flare equivalent duration has a maximum for the star, independent of the flare total duration. The tests made by using the SPSS V17.0 (Green et al. 1999) and GRAHPPAD PRISM V5.02 (Dawson and Trapp 2004) programs indicated that the best function to describe dependence of the logarithm of the equivalent time duration on the total flare duration is the One Phase Exponential Association (hereafter OPEA) for the distributions of flare equivalent durations on the logarithmic scale vs. flare total durations, as it was demonstrated by Dal and Evren (2010, 2011). The OPEA function is a special one, because it has a Plateau term. The OPEA function is defined:

(4)

where the parameter is the flare equivalent duration on a logarithmic scale, the parameter is the flare total duration. The parameter is the shortest equivalent duration logarithm occurring in a flare for a star as described by Dal and Evren (2010). The parameter Plateau value is the upper limit for the flare equivalent duration on a logarithmic scale. Dal and Evren (2011) defined Plateau value as a saturation level for a star in the observed band. Formally, the equivalent duration approaches its saturation value for but for it is a halfway between its minimum and maximum values. This explains the definition of (Dawson and Trapp 2004).

\FigCap

The OPEA model derived from the 113 flares detected in the observations of KIC 7885570. In the figure, the filled circles represent the observed flares, while the smooth red line.

The OPEA Best-fit Values 95 Confidence Intervals
-0.50870.0485 -0.6050 to -0.4125
1.98150.1177 1.7481 to 2.2149
0.00020.00002 0.0001 to 0.0002
5737.9 4785.0 to 7164.5
3977.2 3316.7 to 4966.0
2.49030.1048 2.2823 to 2.6982
Goodness of Fit
R 0.914
(D’Agostino-Pearson) 0.001
(Shapiro-Wilk) 0.001
(Kolmogorov-Smirnov) 0.001
Table 5: The OPEA model parameters by using the least-squares method.

The derived model is shown in Fig. 7 together with the observed flare equivalent durations. The parameters computed from the model using the least-squares method are listed in Table 5. The span value listed in Table 5 is the difference between Plateau and values.

To understand whether there are any other functions to model the distributions of flare equivalent durations on the logarithmic scale vs. flare total durations, the derived OPEA model was tested by using three different methods: the D’Agostino-Pearson normality test, the Shapiro-Wilk normality test and the Kolmogorov-Smirnov test (D’Agostino and Stephens 1986). In these tests (Table 5), the probability value called as p-value was found to be . This means that there is no other function to model the distributions of flare equivalent durations (Motulsky 2007, Spanier and Oldham 1987).

KIC 7885570 was observed for 1301.6 d in total, from HJD 2455002.51034 to 2456304.14644 without any remarkable interruptions. The significant 113 flares were detected in the available data. The total flare equivalent duration computed from all the flares was found to be 1198.65710 s (0.33296 hours). Ishida et al. (1991) described two frequencies for the stellar flare activity. These frequencies are defined:

(5)
(6)

where is the total flare number detected in the observations, and is the total observing time duration, while is the total equivalent duration obtained from all flares. In this study, frequency was found to be 0.00362 h, while frequency - 0.00001.

3 Results and Discussion

There are several determinations of the components temperature, which vary from 5398 K (Coughlin et al. 2011) to 8254 K (Armstrong et al. 2014). We computed the temperature of the system taking the JHK magnitudes from the 2MASS All-Sky Survey Catalog (Cutri et al. 2003), and using the calibrations given by Tokunaga (2000). Firstly, the reddened colors of the system were calculated as mag and mag, and the temperature was found to be 6530 K. In the light curve analysis, this value, which is in agreement with the older values in the literature, was assumed as the temperature of the primary component. On the other hand, it should be noted that Armstrong et al. (2014) derived 8254 K and 8233 K for the temperatures of the primary and secondary components, respectively, using the same data taken by both the 2MASS All-Sky Survey and the Kepler Mission. The differences in the temperature values between the two studies are likely caused due to different calibrations used. However, if the temperature of the primary component was taken as 8254 K, the temperature of the secondary component would be about 7500 K. If these values were right, it would be difficult to explain how the stellar cool spot and the flare activity occurs at very high level. Thus, we assumed that the temperature of the primary component is equal 6530 K Under this assumption, the temperature of the secondary component was found to be 57324 K (formal fit error). The mass ratio of the component is 0.430.01, while the inclination: 80.560.01. The dimensionless potentials ( and ) of the components were found to be 3.7970.002 and 5.7060.004, respectively, while the fractional radii of the components: 0.3030.002 and 0.0980.001, respectively.

