KOI-256’s Magnetic Activity under the Influence of the White Dwarf

KOI-256’s Magnetic Activity under the Influence of the White Dwarf

1 Introduction

65 of the stars in our galaxy are red dwarf stars, and 75 of them show flare activity (Rodonó 1986). The vast majority of the red dwarfs found in the open star clusters and association show flare activity (Mirzoyan 1990; Pigatto 1990), while the number of UV Ceti stars in the clusters decrease from a young cluster to the older one (Skumanich 1972; Marcy & Chen 1992; Pettersen 1991; Stauffer 1991). The flare activity results in mass loss, which plays an important role in stellar evolution.

Although various studies have been carried out since the first flare was observed by R. C. Carrington and R. Hodgson on September 1, 1859 (Carrington 1859; Hodgson 1859), it is not fully understood what the flare and its process are. However, the flare activity of the dMe stars is modelled on the basis of the Solar Flare Event (Gershberg 2005; Benz & Güdel 2010). The studies, which have been continuing to understand the flare events of dMe stars have revealed that there are some differences between the flare energy levels of stars (Gershberg & Shakhovskaya 1983).

The level of highest energy releasing on the Sun are about - erg in the flare events (Gershberg 2005; Benz 2008). It seems that this level is about erg (Haisch et al. 1991), if RS CVn stars, the chromospheric active binaries, are considered. The observations lasting over decades show that the energy levels of flares occurring on dMe stars could have increased from erg to erg (Gershberg 2005). Considering the stars in the Pleiades cluster and Orion association, it is seen that these values have reached erg (Gershberg & Shakhovskaya 1983). There are significant differences between the energy level of flare stars from different spectral types. For example, it is well known that there are serious differences between the mass loss rates and the flare energy level, if the Sun is compared to a dMe star. Nevertheless, the flare events occurring on the dMe stars are tried to be explained with the Solar Flare processes. As a result, it is clear that the flares in the different stars should be well studied and the similarities and differences between them should be analyzed. Gershberg (2005) and Hudson & Khan (1997) have suggested that magnetic reconnection processes are the source of energy for flare events. In order to determine the important points in the flare process, it is necessary that the cause of the differences in the flare frequency and also the flare energy spectra should be determined.

Besides Gershberg & Shakhovskaya (1983), there are several studies about the flare energies in the literature such as Gershberg et al. (1972); Lacy et. al. (1976); Walker (1981); Pettersen et al. (1984); Mavridis & Avgoloupis (1986). However, according to Dal & Evren (2010, 2011), the results obtained in these studies are unsatisfactory for comparing the stars from different spectral types. For example Gershberg et al. (1972) derived the flare energy spectra for several dMe stars, such as AD Leo, EV Lac, UV Cet and YZ CMi, while Gershberg & Shakhovskaya (1983) derived the flare energy spectra for lots of stars from the galactic field to compare with the flare energy spectra of some stars from Pleiades and Orion association. They showed that these stars are located in different points in the distribution of energy. They correctly indicated that this distribution is caused due to different ages of the stars. On the other hand, Dal & Evren (2010, 2011) indicated that there is one more reason to cause this distribution. The second reason is including the luminosity parameter in calculations, of flare energies, which leads to incorrect results, as this caused the stratifying in the flare energy spectra. Indeed, the studies of Dal & Evren (2010, 2011) show that the flare equivalent durations in the logarithmic scale vary within a certain rule versus the flare total time, and it depends on the spectral type of the stars, on which the flares occur, when the relations between the flare parameters are examined. On the other hand, two different flare frequencies were defined by Ishida et al. (1991) for the flare activity. The frequency of indicates the number of flares per an hour, while the frequency of describes the flare-equivalent duration emitting per an hour. Leto et al. (1997) clearly show that the frequency of EV Lac’s flares vary over time.

On the other hand, for the first time in the literature, Kron (1952) discovered that UV Ceti-type stars also exhibited spot activity known as BY Dra Syndrome. Kron (1952) observed sinusoidal variations out-of-eclipses in the light curves of the YY Gem, which is a binary system, and Kunkel (1975) called this phenomenon BY Dra Syndrome and explained as a fact that these variations were caused by heterogeneous temperature distribution on the surface of the star. In the case of the Sun, Berdyugina & Järvinen (2005) found two stable active longitudes separated by 180 degrees from each other, and they indicated that these longitudes are exhibiting semi-rigid behavior. However, according to some authors, these longitudes are not the persistent active structures, which show variation in the time (Lopez 1961; Stanek 1972; Bogart 1982). The difference between the regular activity oscillations shown by these longitudes, called the Flip-Flop, is very important for the north-south asymmetry exhibited by the star’s magnetic topology. It is very important to calculate the angular velocities of these longitudes because these calculations light on the differential rotational velocities in the latitudes of the spots and spots groups.

In the case of binary or single stars, determining the parameters of stellar spot activity, such as spot latitude, radius and longitude, is a controversial phenomenon. In the literature, there are several methods to find out these parameters (Ribárik 2002; Ribárik et al. 2003; Walkowicz et al. 2013a; Jeffers & Keller 2009). For example, the SPOTMODEL program (Ribárik 2002; Ribárik et al. 2003) required two band observation and the inclination of the rotation axis to be able to model the distribution of the spots on the stellar surface. However, it must be noted that the system’s maximum brightness level ever observed has also a very important role to determine the spot radius depending on spot latitude. According to Walkowicz et al. (2013a); Jeffers & Keller (2009), this method does not work for the observations such as the data acquired in the Kepler Mission. Because the Kepler observations provide us monochromatic data, which have been detrended while combining different observation parts.

In this study, we examine the flare and spot activity exhibiting by KOI-256, and examine the parameters derived from the One Phase Exponential Association (hereafter OPEA) model, and also the spot migration considering the sinusoidal variation out-of-the flare. It is seen from the literature that KOI-256 is a system, which the primary component is a white dwarf, the secondary component is a main sequence star from the spectral type of M3. In addition, there are some clues about third body, which could be a planet. Borucki et al. (2011) indicated that KOI-256 is a planet candidate system. There are lots of studies such as Ritter & Kolb (2003); Borucki et al. (2011); Slawson et al. (2011); Walkowicz & Basri (2013b); Muirhead et al. (2013, 2014); Zacharias et al. (2004) in the literature. Several physical parameters of KOI-256 were computed in these studies, using some colour calibrations explained by these authors. As it can be seen from these parameters listed in Table 1, KOI-256 is very interesting system. Although one of the components is a with dwarf, Walkowicz & Basri (2013b) indicated that the system’s age is 0.01 Gyr. However, using the Equation 2.3 given by Gänsicke (1997) with the stellar parameters taken from Muirhead et al. (2013), we estimated the age of the system as 2 Gyr, considering the cooling of the white dwarf component. Indeed, Muirhead et al. (2013) laterly revealed that the system is a post-common envelope binary. In the paper, the stellar spot activity analyses are described in Section 2.1, while the flare models are described in Section 2.2. The orbital period variation analysis is explained in Section 2.3. The results obtained from the analyses are summarised and discussed in Section 3.

2 Data and Analyses

The Kepler Mission project, which was launched to explore the exoplanets, has observed more than 150.000 sources (Borucki et al. 2010; Koch et al. 2010; Caldwell et al. 2010). These observations are one of the highest sensitivity photometric observations ever achieved (Jenkins et al. 2010a, b). With this highest sensitivity of observation, a large number of new eclipsing binaries and lots of new variable stars have been discovered besides the exoplanets (Slawson et al. 2011; Matijevič et al. 2012). Some of these variable stars are single, and some of them are binary stars, which exhibit both the stellar spot activity and flare activity (Balaji et al. 2015). In this study, observational data of KOI-256, which is one of these binary systems, was taken from Kepler Data Base (Slawson et al. 2011; Matijevič et al. 2012). KOI-256’s short cadence data obtained in the Kepler Mission covered the time range from BJD 24 55372.460219 to BJD 24 55552.55836 and from BJD 24 56419.80351 to BJD 24 56424.01160, while the long cadence data of the system covered time ranges BJD 24 54964.51238-55206.21898, BJD 24 55276.51124-55552.54849, BJD 24 55641.51645-55931.30552, BJD 24 56015.77828-56304.13695, BJD 24 56392.24699-56424.00173. All the available data presented in both Long and Short Cadence formats are shown in Figure 1. The short cadence data were used in the analyses of the flares, while the long cadence data were used for the analyses of sinusoidal variation. The detrended data was used among the public data provided in the Kepler Data Base. The data sets were created in appropriate formats, which were edited in the analysis processes for the flare activity, the stellar spot activity and the orbital period variation ().

The whole of KOI-256’s analysed data taken from the Kepler Database is shown in the upper and middle panels of Figure 1. The light curve is plotted versus the Barycentric Julian Date in the upper panel, while it is plotted versus phase in the middle panel of the figure. In the lower panel, the light curve is plotted versus phase, expanding the y-axis to be easily seen the sinusoidal variations out-of-the dominant flare activity.

