Detailed Chromospheric Activity Nature of KIC 9641031

Detailed Chromospheric Activity Nature of KIC 9641031

1 Introduction

The flare stars as known UV Ceti are generally young dwarf stars from the spectral types G, K and M with emission lines in their spectra, such as dMe, which are just coming to the main sequence. As it was indicated by Mirzoyan (1990) and Pigatto (1990), the population rate of the dwarf stars having flare phenomenon is generally high in both the open clusters and the associations. As it is expected due to the Skumanich’s law, the population rate of the stars showing flare activity has a reducing trend, while the age of the cluster gets older (Skumanich 1972; Pettersen 1991; Stauffer 1991; Marcy & Chen 1992).

Strengthening stellar chromospheric activity with increasing the rotation velocity causes much more mass loss from the star. It is known that the stellar mass loss rate of V Ceti type stars is about per year due to flare like events, while the solar mass loss rate is about per year (Gershberg 2005). In the case of UV Ceti type flare stars, this high mass loss rate clarifies how they lose large part of their angular momentum in their main sequence stages (Marcy & Chen 1992). However, the flare activity mechanism resulting high level mass loss has not been completely explained by any theory yet.

Flare events observed on UV Ceti type stars are generally explained with the classical theory of the solar flare. The highest energy detected from the most powerful flares, known as two-ribbon flares, occurring on the sun is found to be - erg (Gershberg 2005; Benz 2008). This level is also observed for RS CVn type active binaries (Haisch et al. 1991). However, in the case of dMe stars, this flare energy level varies from erg to erg (Gershberg 2005). Moreover, some stars of the young clusters such as the Pleiades cluster and the Orion association exhibit some powerful flare events, which energies reach erg (Gershberg & Shakhovskaya 1983). In brief, the stars from different type exhibit some flares with different energy levels. Comparing the sun with a dMe stars, it is seen that there are some remarkable difference between both their flare energy levels and mass loss rate per year. Nevertheless, the flare events occurring on a dMe star are generally tried to explain by the classical theory of solar flare. Therefore, the primary energy source in the flare events is magnetic reconnection processes in the principle (Hudson & Khan 1997; Gershberg 2005). To reach the real situation, examining the flare events occurring on the different type stars, all the differences and similarities should be demonstrated. Then, it should be identified which parameters such as singularity, binarity, mass, age, ect., cause these differences and similarities.

In this study, both flare and stellar cool spot activities observed from a well known eclipsing binary star FL Lyr as a different system apart from classical UV Ceti type flare stars from the spectral type dMe were analysed and modelled. Then, the results were compared with the chromospheric activity behaviour observed on its analogue. The photometric data used in the analyses and models were taken from the Kepler Mission Database (Slawson et al. 2011; Matijevič et al. 2012). In the database, FL Lyr is listed with its catalog number as KIC 9641031.

KIC 9641031 has been listed in the Youngest-Field Star Catalog by Guillout et al. (2009), though the system is not young. Brown (2010) given the age of the system between 3.05 Gy and 15.25 Gy. Morgenroth (1935) listed KIC 9641031 as a variable star for the first time in the literature, while Struve et al. (1950) classified the system as a spectroscopic binary with a single line. Macrae (1952) and Miner (1966) observed the system photometrically, especially in the narrow-bands.

Although the spectral type of the system is given as in some catalogue (Eker et al. 2014), the temperatures of the components are given in a large range in the general literature. The temperatures of the primary component are varying from 5724 K (Guillout et al. 2009) to 6412 K (Eker et al. 2014) in the literature. Its temperature is generally accepted to be 6150 K (Brown 2010; Eker et al. 2014). Similarly, the temperatures stated for the secondary component is changing from 5080 K (Guillout et al. 2009) to 5506 K (Popper et al. 1986). It is accepted as 5300 K in general (Brown 2010; Armstrong et al. 2014). The first light curve analysis of the system was made by Jurkevich et al. (1976). In the study, some parameters such as the fractional radii (), the inclination () of the system, the fractional luminosity () of the primary component were computed. The light curves were analysed together with the radial velocity curve simultaneously by Lacv et al. (1985) for the first time, thus the first approximations were obtained for the masses and radii of the components. The component masses were given as 1.218 and 0.958 , the radii of the components were given as 1.283 and 0.963 by Eker et al. (2014). The semi-major axis () of the system was given as and the inclination () of the system was given as in the same catalogue. According to this view, the components are comparatively far away from each other. Analysing the spectroscopic observations of the system, Cristaldi (1965) asserted existence of some clues for the third body, but Lacy & Evans (1979) did not find any sign for the third body though they obtained the double-lined radial velocity curves of the system. Popper et al. (1986) also obtained the double-lined radial velocity curves of the binary.