Considering both the component temperatures and fractional radii found from the light curve analysis, and also the Kepler’s third law, we tried to estimate the absolute parameters of the components. The masses of the components were found to be 1.59 and 0.98 for the primary and secondary, respectively. The semi-major axis () of the system is 9.68 and the radii of the primary and secondary components - 2.94 and 0.95 , respectively. Thus, the secondary is a main sequence star, while the primary has already evolved from the main sequence. Since our investigation shows that the secondary is chromospherically active star, KIC 7885570 seems to be a RS CVn binary.

Based on derived times of eclipses an updated ephemeris was derived and the residuals were obtained. It may be seen that the residuals have two characteristic variations. First, the residuals exhibit a parabolic variation, which indicates that there is a mass loss from the system or a mass transfer from the secondary component to the primary. It is most likely an indicator of a mass loss from the system due to the flare activity occurring on the chromospherically active component. However, as it can be seen from the bottom panel of Fig. 3, if one considers the residuals of the primary and secondary minima separately, the residuals of both the primary and secondary minima vary synchronously, but in the opposite directions. This phenomenon, which indicates that the residuals of the primary and secondary minima were affected by another variation, was noticed for the first time by Tran et al. (2013) and Balaji et al. (2015). The light curve analysis revealed that the secondary component exhibits stellar spot activity. According to the results obtained by Tran et al. (2013) and Balaji et al. (2015), this explains why the residuals of both the primary and secondary minima vary synchronously in opposite directions.

Based on the out-of-eclipse variations, it is clear that one of the components is a chromospherically active star. To determine the stellar spot configurations on the active component, the data set of all the pre-whitened light curves was separated to 35 sub-data sets, and each of them was modeled by the SPOTMODEL (Ribárik 2002; Ribárik et al. 2003). The results indicate two spotted areas on the star at some time intervals, while there is just one spotted area some other time intervals. The parameters obtained from the SPOTMODEL analysis are listed in Table 3, while the variations of these parameters are shown in Fig. 5. There are two active spot regions located around the latitudes of and . However, their latitudes are not stable. Nevertheless, these two regions are always separated from each other. In addition the longitudes of these areas are also rapidly varying from one cycle to another. It seems that the spotted areas migrate from one longitude to the next one with time, what indicate that there is a differential rotation on the stellar surface. In this case, it is clear why the residuals of both the primary and secondary minima vary synchronously in opposite directions. As it can be seen from the upper panel of Fig. 3 and the middle panel of Fig. 5, both the longitudinal migrations of the spotted areas and also the residuals of the primary and secondary minima are varying in the same way. However, the same behavior is seen in the variation of spot radii.

KIC 7885570 was observed for 1301.636 d. In total, 113 flares, whose parameters were computed, were detected in these data. Using these flare data, the flare frequencies and were computed as 0.00362 h and 0.00001. Comparing these frequencies with those computed from single UV Cet type stars, it is seen that the flare energy level found for KIC 7885570 is remarkably lower than those found for them. For example, the observed flare number per hour for UV Cet type single stars was found to be 1.331 h in the case of AD Leo, and 1.056 h for EV Lac. Moreover, frequency was found to be 0.088 for EQ Peg, and 0.086 for AD Leo (Dal and Evren 2011). However, according to Yoldaş and Dal (2016, 2017), the flare frequencies were found as 0.4163 h and 0.0003 for FL Lyr (B-V=0.74 mag), and 0.0165 h and 0.00001 for KIC 9761199 (B-V=1.303 mag). It is clearly seen that the flare frequencies of KIC 7885570 is also remarkably lower than its analogues.

Examining the parameters found from 113 flares, it was found that the flare equivalent duration on the logarithmic scale was approximately dependent on the flare total durations in a specific way. The same case was seen by Dal and Evren (2011), and they modeled this variation with the OPEA function for different stars. They also found that the Plateau values in these models change from one star to the other according to their spectral types. The Plateau value was found to be 1.9815±0.1177 for KIC 7885570. According to Dal and Evren (2011), this value is 3.014 for EV Lac (B-V=1.554 mag), 2.935 for EQ Peg (B-V=1.574 mag), and also 2.637 for V1005 Ori (B-V=1.307 mag). The maximum flare energy detected from KIC 7885570 is clearly lower than those obtained from UV Cet type single flare stars. On the other hand, Yoldaş and Dal (2016, 2017) found the Plateau values of 1.232 for FL Lyr and 1.951 for KIC 9761199. In this case, the Plateau value obtained from KIC 7885570 is close to that found from KIC 9761199. The Plateau values obtained for KIC 7885570 and for KIC 9761199 have close values, but their flare frequencies are very different.