2.1 Stellar Spot Activity

Examining the out-of-eclipses light variations, it is seen that the system exhibits also sinusoidal variations. Considering the surface temperatures of the components of the system, it is understood that the variations is caused by the rotational modulation of the cool stellar spots. It is seen that both minima times and amplitudes of the light curves are varying once in a few cycles, when the consecutive cycles depend on the orbital period are examined in the light curves, in which both the flares and eclipses are removed. This situation indicates that the active regions on the components of the system evolved rapidly. Because of this, it is not possible to model the entire light curve in a single analysis, so the data of sinusoidal variation are separated into several sets. When dividing into data sets, consecutive cycles in which some characters of the light curve such as a light curve asymmetry, a spot minima phase, and the minima and maxima level were the same were collected in a single set. In this format, 138 sub-sets are obtained, thus, each sub-set is modelled separately.

To be able to model the sinusoidal variations, the pre-whitened light curves were obtained. In this step, we firstly removed data parts, in which all instant light increase due to the flares are seen, from whole data. In addition, the data parts, in which the primary minima are seen due to eclipses, were also removed from whole data.

The pre-whitened light curves are modelled with the SPOTMODEL program (Ribárik 2002; Ribárik et al. 2003) to find out the spot distribution parameters, such as the spot radius, latitude and especially longitudinal distribution, on the stars. To model the spots, the SPOTMODEL program requires two band observations or a temperature factor () for the stellar spot. However, the data analysed in this study consist of monochromatic observations that are presented publicly in the Kepler Database. In this point, considering both the study of Botsula (1978), which first revealed the spot temperature factor for the stellar activity, and also the light curve analysis obtained from analogue systems (Clausen et al. 2001; Thomas & Weiss 2008), it was assumed that the secondary component exhibits magnetic activity. The inclination of rotation axis is taken 89.1 as it was given by Muirhead et al. (2013). Then, taking the different values from to for the spot temperature factor in agreement with the values found by these studies for analogue systems, the first few sets were tried to be modelled. As a result, it was seen that the best solution can be obtained by taking the spot temperature factor of for both spots. For this reason, the spot temperature factors were taken as for both spots in the all sets. Taking the spot temperature factor as constant value in the models for each set, the longitudinal, latitudinal distributions and radius variations of the spot area on the active component were determined.

In the analysis, the parameters such as the longitudes (), latitudes (), and radii of the spots () parameters were taken as free parameters. The parameters obtained from the models for each set are listed in Table 2, while six examples for the derived models are shown in Figure 2. In the left panel of the figure, the observations and models are plotted versus Heliocentric Julian Day as a time, while they were plotted versus phase computed using by orbital period. As seen from the figure, the synthetic models absolutely fit the observations. The variations of latitude () and radius () for both spots are shown in Figures 3. In addition, the most important parameter of the models, longitude (), is plotted versus time in Figure 4. The longitudinal variations were fitted by a linear function for both spots. Using these linear fits, the migration periods were computed. The migration period was found to be 3.95 year for first spotted area, and 8.37 year for second area.

To test whether the findings about longitudinal variations are close to the real nature of the stellar surface, it was tested by another method. Using the Fourier Transform, the minima times of sinusoidal variations, where the amplitude is larger, were computed. Then, the orbital phases called as were computed for these sinusoidal minima times. In figure 5, the variation of are plotted versus time. This variation was fitted by a linear function similar to the longitudinal variations. In the same process, the migration period was computed from the phase shift of the using this linear function. In a result, the period of the spotted area migration was found to be 9.126 year. As it is expected, this value is in agreement with one of the migration periods found from the longitudinal variations.

2.2 Flare Parameters and Models

In order to understand the nature of the flare activity and to find out the flare behaviour of the system, we tried to determine the flares occurring on the active component. For the reason, using the synthetic light curves, all the other variations apart from the flares were removed from the entire light curve. Since the system is an eclipsing binary, all minima light variations between the phases of 0.04 around the minima points, where two components are external tangent to each other, were removed from the entire light curve. However, the separated observations due to the technical reasons were also removed from the data.

In order to specify the flare parameters, such as start and end points of a flare and its energy, it should be defined the quiet level of the light curve. However, it was seen some sinusoidal variations due to the rotational modulation exhibited by one of the components in addition to the flares. For this reason, the synthetic light curves were derived for the light variations out-of-the flares using the Fourier transform given by Equation (1), and all the data were modelled with these synthetic light curves for the all phases.

(1)

here is the zero point, is the phase, while and are the amplitude parameters (Scargle 1982). The synthetic light curves derived by Equation (1) were assumed as the quiescent level for each flare. Two examples for the flares detected from the observations and their quiescent levels are shown in Figure 6. After modelling light variations out of both the eclipses and flares, the flare parameters are calculated, as it was previously described by Dal (2012) in detail.

The flare rise () and decay () times, the flare amplitudes and the equivalent durations () were calculated after the start and end points of a flare were determined. These flare parameters calculated for each flare detected from entire data sets are listed in Table 3. In this table, the times of flare maxima in the first column, the flare equivalent durations (s), the flare rise times (s), the flare decay times (s), the flare total times (s) and the flare amplitudes in the last column were listed, respectively.

225 flares in the total were detected from the available observational data of the system taken from the Kepler Database. The equivalent duration values for each flare are calculated by Equation (2) given by Gershberg et al. (1972).

(2)

where is the flare equivalent duration in seconds, is flux at the moment of a flare, and is the flux of the system in the quiescent level, which were modelled by the Fourier method for the parts out-of-eclipses. Considering the reason explained by Dal & Evren (2010, 2011), which is mentioned in Section 1, the flare energies were not used in this study. In order to derive the models, the equivalent duration parameter was used instead of the flare energy. Using the orbital period of the system, the phases for each flare was calculated, and the phase distribution of these 225 flares is shown in Figure 7. In the figure, it is plotted the flare total number computed for each phase range of 0.10.

When the relationship between some flare parameters is examined, it can be seen that the flare equivalent duration varies versus the flare total time within a certain rule. In fact, as it had been demonstrated by Dal & Evren (2010, 2011), the regression calculations processed with the SPSS V17.0 (Green et al. 1999) and GraphPad Prism V5.02 (Dawson & Trapp 2004) programs in this study show that the One-Phase Exponential Association (hereafter OPEA) is the best function to model the distribution of the flare equivalent durations in the logarithmic scale versus the flare total time. The OPEA function is a special function that has a term ”” and is represented by Equation (3) (Motulsky 2007; Spanier & Oldham 1987):

(3)

where the parameter is equivalent duration in the logarithmic scale, is the total time of a flare, and is the theoretical equivalent duration in the logarithmic scale for the minimum flare total time, as it had been previously defined by Dal & Evren (2010). In other words, the parameter defines the minimum equivalent duration that someone can obtain for a flare occurring on the active component. Therefore, value depends on the brightness of the observed target and on the sensitivity of the used optical system. The value defines the upper limit of the equivalent durations for the flares observed on a particular star. According to Dal & Evren (2011), this parameter is defined as the saturation level for the flare activity in the observed wavelength range for the observed target.

Using the least-squares method, the distribution of the equivalent duration versus the flare total time was modelled by the OPEA function for the flares. The obtained model is shown in Figure 8 with a 95 confidence interval. The computed parameters from the OPEA model are listed in Table 4. The span value listed in the table is the difference between Plateau and values. The value is half of the first value, which the flare equivalent durations in the logarithmic scale reach the maximum level defined as the value. In other words, it is half value of the first total time, where the highest flare energy is seen for the flare.

In the Kepler Mission database, KOI-256’s short cadence data are available for the time range from BJD 24 55372.460219 to BJD 24 55552.55836 and from BJD 24 56419.80351 to BJD 24 56424.01160. In total, the KOI-256 has been observed in short cadence format during 184.30624 days (4423.34976 hours). From these data, 225 flares were obtained and their total equivalent durations were computed of 8169.834 seconds. In the literature, two different flare frequencies were defined by Gershberg et al. (1972). These frequencies are given by Equation (4, 5):

(4)
(5)

where is the total number of the obtained flare, while defines the total observing time of the star. is the sum of the equivalent durations of all detected flares. According to these definitions, the frequency was found to be , while the frequency was found to be .

Gershberg et al. (1972) described the flare frequency distribution separately calculated for the different energy limits of the flares detected from a star, which defines the flare energy character for that star. However, using the flare equivalent duration instead of the flare energy parameter in this study, since the flare energy parameter depends on the quiet intensity level of the star in the observing band, the flare frequencies were calculated for different flare equivalent duration limits for the 225 flares. The obtained cumulative flare frequency distribution is shown in Figure 10.