As it is seen from the literature, KIC 9641031 is a well studied eclipsing binary for some decades, but the chromospheric activity nature of the system has not been exhaustively studied yet. Botsula (1978) stated that one of the components exhibits magnetic activity. Then, Balona (2015) listed some statistical information about flare activity occurring on the components some decades later. However, there is no detailed study about its chromospheric activity nature or any comparison with the other chromospherically active stars about the similarities or differences between them.

In this study based on the Kepler Mission short-cadence light curves, to understand the magnetic activity nature of the system, we analysed and modelled KIC 9641031’s light variations due to the stellar cool spots and the flare events occurring on the components as the chromospheric activity indicators. Then, comparing with the results obtained from other stars, our results were discussed for both the cool spots and the flares.

2 Data and Analyses

More than 150.000 targets have been observed in the Kepler Mission, which is aimed to find out exo-planet (Borucki et al. 2010; Koch et al. 2010; Caldwell et al. 2010). The observations in this Mission have the highest quality and sensitivity ever reached in the photometry (Jenkins et al. 2010a, b). In this case, lots of variable targets such as new eclipsing binaries, etc. have been also discovered apart from the exo-planets (Slawson et al. 2011; Matijevič et al. 2012). Many targets among these newly discoveries are single or double stars exhibiting chromospheric activity. Some of the double stars are the eclipsing binaries (Balona 2015).

The photometric data of KIC 9641031 were taken from the Kepler Mission Database. All the light curves obtained from these data are together with error bars shown in Figure 1. The error of each point is 0.00008 mag or smaller. Instead of long-cadence light curves, the short-cadence data were used in the analyses and models (Slawson et al. 2011; Matijevič et al. 2012). In order to analysis the cool spots, the flare events and the orbital period variation (O-C), the data were arranged as the suitable formats.

2.1 Flare Activity and the OPEA Model

To determine the light variations just due to the flare events, in the first step, all the light variations except the flares were removed from the general light variation. For this purpose, the data of all the primary minima observations between the phases of 0.96-0.04 and all the secondary minima observations between 0.46 and 0.54 in phase were removed from the general light curve data. By the way, all the deviated observations with large error due to the technical problems were also removed from the data sets. And thus, the pre-whitened light curves were obtained.

In the second step, to determine the basic flare parameters such as the first point of the flare beginning, the last point of the flare end and the flare energy, the quiescent levels for each flare should be derived from the residual data of the pre-whitened light curves. However, it was seen that there is a sinusoidal variation due to rotational modulation variation because of the cool spots occurring on the components. Therefore, considering the pre-whitened light curve just out-of-flare, the light variations seen due to rotational modulation were modelled with the Fourier transform, using the least-squares method. Thus, these synthetic models lead us to definite the quiescent levels for each flare at the same time of that flare. Using these synthetic models as the quiescent levels, the parameters of the flares were computed. Two flare light curves taken from the observation data and the quiescent levels derived for these flares are shown in Figures 2 and 3.

Using the synthetic models derived for the quiescent levels, flare rise times (), decay times (), amplitudes of flare maxima, flare equivalent durations () were computed, after defining both the flare beginning and the end for each flare. In total, 240 flares were detected from the available data in the Kepler Mission Database. All the computed parameters are listed in Table 1 for these 240 flares. In the table, flare maximum times, equivalent durations, rise times, decay times and amplitudes of flare maxima are listed from the first column to the last, respectively.