As it is seen from Table 5, the half-life value was found to be 3977.2 s, which is remarkably larger than those found from the single UV Cet type stars. For instance, it was found to be 433.10 s for DO Cep (B-V=1.604 mag), 334.30 s for EQ Peg, and 226.30 s for V1005 Ori (Dal and Evren 2011). It means that the flares can reach the maximum energy level at their Plateau value, when their total durations reach about a few5 minutes, while it requires a few66 minutes for KIC 7885570, a few39 minutes for FL Lyr and a few17 minutes for KIC 9761199 (Yoldaş and Dal 2016, 2017). In addition, the maximum flare rise time () was found to be 7768.210 s for KIC 7885570. In the case of the single UV Cet type stars, the maximum flare rise time was found to be 2062 s for V1005 Ori and 1967 s for CR Dra. In the same way, the maximum flare total time () was found to be 5236 s for V1005 Ori and 4955 s for CR Dra. However, it was derived as 16890.30 s for KIC 7885570. The maximum flare rise and total times were computed as 5179 s and 12770.62 s for FL Lyr, and as 1118.1 s and 6767.72 s for KIC 9761199 (Yoldaş and Dal 2016, 2017), According to these results, the flare time scales in KIC 7885570 are clearly longer than those obtained from the single UV Cet type stars. However, the flare time scales of KIC 7885570 are moderately longer than those found for FL Lyr.

In general, KIC 7885570 behaves like KIC 9761199 in terms of the Plateau parameter, and behaves like FL Lyr in terms of the flare time scales. However, in the case of the flare frequencies, KIC 7885570 is similar to none of them, because, its flare frequencies are clearly lower than those obtained for these two systems. On the other hand, this is in agreement with the results of Dal and Evren (2011). They demonstrated that the values of the parameters derived from the OPEA model depend on the B-V color of the stars. Our determination of the temperature KIC 7885570 secondary component indicates B-V=0.643 mag.

\Acknow

The authors thank O. Özdarcan for his help with the software and hardware assistance in the analyses. We also thank the referee for useful comments that have contributed to the improvement of the paper.