2.3 Orbital Period Variation

The minima times were computed from the KOI-256’s short cadence data from the first quarter to the Quarter 17, which were taken from the publicly available Kepler Database, without any corrections. The minima times were computed with a script depending on the method described by Kwee & van Woerden (1956). In this method, taking symmetrically increasing and decreasing parts of minima, the minima times were computed by fitting this parts with polynomial function. Before computing the minima times, the flares as the activity exhibited by the system were removed from the light curves. In the second step, residuals were determined for the obtained minima times. However, some of them include very large errors. It is seen that the flare activity occurred during these minima, when the light curves were examined for these minima times with large errors. Thus, these minima times were removed from the data. As a result, 125 minima times were determined in the analyses. The obtained residuals were adjusted by the linear correction given in Equation (6):

(6)

The computed minima times and the residuals obtained by applying a linear correction are listed in Table 5. In the table, the minima times, cycles, the minima type, and residuals are listed, respectively. An interesting variation is seen in the variation of obtained residuals versus time in Figure 11.

Firstly, checking the minima types given in the third column of Table 5, it was practically examined whether there is a marker about the existence of secondary minimum, which is the subject of discussion in the literature. Secondly, it was examined whether there was any separation in the residuals plotted in Figure 11. If there was any secondary minima, it would be expected a separation between the primary and secondary minima time residuals due to stellar spot activity, as it was demonstrated by Tran et al. (2013) and Balaji et al. (2015) for the first time. However, as it is seen from Figure 11, there is no decomposition in the minima time residuals as the primary and secondary minima.

3 Results and Discussion

The analysis of KOI-256’s data taken from the Kepler Database (Slawson et al. 2011; Matijevič et al. 2012) indicates that the system has high chromospheric activity. However, it is necessary to compare the activity level between similar stars in order to reach a more definite result about the activity nature. In the literature, KOI-256 is an eclipsing binary system, with a white dwarf as a primary component and a main sequence star from M3 spectral type as a secondary component (Muirhead et al. 2014). The temperatures of the components were determined as 7100 K and 3450 K in the analyses of the spectral data together with the photometrical data of the system (Muirhead et al. 2014).

The eclipsing binary system KOI-256 was observed in the short cadence format from HJD 24 54964.51238 to HJD 24 56424.011602 in total of 184.30624 days (4423.34976 hours). Within this study, 225 flares were determined and the parameters of each flare were calculated. Using the frequency descriptions defined by Gershberg et al. (1972), the flare frequencies for KOI-256 were calculated as 0.05087 and 0.00051, respectively. The flare frequencies of KOI-256 were compared with the flare frequencies found from the young main sequence dMe dwarfs, known as UV Ceti-type, exhibiting flare activity. The flare frequencies of KIC 9761199 were found to be 0.01351 and 0.00006 (Yoldaş & Dal 2016), while they were found to be 0.01735 and 0.00001 for KIC 9641031 (Yoldaş & Dal 2017). KOI-256, when compared to these two systems, seems to have the highest flare frequency values among similar systems. On the other hand, the frequencies were computed to be 0.088 for EQ Peg and 0.086 in the case of AD Leo, while the frequencies were determined as 1.331 for AD Leo, a UV Ceti type single star, and 1.056 for EV Lac (Dal & Evren 2011). Compared to these single stars of the UV Ceti type, the flare frequencies of KOI-256 are found to be quite low. However, it is known in the literature that the flare frequency of EV Lac varies with time (Leto et al. 1997). As it is seen in Figure 9, the monthly frequencies vary with time like EV Lac, when the flare frequencies are computed for each month in the case of KOI-256.

The value of the OPEA model depending on the flare equivalent duration distribution in the logarithmic scale versus the flare total time is found to be 2.31210.0964 s over detected 225 flares. This value is 3.014 s for EV Lac (), 2.935 s for EQ Peg () and 2.637 s for V1005 Ori () (Dal & Evren 2011). The value was found to be 1.2320.069 s for KIC 9641031 () (Yoldaş & Dal 2016) and 1.9510.069 for KIC 9761199 () (Yoldaş & Dal 2017). If it is considered that one of the components is a white dwarf in the case of KOI-256, it is clear in this study that the chromospherical active component is the main sequence star from the spectral type of M3. The B-V color index for this component is given as () in the literature (Walkowicz & Basri 2013b). Therefore, the flares with high energy exhibited by KOI-256 are strong enough to be compared with the flares exhibited by the single UV Ceti type stars. Dal & Evren (2011). found that the value is constant for a star, but varies from one star to another depending on their color indexes. The authors have defined this value as the saturation level of flares on a star, which is maximum energy limit a flare can reach.

On the other hand, the parameter of the OPEA model was found to be 2233.6 s for KOI-256. This value is almost 10 times higher than the value obtained on single flare stars. This value is 433.10 s for DO Cep (), 334.30 s for EQ Peg and 226.30 s for V1005 Ori (Dal & Evren 2011). In the same way, the parameter is 2291.7 s for KIC 9641031, while it is 1014 s for KIC 9761199, which are binary systems including a dMe type component (Yoldaş & Dal 2016, 2017). As a result, when the flare total time for the stars such as EQ Peg, V1005 Ori and DO Cep reaches a few minutes, the their flare energies can easily reach the Plateau level. However, in the case of KOI-256, a flare event must last at least 37 minutes, about a few tens of minutes, in order to reach the maximum flare energy described as the Plateau level for this system. Similar durations are also observed in the case of both flare rise and total times. The maximum flare rise time () observed in the single UV Ceti type stars is about 2042 s for V1005 Ori, 1967 s for CR Dra (Dal & Evren 2011), while the longest flare rise time obtained in KOI-256 is 3942.749 s. The longest flare rise time obtained flares on KIC 9641031 is 5178.87 s (Yoldaş & Dal 2016), while it is 1118.099 s for KIC 9761199 (Yoldaş & Dal 2017). Similarly, the maximum flare total time for the flares obtained on the V1005 Ori is 5236 s, while it is 4955 s for CR Dra flares (Dal & Evren 2011). However, the longest flare obtained on KOI-256 lasts along 22185.361 s.

Considering the stellar spot activity together with the flare activity detected from KOI-256, it is obvious that the system exhibits a high level of chromospheric activity. Using very sensitive observations provided by Kepler Mission (Jenkins et al. 2010a, b), some variations with small amplitudes, which are impossible to observe with ground-based classic telescopes, can be easily detected. When the system light variations out-of-eclipses without any flares is carefully examined, it is seen that the shape of eliminated light curve can vary per two or three cycles at most. This variation is caused due to both rapid evolutions and migrations of the cool stellar spots on the surface of the M3 star. It needs about 4-5 days for the evolution of the stellar spots on the active component in the case of KOI-256, while it takes a few weeks for the cool spot groups on the solar surface (Gershberg 2005). In this study, the stellar spot distribution on the surface of the active component was modelled by the SPOTMODEL program (Ribárik 2002; Ribárik et al. 2003), though there are some deficiency in the method of this program. As it was mentioned in Section 1, the method using in the SPOTMODEL program do consider neither the spot evolution nor spot migration on the surface during long time. However, separating the data into suitable sub-sets by considering the light curve shape change point, we solved out this problem. The whole data were separated into 138 sub-sets. The cycle shapes of sinusoidal light variation are different from one sub-set data to the next, while the shapes of the cycles are the same among themselves in each sub-set data. Thus, each sub-set data was individually modelled. On the other hand, maximum level of the obtained brightness is not suitable for modelling by the SPOTMODEL program due to detrended data. However, the spot longitude parameters is calculated in this study, because it is an important parameter to reveal the spot migration instead of the spot latitude or radius.

The result parameters of the modelling spot variation are plotted in Figures 2, 3 and 4. As it is seen from Figure 2, the models of 138 sub-sets indicate that two cool spots (or spotted areas) are enough to absolutely fit the observed light variation out-of-eclipses. Although both latitude and radius parameters of the spots do not externalize the realistic nature of the spots on the stellar surface as discussed earlier, their variations are also plotted in Figure 3 to note as an initial approach. The main goal of these models is longitudinal variation and it is shown in Figure 4. Observations of the cool spot groups on solar surface reveal the existence of two permanently active longitudes separated by 180 degree from each other. These active longitudes known as the Carrington Coordinates are constant structure according to some authors, while some authors indicate that the rotation speeds of these active longitudes are not constant, but slowly change (Lopez 1961; Stanek 1972; Bogart 1982). Similarly, in this study, it was found that there are two stellar cool spots on the active component of KOI-256, which show the migration behaviour with different speeds. Modelling the migration movements shown in Figure 4 by the linear fits, it is estimated that the migration of the first stellar spot is 3.95 years and the migration period of the second one is 8.37 years.