The equivalent durations of the flares were computed using Equation (1) taken from Gershberg et al. (1972):

(1)

where is the flux of the star in the observing band while in the quiet state. was computed using the models derived with the Fourier transform. is the intensity observed at the moment of flare. Finally, is the flare-equivalent duration in the observing band. In this study, the flare energies were not computed to be used in the following analyses due to the reasons described in detail by Dal & Evren (2010, 2011). Before computing the flare-equivalent duration, comparing synthetic models of the quiescent levels with the observations, the times of flare beginning, end and also maximum were defined, and then computing time differences of these points, the flare rise and decay times were calculated.

Examining the relationships of the flare parameters among each other, it is seen that the distributions of flare equivalent durations on the logarithmic scale versus the flare total durations are varying according to a rule. The distributions of flare equivalent durations on the logarithmic scale can not be higher than a specific value for the star, and it is no matter how long the flare total duration is. Using the SPSS V17.0 (Green et al. 1999) and GrahpPad Prism V5.02 (Dawson & Trapp 2004) programs, Dal & Evren (2010, 2011) indicated that the best function is the OPEA Model to fit the distributions of flare equivalent durations on the logarithmic scale versus flare total durations. The OPEA function has a term, and this makes it a special function in the analyses. The OPEA function is defined by Equation (2):

(2)

where the parameter is the flare equivalent duration on a logarithmic scale, the parameter is the flare total duration, according to the definition of Dal & Evren (2010), and the parameter is the flare-equivalent duration in on a logarithmic scale for the least total duration. In other words, the parameter is the least equivalent duration occurring in a flare for a star. Here is an important point that the parameter does not depends on only flare mechanism occurring on the star, but also depends on the sensitivity of the optical system used for the observations. The parameter value is upper limit for the flare equivalent duration on the logarithmic scale. Dal & Evren (2011) defined value as a saturation level for a star in the observing band.

Using the least-squares method, the OPEA model was derived for the distributions of flare equivalent durations on the logarithmic scale versus the flare total durations. The derived model is shown in Figure 4 together with the observed flare equivalent durations, while the parameters computed from the model are listed in Table 2. The value listed in the table is difference between and values. The value is half of the first value, at which the model reaches the value. In other words, it is half of the minimum flare total time, which is enough to the maximum flare energy occurring in the flare mechanism.

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

KIC 9641031 was observed as long as 576.47474 days from JD 2454964.50251 to JD 2456424.01145 without any remarkable interruptions. In total, significant 240 flares were detected in these observations. The total flare equivalent duration computed from all the flares was found to be 556.81321 s (0.15467 hours). Ishida et al. (1991) described two frequencies for the stellar flare activity. These frequencies are defined as given by Equations (3) and (4):

(3)
(4)

where is the total flare number detected in the observations, and is the total observing duration, while is the total equivalent duration obtained from all the flares. In this study, frequency was found to be 0.41632 , while frequency was found to be 0.00027.

2.2 Rotational Modulation and Stellar Spot Activity

The light curves of the system indicate the existence of the sinusoidal variations out-of-eclipses. Considering the temperatures of the components, the sinusoidal variations are more likely caused by rotational modulation due to the cool stellar spots. As it is clearly seen from the temperature ranges given in the literature for the components, both the primary and secondary components are potential candidates to exhibit the chromospheric activity. In this study, we assumed that the secondary component is a chromospherically active star. To demonstrate just the sinusoidal variations, both all the minima due to the eclipses of the components and all the flare as seen sudden - rapid increasing in the light were removed from general light curves, thus the remaining light curves were obtained, which is hereafter called as the pre-whitened light curves. Comparing the variations seen in the pre-whitened light curves cycle by cycle according to the orbital period of the system, it was seen that both the phases and levels of maxima and minima are rapidly changing from one cycle to the next. The situation is clearly an indicator for the rapid evolution of the magnetically active regions on the components. In this case, all the pre-whitened light curves can not be modelled as just one data set, because of this, the data set of whole pre-whitened light curves were separated to sub-data sets. In this process, the consecutive cycle data, which have almost the same phase distributions and brightness levels, were arranged as one sub-data set. Thus, all the available data were arranged as 92 sub-data sets and each sub-data set was individually modelled.