References

\refitem

Ammons, S.M., Robinson, S.E., Strader, J., Laughlin, G., Fischer, D., Wolf, A.2006ApJ6381004 \refitemArmstrong, D.J., Gómez Maqueo Chew, Y., Faedi, F., Pollacco, D.2014MNRAS4373473 \refitemBalaji, B., Croll, B., Levine, A.M., Rappaport, S.2015MNRAS448429 \refitemBalona, L.A.2015MNRAS4472714 \refitemBenz, A.O.2008Living Rev. Solar Phys.51 \refitemBorucki, W.J., Koch, D., Basri, G., et al.2010Sci327977 \refitemBotsula, R.A.1978Perem. Zvezdy20588 \refitemCaldwell, D.A., Kolodziejczak, J.J., & Van Cleve, J.E.2010ApJL713L92 \refitemChristiansen, J.L., Jenkins, J.M., Caldwell, D.A., Burke, C.J., Tenenbaum, P., Seader, S., Thompson, S.E., Barclay, T.S., Clarke, B.D., Li, J., & 4 coauthors2012PASP1241279 \refitemWatson, C.L.2006SASS2547 \refitemClausen, J.V., Helt, B. E., & Olsen, E.H.2001A&A37498 \refitemConroy, K.E., Prsa, A., Stassun, K.G., Orosz, J.A., Fabrycky, D.C., Welsh, W.F.2014AJ14745 \refitemCoughlin, J.L., López-Morales, M., Harrison, T.E., Ule, N., Hoffman, D.I.2011AJ14178 \refitemCutri, R.M., Skrutskie, M.F., van Dyk, S., Beichman, C.A., Carpenter, J.M., Chester, T., Cambresy, L., Evans, T., Fowler, J., Gizis, J., et al.2003The IRSA 2MASS all sky point source catalog. NASA/IPAC Infrared Science Archive http://irsa.ipac.caltech.edu/applications/Gator \refitemD’Agostino, R.B., Stephens, M.A.1986”Tests for Normal Distribution” in Goodness-Of-Fit Techniques, Statistics: Textbooks and MonographsNew York: Dekkeredited by D’Agostino, R.B., Stephens, M.A. \refitemDal, H.A. & Evren, S.2010AJ140483 \refitemDal, H.A. & Evren, S.2011AJ14133 \refitemDawson, B., & Trapp, R.G.2004”Basic and Clinical Biostatistics”(New York: McGraw-Hill)61 \refitemDebosscher, J., Blomme, J., Aerts, C., De Ridder, J.2011A&A52989 \refitemEgret, D., Didelon, P., McLean, B.J., Russell, J.L., Turon, C.1992A&A258217 \refitemGershberg, R.E., & Shakhovskaya, N.I.1983Astrophys. Space Sci.95235 \refitemGershberg, R.E.1972Astrophys. Space Sci.1975 \refitemGershberg, R.E.2005”Solar-Type Activity in Main-Secauence Stars”Springer Berlin Heidelberg, New Yorkp.53, p.191, p.192, p.194, p.360 \refitemGreen, S.B., Salkind, N.J., & Akey, T.M.1999”Using SPSS for Windows: Analyzing and Understanding Data”(Upper Saddle River, NJ: Prentice Hall)50 \refitemHaisch, B., Strong, K.T., Rodono, M.1991ARA&A29275 \refitemHuber, D., Silva A.V., Matthews, J.M., Pinsonneault, M.H., Gaidos, E., García, R.A., Hekker, S., Mathur, S., Mosser, B., Torres, G., & d 12 coauthors2014ApJS2112 \refitemHudson, H.S., & Khan, J.I.1997in ASP Conf. Ser. 111”Magnetic Reconnection in the Solar Atmosphere”ed. R. D. Bentley & J. T. Mariska (San Francisco, CA: ASP)135 \refitemIshida, K., Ichimura, K., Shimizu, Y., & Mahasenaputra1991Ap&SS182227 \refitemJenkins, J.M., Chandrasekaran, H., McCauliff, S.D., et al.2010bProc. SPIE774077400 \refitemJenkins, J.M., Caldwell, D.A., Chandrasekaran, H., Twicken, J.D., Bryson, S.T., Quintana, E.V., Clarke, B.D., Li, J., Allen, C., Tenenbaum, P., & 20 coauthors2010aApJL713L87 \refitemKharchenko, N.V.2001KFNT17409 \refitemKoch, D.G., Borucki, W.J., Basri, G., et al.2010ApJL713L79 \refitemLucy, L.B.1967Z. Astrophys6589 \refitemMarcy, G.W. & Chen, G.H.1992ApJ390550 \refitemMatijevič, G., Prša, A., Orosz, J.A., et al.2012AJ143123 \refitemMirzoyan, L.V.1990IAUS1371 \refitemMotulsky, H.2007GraphPad Prism 5: Statistics Guide(San Diego, CA: GraphPad Software Inc. Press)94 \refitemPettersen, B. R.1991Mem. Soc. Astron. Ital.62217 \refitemPigatto, L.1990in IAU Symp. 137”Flare Stars in Star Clusters, Associations and the Solar Vicinity” (Dordrecht: Kluwer)117 \refitemPigulski, A., Pojmanski, G., Pilecki, B., Szczygiel, D.M.2009AcA5933 \refitemPinsonneault, M.H., An, D., Molenda-Zakowicz, J., Chaplin, W.J., Metcalfe, T.S., Bruntt, H.2012ApJS19930 \refitemPoveda, A., Allen, C., Herrera, M. A., Cordero, G., Lavalley, C.1996A&A30855 \refitemPrša, A., Batalha, N., Slawson, R.W., Doyle, L.R., Welsh, W.F., Orosz, J.A., Seager, S., Rucker, M., Mjaseth, K., Engle, S.G., & 5 coauthors2011AJ14183 \refitemPrša, A. & Harmanec, P.2010”PHOEBE Manual Adopted for PHOEBE 0.32”Villanova University, Villanova, PA 19085ABD \refitemPrša, A., Zwitter, T.2005ApJ628426 \refitemRibárik, G.2002Occasional Technical Notes from Konkoly ObservatoryNo. 12 available at http://www.konkoly.hu/staff/ribarik/SML/ \refitemRibárik, G., Oláh, K. & Strassmeier, K. G.2003AN324202 \refitemRodonó, M.1986NASSP492409 \refitemRucinski, S.M.1969AcA19245 \refitemSkumanich, A.1972ApJ171565 \refitemSlawson, R., Prša, A., Welsh, W.F., et al.2011AJ142160 \refitemSpanier, J., & Oldham, K.B.1987”An Atlas of Function”(Washington, DC: Hemisphere Publishing Corporation Press)233 \refitemStauffer, J. R.1991in Proc. NATO Advanced Research Workshop on ”Angular Momentum Evolution of Young Stars”ed. S. Catalano & J. R. Stauffer(Dordrecht: Kluwer)117 \refitemTokunaga A. T.2000”Allen’s Astrophysical Quantities”Fouth Editioned. A.N.Cox(Springer)p.143 \refitemTran, K., Levine, A., Rappaport, S., et al.2013ApJ77481 \refitemvan Hamme, W.1993AJ1062096 \refitemWilson, R.E.1990ApJ356613 \refitemWilson, R.E., Devinney, E.J.1971ApJ166605 \refitemYoldaş, E. & Dal, H.A.2016aPASA3316 \refitemYoldaş, E. & Dal, H.A.2016bRevMexIn Pres

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