To test whether these results are real, it was tested by another method. Computing parameter, which is the phases of the observed sinusoidal variation out-of-eclipses, the migration behaviour of the dominant spotted area was tried to find out. Indeed, as it is seen from Figure 5, the values obtained for all cycles were plotted versus Heliocentric Julian Day, and then, its trend was fitted by a linear function. The migration period of dominant spotted area is found to be 9.13 year. In addition, the most impressive finding was came from the residual according to the linear fit. The residuals show the same trend with the residuals of the longitudinal variation obtained from the SPOTMODEL analyses. This situation absolutely reveals that the main goal of the SPOTMODEL analyses have been obtained, and it does figure out the migration of active regions close to its real nature.

However, as can be seen in Figure 4, some sinusoidal variations still remain, after a linear correction is applied to the migration movement. All of these migration behaviours are an indicator of the strong differential rotation on stellar surface. However, a high-resolution spectroscopic observation is needed to confirm this case. In the literature, the system’s age is given as 0.01 Gyr by Walkowicz & Basri (2013b). However, as it is described in Section 1, using the Equation 2.3 given by Gänsicke (1997) with the stellar parameters taken from Muirhead et al. (2013),the age of the system is estimated as 2 Gyr in this study. Considering the law expressed by Skumanich (1972), this age is a bit old for rapid rotation, considering high level chromospheric activity. However, KOI-256 is a binary system. In this case, tidal effects can let the components to rotate rapidly, which lets the system has a significant influence on both the flare and spots activity behaviour.

Muirhead et al. (2014) listed the semi-major axis length of the system as , giving the radii of components as 0.54 and 0.01 . This situation indicates that the components are very close to each other, which can cause rapid activity variations due to some tidal effects on each other. On the other hand, the most interesting result in term of stellar spot and flare activity exhibited by the system is that the stellar spot areas exhibit a rapid variation in location due to the migration movement as shown in Figure 5, while it is seen interestingly that the flares are in aim to occur frequently between the phases of 0.10 - 0.20 and also 0.60 - 0.70, when the averaged phases are calculated in each 0.10 phase range for 225 flares. In the case of both spot and flare activities, the phases were computed with using the orbital period of binary system with a white dwarf and a main sequence M3 components. This case is an unexpected situation, because the locations of flares are quite stable compared to the behaviour of the spot activity. Although flare activity is seen in all phases, it is observed that the flare activity most frequently occurs in these phase intervals. The location of the white dwarf is as close as 4.51 to the active component, which indicates that the components are interacting magnetically. A possible explanation is that the quickly evolving stellar spot areas under both the differential ration and tidal effects exhibit rapid migration movements, while the flares are frequently occurring in some definite longitudes on the active component surface due to the magnetic interaction of the white dwarf and active components. This situation leads KOI-256 to take an important position among its analogues for especially the future spectral studies.

125 minima times were determined from the all available data. It is seen that the light curve has only the primary minimum, when entire the light curves are examined. According to Tran et al. (2013) and Balaji et al. (2015), the residuals of the primary and secondary minima show some sinusoidal variation versus time, but in the opposed phase, if one of the components in an eclipsing binary system is a magnetically active star. However, the residuals obtained from the minima detected from the light curves of KOI-256 do not exhibit any separation. This situation also confirms that all the minima detected from the light curves are primary ones.

As it is seen from Figure 11, considering all 125 minima times, there is not any clear variation in the residuals distribution versus time obtained by improving linear correction. As shown in Figure 11, the residuals scatter in a range of about 50-60 sec. Whereas according to Szabó et al. (2013) in the literature, KOI-256 shows an variation with an amplitude of 0.4464 minute and a period of 41.755397 day. However, the results obtained in this study do not confirm the variation found by Szabó et al. (2013). The problem, which cause the different results can be due to the method used to compute the minima times or due to the different data formats used in these studies. In this study, the minima times were computed from the short cadence data, while the minima times were calculated from the long cadence data by Szabó et al. (2013). In addition, although the flares as the activity exhibited by the system were removed from the light curves before computing the minima times, the sinusoidal variation due to the stellar spot activity was not cleared from the data in order to test whether the primary and secondary minima were separated, as described by Tran et al. (2013) and Balaji et al. (2015). Although there is no any clue for the secondary minima, the situation can cause a scattering in a wide range for the residuals variation obtained in this study.

Acknowledgments

We wish to thank the Turkish Scientific and Technical Research Council for supporting this work through grant No. 116F213. We also thank the referee for useful comments that have contributed to the improvement of the paper.

Figure 1: All of the Long Cadence and Short Cadence data taken from the Kepler Database for the KOI-256 are shown. The light variation was plotted in the plane of intensity taken from database as detrended form versus the phase computed by using orbital period.
Figure 2: The observed light curve samples and their synthetic model fits derived by the SPOTMODEL analyses. In the figure, the filled circles represent the observations as intensity in detrended form, while the lines (red) represent the synthetic fits. In the left panels, the data and synthetic model are plotted versus time as Heliocentric Julian Day, while they are plotted versus phase computed using epoch and orbital period given in Equation (6) in the right panels.
Figure 3: The variations of both spot latitude and spot radius parameters obtained with the SPOTMODEL program versus time. The filled blue circles represent the first spot and the filled red circles represent the second spot.
Figure 4: The variations of the first spot longitude as degree (left) and the second spot (right) are shown in the upper, while the residuals after the linear correction to the longitude variations are shown in the lower panel.
Figure 5: diagram for the observed minima times of sinusoidal variation versus time in each data subset shown with term and its linear fit are shown in the upper panel. The filled circles represent the variation, while the line (red) show the linear fit. In the bottom panel, the residuals of is shown with its parabolic fit, which is plotted to show the trends clearly for the readers.
Figure 6: Two flare examples detected from the system. The light variation was plotted in the plane of intensity taken from database as detrended form versus time. The filled black circles represent the observations, while the red lines represent the quiescent level modelled by the Fourier method.
Figure 7: The distribution of flare total number in phase range of 0.10 is plotted versus the phase computed by using orbital period for 225 flares.
Figure 8: The distribution of the equivalent duration in the logarithmic scale () are plotted versus the flare total time, which were sum of flare rise and decay times. The OPEA model obtained over 225 flare determined in the analyses. The fill circles represent the observed flares, while the red line represents the OPEA model.
Figure 9: The cumulative flare frequencies () and model computed for 225 flares obtained from KOI-256. In the upper panel, it is seen the variation of the flare equivalent durations in logarithmic scale () versus the cumulative flare frequency, which is called the flare energy spectrum (Gershberg 2005), while the residuals obtained from the model are shown in the middle and bottom panels.
Figure 10: The monthly variation of the flare frequency of , which indicates total flare number per each hour, for KOI-256 is shown for the entire observing season.
Figure 11: The variations of minima time’s residuals obtained by applying a linear correction to minima times are shown versus time. All the residuals are shown with filled circles, while the red line represents a linear fit.
() 1.3786548
() 0.0250
() 89.3
() 1.42
() 0.540
() 0.01345
() 3450
() 7100
() 0.51
() 0.592
- 0.31
() 155
J, H, K () 12.701 - 12.000 - 11.782
Spectral Type - M3 V + WD

- Muirhead et al. (2013)
- Slawson et al. (2011)
- Walkowicz & Basri (2013b)
- Muirhead et al. (2014)
- Zacharias et al. (2004)