To find out the parameters of spot distribution on the stellar surface such as the spot radius, latitude and especially longitude, we modelled the sub-data sets under some assumptions using the SPOTMODEL program (Ribárik 2002, et al. 2003). In this program, the analytic models of Budding (1977) were used to model the sinusoidal variations out-of-eclipses. The program needs two-band observations or spot temperature factor () parameter. However, the available data in the Kepler Mission Database contain only monochromatic observations. Therefore, considering the clues of the spot activity for this system stated firstly by Botsula (1978) and also the results obtained from the light curve analyses of its analogue systems (Clausen et al. 2001; Thomas & Weiss 2008), it was assumed that the secondary component exhibits chromospheric activity.

(5)

Considering the coefficients and , the dominant term is for the first () and second () orders in the analysis with the Fourier transform described by Equation (5). According to Hall (1990), the term is an indicator for the spotted areas on the surface of a star. In this case, the previous analyses with the Fourier transform indicate that there are two active regions on the active component. Considering the results of the analogue systems, it was assumed that the spot temperature factors are in the range of for these cool spots. The initial models by changing the factors from 0.70 to 0.95 reveal that the best solutions are obtained if the spot temperature factor is taken as for the primary spot (Spot 1), while it is taken as for the secondary one (Spot 2). Consequently, it was assumed that the spot temperature factors are constant parameters for each sub-data set, and they are taken as for the first spot and for the second spot in the each model. Finally, taking the spot temperature factor as a constant, the longitudes (), latitudes () and radii of the spots () parameters are taken as the adjustable free parameters in the each model.

Five examples selected from different time intervals among all 92 models derived by SPOTMODEL program are shown in Figure 5. In the figure, both the model fits and the cool spot distributions on 3D surface are seen side by side for these five selected sub-data sets. All the spot parameters derived by SPOTMODEL program are also listed in Table 3. In the table, the average Heliocentric Julian Date of the time interval for each sub-data set (HJD), spot latitudes (), radii of the spots () and spot longitudes () are listed from the first column to the last, respectively.

The variations of spot latitude (), spot radius () and spot longitude () values versus the time are shown in Figure 6. In this point, it must be noted that if it was assumed that chromospherically active star is not the secondary component, but the primary one, there would be no 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 so close to the each other.

2.3 Orbital Period Variation

The minima times were computed with a script depending on the method described by Kwee & van Woerden (1956). Each minimum in the light curves was separately fitted with the high order spline functions. Using these fits, the minima times were computed from the available short cadence detrended data of the system in the Kepler Mission Database (Slawson et al. 2011; Matijevič et al. 2012) without any extra correction on these detrended data. For all the minima times, the differences between the observations and the calculations were computed to determine the residuals . Some minima times have very large error, for which the minima light curves were examined. It was seen that there is a flare activity during these minima, then, these minima times were removed from analyses. Finally, 532 minima times were obtained from the observations in 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 , new ephemerides were calculated as following:

(6)

The minima times, epoch, minimum type, and residuals are listed in Table 4, respectively. The error of each minimum time in the table is 0.00001 day or smaller. The residual variations versus time are shown in Figure 7. As seen from the figure, the residuals exhibit some distorted sinusoidal variations in opposite directions relative to each other. A similar phenomenon has been recently demonstrated for chromospherically active other systems by Tran et al. (2013) and Balaji et al. (2015).

3 Results and Discussion

The analyses of data taken from the Kepler Mission Database (Slawson et al. 2011; Matijevič et al. 2012) indicated that KIC 9641031 is a chromospherically active system. However, to reach the certain results about the activity level of the system, it needs to compare the results with its analogues. Considering the temperatures of the components, both components seem to be potential candidates to exhibit the chromospheric activity. However, in this study, we assumed that the secondary component is a chromospherically active star. Using the calibrations given by Tokunaga (2000), we derived color index for the secondary component depending on its temperature generally accepted as 5300 K. According to the calibrations, the color index of a main sequence star with the temperature of 5300 K was found to be .