Table 1: Physical parameters of KOI-256 taken from the literature.
JD (Latitude) (Latitude) (Radius) (Radius) (Longitude) (Longitude)
54966.749927 63.277 3.430 79.015 0.252 15.917 1.808 31.179 0.410 77.848 1.494 378.418 2.961
54971.061541 57.628 4.704 78.572 0.234 14.244 1.643 30.481 0.313 79.038 1.083 342.094 2.181
54975.230111 64.687 2.303 77.990 0.323 17.743 1.498 29.433 0.492 75.469 1.578 336.431 3.112
54979.960614 64.074 2.669 78.130 0.250 16.693 1.533 30.294 0.401 73.857 1.447 336.859 2.638
54984.742199 56.901 5.588 79.318 0.190 13.122 1.723 31.410 0.259 80.089 1.018 343.844 1.955
54988.992489 56.368 4.173 78.341 0.173 13.458 1.272 31.008 0.204 82.514 0.806 340.931 1.367
54993.058867 62.702 3.014 78.436 0.211 15.332 1.407 30.875 0.289 78.478 1.145 338.160 1.944
54996.491784 56.142 6.666 78.138 0.259 13.270 2.007 30.898 0.325 77.494 1.324 337.974 2.173
55004.481471 65.054 3.030 79.779 0.218 16.620 1.904 32.811 0.426 72.950 1.555 338.632 3.309
55007.985892 64.527 2.464 78.929 0.234 17.507 1.559 31.759 0.409 69.841 1.448 332.064 2.888
55011.061195 61.244 5.076 78.986 0.349 16.060 2.370 32.337 0.489 72.068 1.765 331.181 3.486
55013.492827 59.668 4.704 77.560 0.759 16.324 1.498 32.693 0.289 73.878 3.926 331.057 2.571
55017.640899 66.308 2.303 77.999 0.759 17.122 1.533 31.309 0.325 69.324 9.060 332.951 3.291
55019.949921 65.718 2.988 80.074 0.234 17.455 2.071 33.626 0.482 66.448 1.757 330.176 3.845
55022.422411 61.803 6.938 79.715 0.316 15.211 3.222 33.209 0.581 67.316 2.231 335.756 4.538
55024.496438 64.030 4.381 79.073 0.383 16.711 2.566 32.067 0.613 67.204 2.127 328.939 4.392
55027.520633 62.317 3.422 78.843 0.207 15.440 1.623 31.722 0.325 68.190 1.271 331.344 2.327
55032.475806 74.406 2.185 76.669 0.207 26.567 3.707 26.866 3.598 47.323 1.324 301.919 2.630
55036.991646 64.178 3.007 78.693 0.272 16.326 1.647 32.266 0.363 68.294 1.406 324.269 2.377
55036.991646 64.124 3.020 78.697 0.271 16.296 1.645 32.273 0.361 68.314 1.399 324.309 2.366
55044.051454 64.961 2.458 78.258 0.285 17.635 1.564 32.375 0.403 65.672 1.476 321.194 2.559
55047.525157 61.982 3.970 78.775 0.290 15.990 1.888 32.788 0.375 68.351 1.422 323.413 2.575
55050.304115 61.227 4.059 79.092 0.294 15.909 1.874 32.386 0.386 64.700 1.411 320.649 2.736
55053.767589 62.461 2.430 78.973 0.210 16.465 1.245 32.507 0.276 66.362 0.981 321.805 1.907
55057.874710 59.698 3.869 79.232 0.199 15.005 1.542 33.013 0.265 66.069 1.045 324.048 1.938
55061.634456 63.015 2.974 78.326 0.269 17.080 1.633 32.120 0.393 62.205 1.452 321.125 2.605
55065.230727 35.995 2.974 77.523 0.798 9.311 1.633 30.464 0.826 61.544 3.690 328.098 4.977
55067.182111 75.691 1.294 69.690 5.531 31.217 1.982 19.782 5.433 24.124 9.473 279.457 2.929
55070.277756 63.922 3.508 78.844 0.169 15.607 1.909 33.771 0.352 56.672 1.575 325.965 2.571
55074.425711 66.321 3.445 78.750 0.187 16.152 2.283 33.518 0.458 53.919 2.210 324.187 3.291
55077.848279 67.671 4.066 77.458 0.357 17.269 3.311 32.052 0.865 50.804 1.324 321.033 5.382
55083.824984 68.052 2.600 77.793 0.203 17.142 2.122 33.066 0.505 53.435 2.540 322.217 3.232
55084.734264 66.361 5.317 77.680 0.478 17.179 3.827 32.598 0.952 52.764 1.324 318.453 2.377
55087.278192 71.806 3.214 76.954 0.719 21.685 4.859 31.254 2.171 46.173 1.324 313.208 2.366
55094.102831 61.631 6.295 75.903 0.504 15.308 2.932 31.042 0.669 55.341 2.659 320.091 3.583
55096.421985 63.947 4.856 76.563 0.390 15.843 2.604 32.215 0.557 57.951 2.617 318.779 3.213
55100.978555 57.876 5.887 77.649 0.170 12.960 1.872 34.039 0.236 62.181 1.227 324.958 1.532
Table 2: The Spot parameters obtained with SPOTMODEL.
JD (Latitude) (Latitude) (Radius) (Radius) (Longitude) (Longitude)
55105.453390 58.804 5.542 76.923 0.338 15.505 2.264 32.774 0.450 53.787 1.688 314.621 2.377
55108.089248 73.020 2.975 74.902 0.241 27.145 5.195 27.606 4.971 32.067 1.324 291.603 2.366
55111.430042 58.736 3.466 75.829 0.241 15.596 1.416 31.835 0.305 51.917 1.171 313.049 1.653
55116.763048 63.599 2.688 76.973 0.264 17.157 1.592 32.509 0.396 52.047 1.535 312.718 2.365
55120.236651 67.100 2.534 77.592 0.382 19.611 2.222 32.561 0.719 47.943 2.692 308.686 4.336
55122.484275 65.708 2.534 78.011 0.594 17.748 4.261 33.933 1.028 54.446 4.318 314.813 2.782
55125.610515 68.529 2.427 78.667 0.360 20.282 2.677 33.143 0.921 47.553 3.319 312.377 2.022
55128.225931 67.447 3.104 78.347 0.393 19.391 2.933 32.574 0.945 48.032 3.430 313.894 2.197
55130.514420 61.196 6.095 75.843 0.615 16.127 2.980 30.903 0.782 59.660 2.665 322.497 4.008
55132.710959 67.228 2.467 78.319 0.351 18.628 2.028 32.079 0.614 49.971 2.332 309.434 3.950
55140.403958 68.362 1.572 78.515 0.253 19.713 1.621 31.138 0.598 42.595 2.093 307.516 3.901
55150.589779 68.603 2.413 79.115 0.203 18.488 2.404 31.868 0.727 42.700 2.881 314.182 2.219
55158.415607 67.166 3.511 77.979 0.500 19.066 3.177 30.642 1.132 41.285 3.827 308.543 2.145
55161.858566 73.557 1.875 74.930 0.500 28.440 2.855 24.497 0.289 22.522 2.332 273.844 2.366
55165.352611 70.567 3.037 78.492 0.562 22.987 4.487 30.529 0.325 32.892 2.093 295.508 1.653
55169.888745 68.733 3.314 78.484 0.562 20.493 3.744 31.984 1.419 36.448 1.324 301.355 2.571
55173.862975 68.021 4.607 78.484 0.715 19.730 4.602 32.198 1.587 35.569 1.324 299.308 3.291
55176.887073 65.779 3.268 77.793 0.463 18.602 2.495 32.093 0.767 38.022 2.685 298.566 4.758
55180.493518 63.531 4.174 77.176 0.476 17.253 2.451 31.224 0.674 37.329 2.391 297.495 3.965
55187.440787 68.403 3.204 78.177 0.544 19.051 2.973 32.592 0.932 37.112 1.147 295.397 2.693
55191.159632 69.524 3.215 78.457 0.610 20.404 3.621 32.022 1.342 29.811 1.449 290.715 2.285
55194.786534 65.594 4.560 78.938 0.273 15.563 2.677 33.146 0.509 37.822 2.447 302.929 3.696
55198.556476 67.491 3.688 79.212 0.268 16.620 2.751 32.992 0.616 36.101 2.754 303.617 2.496
55203.368529 66.201 3.404 79.536 0.149 15.008 1.965 33.587 0.326 38.443 1.768 305.854 2.577
55278.564869 69.191 2.174 77.595 0.736 21.329 2.214 30.962 0.977 31.706 3.075 279.055 2.056
55282.110192 61.455 3.692 78.379 0.358 16.646 1.801 32.119 0.421 38.373 1.415 289.975 2.653
55286.115289 68.067 2.204 78.100 0.702 21.246 2.111 31.863 0.875 33.457 2.514 278.883 2.760
55290.477987 67.725 2.826 77.905 0.809 21.153 2.580 32.151 1.016 31.765 3.020 277.276 2.495
55294.299182 66.081 2.682 77.905 0.629 20.212 2.098 32.634 0.728 29.837 2.170 274.620 4.009
55297.916038 64.709 3.003 78.589 0.350 17.892 1.877 33.916 0.445 34.050 1.583 283.230 2.813
55301.829192 59.677 3.514 78.421 0.271 16.143 1.513 33.575 0.300 33.796 1.050 282.969 1.885
55305.967125 63.953 2.074 78.028 0.303 18.464 1.283 33.333 0.344 30.741 1.147 277.405 1.998
55311.729577 64.647 2.103 77.422 0.488 20.267 1.502 32.553 0.528 29.781 1.449 272.577 2.740
55314.723194 65.233 1.989 77.395 0.588 21.063 1.526 31.947 0.610 28.626 1.609 268.837 3.056
55318.248101 64.094 2.395 78.449 0.471 19.721 1.567 32.508 0.499 29.410 1.307 270.048 2.801
55321.507363 67.747 2.158 77.049 0.830 22.326 1.986 31.277 0.930 23.642 2.585 263.668 2.343
55324.327288 63.231 1.828 77.392 0.361 19.259 1.119 32.241 0.360 30.961 1.027 270.101 1.825
55327.893061 66.778 2.175 78.474 0.570 20.473 1.753 32.267 0.632 28.538 1.718 269.419 3.508
Table 2: Continued.
JD (Latitude) (Latitude) (Radius) (Radius) (Longitude) (Longitude)
55331.346445 65.131 1.995 77.933 0.491 19.913 1.409 31.583 0.504 27.701 1.431 267.882 2.688
55334.850912 61.023 3.036 77.925 0.411 17.550 1.484 31.577 0.394 27.811 1.149 269.490 2.184
55339.489476 66.995 2.168 76.507 0.859 21.517 1.808 30.605 0.845 26.610 2.198 263.648 3.641
55343.126760 66.924 1.603 76.246 0.673 22.089 1.338 30.500 0.656 24.992 1.652 260.579 2.749
55347.601842 66.501 1.506 75.809 0.605 22.068 1.207 30.153 0.593 23.722 1.523 260.257 2.451
55351.157383 61.440 2.749 77.325 0.496 18.424 1.453 31.620 0.446 28.428 1.200 266.097 2.191
55353.486873 68.538 1.992 77.246 0.897 22.360 1.850 30.903 0.913 25.707 2.319 258.643 3.919
55356.490687 68.026 2.091 78.397 0.784 21.722 1.892 31.396 0.835 24.741 2.067 260.950 4.201
55359.494498 69.289 2.484 79.019 0.361 22.689 2.538 31.424 0.289 25.281 2.819 258.597 2.118
55362.978506 70.732 1.760 78.142 0.570 24.305 1.956 30.223 0.325 23.033 2.644 255.656 2.010
55366.636200 67.624 1.958 78.918 0.847 22.111 1.787 30.882 0.858 25.284 1.788 259.436 4.395
55369.783038 65.885 2.325 79.667 0.717 20.771 1.808 31.341 0.721 25.963 1.545 261.395 4.223
55373.723379 69.688 0.734 78.148 0.519 24.727 0.741 29.172 0.517 20.718 0.884 248.008 1.984
55376.393757 67.823 0.835 78.289 0.447 22.743 0.775 28.870 0.459 20.538 0.897 256.363 2.215
55379.845729 66.688 0.657 79.422 0.266 21.339 0.554 28.900 0.282 19.259 0.559 257.882 1.646
55383.285777 66.523 0.764 79.697 0.297 21.045 0.628 28.839 0.311 19.361 0.608 257.566 1.866
55387.551685 66.708 0.595 80.077 0.213 20.520 0.486 28.623 0.231 18.404 0.466 258.571 1.482
55392.343077 66.536 0.711 80.006 0.264 20.452 0.566 27.872 0.283 14.864 0.561 254.923 1.804
55396.930800 71.601 0.462 76.197 0.556 25.365 0.441 23.531 0.519 6.999 0.799 234.162 1.513
55401.464365 74.165 0.778 75.475 1.243 26.908 0.738 21.316 1.208 3.240 1.728 230.587 2.751
55404.659853 69.298 0.678 80.712 0.441 22.353 0.661 27.070 0.433 12.554 0.654 241.520 2.359
55408.234381 71.552 0.702 79.246 0.707 24.458 0.692 25.333 0.641 10.011 0.757 226.661 2.048
55410.950691 70.428 0.765 78.487 0.739 24.069 0.675 24.809 0.628 9.584 0.743 225.428 1.920
55414.314060 67.766 0.758 82.063 0.363 20.547 0.635 27.598 0.327 13.545 0.460 238.909 2.124
55417.755753 67.843 0.951 82.471 0.418 20.333 0.817 27.539 0.413 11.979 0.619 243.091 3.137
55421.889452 68.636 0.774 83.132 0.284 19.923 0.717 27.831 0.338 14.122 0.559 253.879 3.132
55426.614352 67.900 0.822 83.328 0.236 19.255 0.702 28.520 0.289 14.666 0.522 256.507 2.886
55429.912649 69.051 1.108 83.615 0.400 20.039 1.077 29.060 0.470 15.990 0.770 253.600 4.560
55433.240206 72.787 2.094 84.692 1.007 21.453 2.940 27.567 1.691 10.110 2.408 255.676 18.000
55435.678588 72.312 0.851 81.306 0.802 24.269 0.965 26.261 0.811 11.136 0.960 231.213 3.429
55438.429596 75.418 0.567 75.819 1.028 27.761 0.512 21.045 0.940 6.928 0.997 220.547 1.531
55441.877717 72.414 0.732 81.364 0.679 23.981 0.821 26.171 0.677 11.250 0.800 230.361 2.831
55445.513138 65.529 1.033 84.504 0.178 17.364 0.663 29.201 0.202 14.208 0.373 254.044 2.528
55448.922765 67.560 0.842 83.195 0.306 19.168 0.660 27.787 0.284 12.294 0.436 240.545 2.369
55452.903836 71.702 0.642 79.618 0.654 23.844 0.611 24.590 0.570 9.030 0.615 221.961 1.739
55458.651004 67.454 0.602 83.186 0.298 20.039 0.475 27.345 0.234 13.438 0.248 225.998 1.374
55464.327988 64.347 1.018 83.193 0.313 18.492 0.611 27.115 0.251 13.667 0.346 230.084 1.759
55467.113359 75.280 0.418 71.792 0.986 27.533 0.285 18.648 0.678 5.116 0.399 203.328 0.491
55470.866573 71.397 0.516 78.158 0.634 24.780 0.436 23.353 0.497 9.349 0.344 210.027 0.862
55474.258800 67.772 0.884 82.891 0.587 21.131 0.732 26.546 0.438 11.610 0.334 215.610 1.840
Table 2: Continued.
JD (Latitude) (Latitude) (Radius) (Radius) (Longitude) (Longitude)
55477.719474 67.483 0.709 81.740 0.445 20.901 0.544 26.305 0.323 14.101 0.265 215.318 1.092
55482.134025 70.552 0.486 76.821 0.567 23.782 0.370 22.756 0.410 10.330 0.302 209.804 0.649
55486.917386 71.526 0.541 78.525 0.583 23.993 0.459 23.859 0.461 8.352 0.355 210.133 0.868
55491.373477 73.059 0.638 75.799 0.844 24.945 0.517 22.085 0.669 8.792 0.687 214.372 1.077
55495.871451 73.925 0.403 70.787 0.776 25.801 0.260 19.198 0.499 7.578 0.319 204.576 0.374
55499.097473 72.097 0.543 74.413 0.689 24.582 0.388 22.083 0.490 10.643 0.318 205.162 0.476
55501.742858 73.291 0.506 71.403 0.825 25.372 0.339 20.259 0.550 7.233 0.426 204.146 0.470
55504.467590 72.524 0.462 71.336 0.772 25.018 0.297 20.040 0.491 9.101 0.280 203.230 0.385
55507.360894 67.462 0.627 76.505 0.487 21.467 0.401 23.736 0.317 13.054 0.234 208.283 0.462
55510.117978 71.784 0.618 73.560 0.827 23.813 0.418 21.027 0.554 11.875 0.375 207.317 0.535
55512.869273 70.697 0.476 72.657 0.551 23.350 0.307 21.827 0.355 11.878 0.250 205.546 0.331
55516.326187 69.021 0.592 77.486 0.453 21.440 0.416 24.709 0.303 13.343 0.212 205.681 0.400
55519.665612 69.159 0.778 77.485 0.562 21.107 0.540 24.592 0.380 13.768 0.289 205.216 0.448
55522.058312 71.307 0.671 73.982 0.728 22.541 0.450 22.173 0.476 12.652 0.295 202.894 0.441
55524.814719 71.323 0.815 73.845 0.836 21.754 0.529 21.647 0.535 12.264 0.379 203.441 0.472
55527.451254 72.219 0.551 74.986 0.485 21.968 0.381 23.235 0.334 15.422 0.205 201.570 0.232
55530.126272 78.627 0.245 -1.110 98.070 26.256 0.134 8.622 0.427 10.499 0.479 186.390 0.446
55532.172637 73.401 0.513 71.201 0.652 22.975 0.322 20.574 0.411 15.939 0.219 199.223 0.223
55534.780911 71.429 0.603 73.233 0.630 22.334 0.388 21.695 0.405 17.332 0.239 198.730 0.245
55536.878020 69.268 0.866 74.579 0.801 21.263 0.535 22.150 0.498 20.782 0.238 202.037 0.371
55538.400281 72.296 0.638 70.433 1.057 23.209 0.381 18.925 0.606 18.506 0.324 207.543 0.393
55541.482607 72.195 0.414 73.048 0.475 22.644 0.270 21.419 0.307 15.201 0.162 199.068 0.194
55546.558864 72.005 0.557 74.864 0.465 22.111 0.394 24.176 0.323 16.019 0.208 202.905 0.235
55550.658428 73.082 0.560 74.177 0.524 22.881 0.399 23.505 0.373 14.069 0.245 200.617 0.240
56421.907557 74.336 0.319 112.006 0.807 26.349 0.199 18.653 0.451 102.414 0.212 111.379 0.257
Table 2: Continued.
(+24 00000) (s) (s) (s) (s) (Intensity)
55375.342090 44.20740 235.39162 2353.99133 2589.38294 0.07436
55375.947616 16.56043 176.54371 1118.15597 1294.69968 0.02621
55376.350846 15.26603 411.94483 765.05904 1177.00387 0.04393
55376.476174 22.31022 58.84790 1176.99523 1235.84314 0.05763
55377.033340 12.30394 176.55322 1176.98573 1353.53894 0.02639
55377.296257 27.67483 588.49718 882.75485 1471.25203 0.03511
55378.175597 20.63149 176.55235 2236.29206 2412.84442 0.03071
55378.328852 1.99895 58.85654 235.39248 294.24902 0.01837
55380.097067 34.60774 235.40026 2824.77888 3060.17914 0.02929
55380.590205 7.63004 58.84790 765.05731 823.90522 0.02825
55380.741416 8.25863 294.24816 823.90522 1118.15338 0.01060
55381.267930 19.27064 235.40026 1176.99264 1412.39290 0.04652
55381.637784 7.80086 529.63978 647.34336 1176.98314 0.01822
55383.117879 1.83830 58.83926 58.84704 117.68630 0.03887
55383.318131 1.72242 58.84790 58.85654 117.70445 0.02840
55385.586972 6.76596 1176.99005 235.39939 1412.38944 0.00939
55385.605363 15.97846 1176.99005 2118.58157 3295.57162 0.01176
55386.161845 1.38046 176.54285 117.70445 294.24730 0.01294
55386.294665 9.55332 176.56099 1353.53290 1530.09389 0.02204
55386.812322 10.15885 1059.29424 823.90349 1883.19773 0.01717
55389.135650 15.95644 1412.38771 1176.98832 2589.37603 0.01390
55390.912711 8.01176 470.79878 823.90176 1294.70054 0.02250
55391.021692 4.32847 353.08570 353.09520 706.18090 0.01673
55391.457613 9.42058 117.70358 706.19731 823.90090 0.02878
55392.580110 4.03619 117.70358 470.79792 588.50150 0.01606
55392.744261 9.80095 294.24643 1471.23302 1765.47946 0.01100
55393.700563 23.57782 235.39853 2118.56429 2353.96282 0.03602
55394.247507 4.93193 117.70358 529.64496 647.34854 0.02670
55395.160216 13.90038 117.70358 706.19558 823.89917 0.04806
55395.578427 404.82960 1118.12832 13417.62970 14535.75802 0.27309
55397.006747 38.35936 765.04262 2118.56947 2883.61210 0.03148
55401.269904 42.89049 117.69408 1412.37994 1530.07402 0.13944
55404.761341 7.68292 176.54198 765.04003 941.58202 0.03032
55405.599122 3.58347 117.70272 353.09174 470.79446 0.01701
55406.776100 7.62807 176.54976 529.63373 706.18349 0.03081
55407.746018 9.85367 176.54198 823.88534 1000.42733 0.02354
55408.136300 58.03656 470.79360 3060.13853 3530.93213 0.05706
Table 3: The parameters calculated for each flare detected with analysis of the Short Cadence data obtained by Kepler Mission for KOI-256 are listed.
(+24 00000) (s) (s) (s) (s) (Intensity)
55409.594580 75.45501 235.38902 2824.75555 3060.14458 0.13119
55409.832291 34.40761 176.54976 3001.29667 3177.84643 0.04241
55409.890187 26.17318 117.70272 1824.31181 1942.01453 0.05453
55412.681417 50.01182 294.23434 2765.89642 3060.13075 0.05973
55412.876899 6.91584 176.54976 588.47904 765.02880 0.02533
55413.391825 6.37731 58.84704 529.63978 588.48682 0.02509
55414.867810 5.48103 117.70186 588.49546 706.19731 0.02086
55414.925024 12.11842 235.39680 1294.67549 1530.07229 0.01774
55416.699338 12.14917 176.54112 1647.76464 1824.30576 0.02079
55417.073953 4.53704 176.54112 647.33299 823.87411 0.01461
55417.940336 2.68543 58.84704 294.24298 353.09002 0.01618
55418.479781 7.96692 294.24298 1000.42214 1294.66512 0.01591
55418.700463 40.81725 1353.52080 2589.33802 3942.85882 0.03181
55418.793776 4.98763 176.54026 588.48595 765.02621 0.01339
55419.427897 82.95145 823.87238 4237.09920 5060.97158 0.04302
55419.497371 185.47791 1118.12400 8827.28755 9945.41155 0.07175
55421.411309 8.11929 235.38730 941.58288 1176.97018 0.02561
55423.293915 68.96291 353.08915 5237.51011 5590.59926 0.05211
55425.451690 5.81840 58.85568 588.48336 647.33904 0.02426
55425.581783 11.64399 941.58029 647.33040 1588.91069 0.02157
55427.109523 10.32274 235.38643 1000.42646 1235.81290 0.02436
55428.162527 6.31033 117.69322 470.78150 588.47472 0.02500
55429.939553 14.85190 294.24125 1294.66598 1588.90723 0.03114
55431.149892 6.49379 117.70186 882.71424 1000.41610 0.02000
55431.203700 14.69386 411.95088 1294.65648 1706.60736 0.02178
55433.127822 1.64001 176.53939 117.70099 294.24038 0.01724
55433.193209 5.77048 58.84704 1176.96240 1235.80944 0.01492
55434.151534 1.12874 176.55667 58.83754 235.39421 0.01448
55434.157664 2.97310 117.69235 411.94224 529.63459 0.01664
55434.353825 6.63105 117.68371 1588.90378 1706.58749 0.01544
55435.784160 4.06328 117.70099 529.63459 647.33558 0.02182
55435.835924 0.73911 58.84618 58.85482 117.70099 0.01707
55435.926512 3.61430 235.40198 706.17312 941.57510 0.01044
55436.045026 7.41432 58.84618 1294.65389 1353.50006 0.01989
55436.068183 3.51315 117.68371 529.64237 647.32608 0.01205
55436.081125 2.71089 353.08656 588.48077 941.56733 0.00666
55436.558584 23.75906 353.08656 2236.22035 2589.30691 0.01960
55436.636912 7.82704 353.08570 823.87411 1176.95981 0.00867
55436.794249 11.70227 176.54717 882.71165 1059.25882 0.03533
55438.701360 21.11367 117.69235 3413.18621 3530.87856 0.03614
Table 3: Continued.
(+24 00000) (s) (s) (s) (s) (Intensity)
55438.913866 5.61630 353.08570 1118.11363 1471.19933 0.01361
55441.226917 32.58644 647.32522 2412.76147 3060.08669 0.04902
55441.943445 3.33076 235.38470 58.85482 294.23952 0.02369
55443.211671 6.27441 235.39335 941.57251 1176.96586 0.01589
55443.229380 2.03953 470.78582 470.77805 941.56387 0.00682
55443.527706 0.95940 58.84618 117.70099 176.54717 0.01647
55443.531792 11.15569 235.39248 1294.64957 1530.04205 0.02500
55445.415740 11.63756 235.39248 1059.26400 1294.65648 0.02883
55446.473501 11.65998 941.56214 2000.82614 2942.38829 0.01389
55446.954364 23.94391 529.63200 1883.12429 2412.75629 0.03194
55447.452254 37.09812 1176.94598 3942.80266 5119.74864 0.01531
55450.550613 26.19646 235.39248 2353.90579 2589.29827 0.04492
55450.614637 15.81569 1118.10672 1294.65389 2412.76061 0.02139
55451.372709 5.64617 117.70099 353.08397 470.78496 0.03361
55453.086373 20.35148 176.55494 765.01325 941.56819 0.07455
55453.672806 149.01479 235.38384 3118.92422 3354.30806 0.18088
55456.080515 72.95417 529.63805 3942.77933 4472.41738 0.07085
55456.193579 12.16574 176.54544 941.55869 1118.10413 0.03073
55456.308004 15.39212 117.69149 1530.02477 1647.71626 0.02762
55456.611096 5.30449 117.69149 470.77546 588.46694 0.02077
55456.622675 12.84198 235.38298 2118.51763 2353.90061 0.01174
55457.468608 193.53680 411.92842 8827.13117 9239.05958 0.11971
55458.638065 6.67818 235.38298 882.72029 1118.10326 0.01673
55460.915679 9.38679 58.84531 765.02016 823.86547 0.02893
55460.929301 3.05990 117.70013 529.62854 647.32867 0.00933
55461.137038 10.42624 58.84531 1000.41091 1059.25622 0.03052
55461.401988 84.63194 176.54630 5002.01914 5178.56544 0.10579
55462.177765 11.80962 353.08224 1118.11104 1471.19328 0.02530
55463.505896 16.78388 117.70013 823.85597 941.55610 0.05735
55464.891260 15.02389 1471.18291 1353.49142 2824.67434 0.01315
55465.276084 10.70152 117.68198 1294.65475 1412.33674 0.02691
55465.425926 14.17575 176.54544 1176.93734 1353.48278 0.04345
55465.482458 18.31911 235.39939 1530.01958 1765.41898 0.05152
55465.952419 41.43259 58.84618 58.84531 117.69149 0.68383
55467.303046 68.23197 117.70013 3060.06336 3177.76349 0.13012
55469.090940 10.93777 176.53680 941.55350 1118.09030 0.03609
55469.613346 18.50133 823.85424 2530.43395 3354.28819 0.01302
55470.019964 6.44893 117.70013 823.85338 941.55350 0.02676
55470.607755 4.84475 117.69926 823.85424 941.55350 0.01444
55471.355605 15.53370 235.39075 1176.93475 1412.32550 0.03245
Table 3: Continued.
(+24 00000) (s) (s) (s) (s) (Intensity)
55472.217880 19.35750 176.54458 3883.92019 4060.46477 0.01227
55472.319364 5.77485 411.93533 882.69869 1294.63402 0.01891
55472.813844 16.21783 117.70013 882.70733 1000.40746 0.05861
55473.593024 51.78851 235.39075 5531.62435 5767.01510 0.03109
55474.398085 12.41232 294.22742 1294.64179 1588.86922 0.02210
55474.727057 44.88099 176.52730 1941.95923 2118.48653 0.18575
55474.900057 9.91234 176.54458 941.55264 1118.09722 0.03113
55475.423824 5.64696 117.69926 588.47126 706.17053 0.02536
55475.562087 6.45265 58.83667 706.17053 765.00720 0.03652
55476.091984 29.14921 235.38989 1353.48710 1588.87699 0.08591
55476.294952 7.44200 58.84531 941.56042 1000.40573 0.02985
55476.567392 314.03759 706.16189 21479.19898 22185.36086 0.07990
55476.696120 21.90776 529.61731 1883.11219 2412.72950 0.02629
55476.823486 86.57508 117.69926 8650.51920 8768.21846 0.03453
55478.800721 21.97714 765.00634 1647.72144 2412.72778 0.02521
55479.075204 48.89291 235.39853 2000.80195 2236.20048 0.08979
55479.596246 75.63241 411.92582 4413.52886 4825.45469 0.06286
55480.878077 3.63981 235.38125 706.16966 941.55091 0.00691
55480.897829 53.97274 176.54458 2530.42618 2706.97075 0.07388
55480.934608 46.92281 294.23520 4236.99120 4531.22640 0.02365
55481.363701 147.57825 470.77978 5001.99754 5472.77731 0.07048
55481.384815 160.06194 2295.02765 4295.83565 6590.86330 0.07118
55482.448012 25.10970 235.38989 1588.86576 1824.25565 0.07721
55484.817558 7.04579 117.69062 1000.40400 1118.09462 0.03365
55486.206319 8.58246 176.52730 941.55869 1118.08598 0.02701
55486.736215 5.60687 58.84531 588.47818 647.32349 0.01998
55487.396200 39.15742 1941.95318 5119.68989 7061.64307 0.01433
55488.308191 75.29180 353.07965 3530.81722 3883.89686 0.07725
55488.373577 9.90490 529.62422 1883.10701 2412.73123 0.01054
55489.807290 140.09412 3942.74909 9650.89814 13593.64723 0.02690
55490.681140 1049.43937 2471.56790 15947.53056 18419.09846 0.33241
55493.194394 14.87307 176.53594 647.32262 823.85856 0.04763
55494.570213 54.05090 353.07965 2059.64986 2412.72950 0.11057
55494.645815 28.36075 941.54832 2471.57482 3413.12314 0.01765
55498.618661 9.03055 176.54371 1471.17168 1647.71539 0.01734
55498.702436 3.62009 176.54371 470.77891 647.32262 0.01493
55498.718101 13.40445 588.46867 2295.02074 2883.48941 0.01675
55499.032768 5.29147 176.54458 823.84906 1000.39363 0.00952
55500.394283 15.19193 117.68198 1706.55984 1824.24182 0.03291
55501.954679 6.79482 58.85395 1118.09117 1176.94512 0.02542
Table 3: Continued.
(+24 00000) (s) (s) (s) (s) (Intensity)
55502.011891 18.73455 588.46781 2236.18406 2824.65187 0.01551
55502.410333 11.46807 176.53507 765.01238 941.54746 0.03713
55504.495855 9.53926 117.69840 1118.08339 1235.78179 0.02625
55505.411932 55.53928 176.54371 2883.49718 3060.04090 0.08309
55505.476636 60.13398 117.69840 5001.98198 5119.68038 0.10543
55508.166292 1.79399 58.84531 58.85395 117.69926 0.03583
55508.891661 14.28894 235.38902 1000.40141 1235.79043 0.04915
55509.218588 21.62582 706.16794 2706.95347 3413.12141 0.01718
55509.391587 31.00352 294.24298 2824.65274 3118.89571 0.03682
55510.390758 36.78295 176.55235 4236.96960 4413.52195 0.05801
55510.739480 11.95360 882.70214 941.54832 1824.25046 0.02207
55511.376307 51.67114 588.46867 3177.72288 3766.19155 0.05542
55513.722008 9.63831 176.53507 1883.10442 2059.63949 0.01544
55514.407193 8.84904 117.69062 1471.17946 1588.87008 0.02198
55515.838861 13.31654 235.38902 1941.94195 2177.33098 0.01942
55516.291791 11.92080 353.07965 1353.48106 1706.56070 0.02661
55516.392594 39.99328 3118.89658 2177.32234 5296.21891 0.01812
55516.430735 23.22504 117.68976 2706.95434 2824.64410 0.02021
55517.760920 98.70816 3177.73325 6826.23677 10003.97002 0.02622
55520.294607 67.24819 176.54371 6708.53923 6885.08294 0.03740
55522.737707 39.92723 176.53594 2236.18666 2412.72259 0.03204
55522.816034 75.88575 176.53507 2177.34134 2353.87642 0.19217
55524.700634 23.03246 58.84531 2353.87728 2412.72259 0.03093
55525.479130 50.79022 353.08051 2765.81174 3118.89226 0.09610
55526.711920 9.11512 117.69926 588.47818 706.17744 0.03393
55527.096741 8.51295 117.69840 1235.77661 1353.47501 0.01772
55527.229556 7.92308 353.07965 1176.93907 1530.01872 0.01985
55527.828923 17.13460 176.53507 2059.64467 2236.17974 0.03384
55528.409901 6.92449 176.54458 647.31485 823.85942 0.01744
55530.246145 602.45858 353.08051 5060.84976 5413.93027 0.62493
55530.609853 110.84606 529.62509 2412.72605 2942.35114 0.13490
55530.638459 22.64046 58.84531 1000.40400 1059.24931 0.05504
55531.639676 20.11803 823.86029 765.01498 1588.87526 0.03575
55532.322138 5.99543 58.84531 941.55091 1000.39622 0.02514
55532.377988 17.43303 117.69926 882.69696 1000.39622 0.04528
55532.540771 19.95533 117.69926 1412.32205 1530.02131 0.05189
55534.100491 11.44830 117.69926 1235.78698 1353.48624 0.01969
55534.874221 7.51594 117.70013 765.00634 882.70646 0.03108
55535.983734 69.75887 235.38125 3707.37907 3942.76032 0.07953
55536.041628 40.06649 117.69926 2706.97334 2824.67261 0.04786
Table 3: Continued.
(+24 00000) (s) (s) (s) (s) (Intensity)
55536.117911 27.10988 117.69149 1235.78698 1353.47846 0.07168
55536.827618 59.17967 882.70646 3354.28214 4236.98861 0.03548
55538.078801 357.68647 176.54458 2589.26717 2765.81174 0.71509
55538.144186 40.92859 117.69926 2059.64986 2177.34912 0.07322
55539.366763 7.80770 117.69062 706.17139 823.86202 0.02386
55540.609774 23.02603 235.38125 2412.73296 2648.11421 0.04814
55540.952368 5.51462 117.68285 765.02534 882.70819 0.01524
55540.963266 18.93492 117.69062 2236.19702 2353.88765 0.02537
55541.343321 3.94267 117.70013 765.00806 882.70819 0.01674
55541.395084 14.23128 411.93533 2648.12371 3060.05904 0.01220
55542.043493 1.26695 58.85395 58.84618 117.70013 0.02280
55542.082316 7.81970 176.53594 1294.64438 1471.18032 0.02129
55542.610851 26.84851 529.62682 2883.52397 3413.15078 0.03662
55542.691222 7.77636 117.69926 882.70819 1000.40746 0.02239
55542.725277 4.57177 58.84531 176.53680 235.38211 0.04254
55543.163907 14.31275 411.92669 1059.25363 1471.18032 0.03769
55544.722950 7.26750 176.52816 588.48077 765.00893 0.03342
55545.570242 5.29618 176.54544 823.86374 1000.40918 0.01745
55545.611108 16.07877 235.39075