KIC 9641031 was observed as long as 576.47474 hours between JD 2454964.50251 and JD 2456424.01145. We found 240 flares from these observations. Apart from other flare parameters, the flare frequencies were also computed. flare frequency was computed as 0.41632 , while frequency was found to be 0.00027. Comparing these values with the frequencies found for UV Ceti type flare stars in a wide spectral range, from spectral type dK5e to dM6e, it is clearly seen that the flare energies obtained from KIC 9641031 are remarkably lower than its analogues. In addition, the number of the flare occurring on the star per hour is also remarkably less than its analogues. As it can be seen from the literature, for example, the observed flare number per hour for UV Ceti type single stars was found to be 1.331 in the case of AD Leo, while it was found to be 1.056 for EV Lac. Moreover, frequency was found to be 0.088 for EQ Peg, while it was found to be 0.086 for AD Leo (Dal & Evren 2011). According to these values, the flare frequencies of KIC 9641031 are definitely small. However, it is well known from Dal & Evren (2011) that the flare frequency dramatically changes from one season to the next for some stars, such as V1005 Ori, EV Lac, etc. Because of this, there could be some changes in the flare frequency and flare behaviour of KIC 9641031 in the next observing seasons.

On the other hand, this result obtained from the flare frequencies explained why any flare had not been detected from the system by any ground based telescope before the Kepler Mission. Although the flare frequency indicates that one flare occurs on the star per 2.402 hours, but frequency demonstrates that the energies of these flare are so small that it is very difficult to detect them with the ground based telescopes. Here it should be noted that, the parameters comparing from the literature were derived from the observation obtained in the standard Johnson U band. However, the observation data used in this study is different band.

The value derived from the OPEA model of the flare equivalent duration distributions on the logarithmic scale versus the flare total durations was found to be 1.2320.069 for 240 flares of KIC 9641031. According to Dal & Evren (2011), this value is 3.014 for EV Lac () and 2.935 for EQ Peg (), and also it is 2.637 for V1005 Ori (). As it is seen that the maximum flare energy detected from KIC 9641031 is almost half of the maximum energy level obtained from UV Ceti type single flare stars. Dal & Evren (2011) found that the value is always constant for a star, while it is changing from one star to the next depending on their color indexes. The authors defined the value as the energy saturation level for the flare mechanism occurring on the target star.

The value was found to be 2291.7 s. This value is 10 times bigger than those found from UV Ceti type single flare stars. For instance, it was found to be 433.10 s for DO Cep (), and 334.30 s for EQ Peg, while it is 226.30 s for V1005 Ori (Dal & Evren 2011). It means that in the case of the stars such as EQ Peg, V1005 Ori and DO Cep, the flares can reach the maximum energy level at their value, when their total durations reach some 10 minutes, while it needs a few hours for KIC 9641031.

The similar extended durations are seen for the maximum flare rise and total times found from KIC 9641031, whereas these times obtained from UV Ceti type single stars are absolutely shorten than those seen in this system. For example, the maximum flare rise time was found to be 2062 s for V1005 Ori and 1967 s for CR Dra. However, it was found to be 5179 s for KIC 9641031. Similarly, the maximum flare total time was found to be 5236 s for V1005 Ori and 4955 s for CR Dra. In the case of KIC 9641031, it was obtained as 12770.62 s.

As a result, the flare activity level of KIC 9641031 is considerably lower than that seen in the others. However, this is in agreement with the results revealed by Dal & Evren (2011). The authors demonstrated that the parameters derived from the OPEA model get values depending on the color index of the star. Therefore, according to the general trends found by Dal & Evren (2011), the parameters of the KIC 9641031’s flares are in agreement with the color index of the secondary component. This situation also indicates that the general trends found by Dal & Evren (2011) are valid around the spectral types of . On the other hand, KIC 9641031 is an eclipsing binary system, so it is a double star. In this case, it is expected that the tidal interactions between the components make the magnetic activity level increase. However, it is not realized in the case of the flare activity patterns.

As seen from the literature, Brown (2010) given the age of the system between 3.05 Gy and 15.25 Gy. According to the relations among the age, rotational period and the magnetic activity level described by Skumanich (1972), the given ages are too high that it should not be expected any high level magnetic activity on the components. Therefore, in the case of KIC 9641031, it is seen that being a component in a binary system does not affect the chromospheric activity as much as it is expected. Because, according to the semi-major axis () of the system, the components are too far away from each other to not affect the chromospheric activity.

On the contrary, it seems that KIC 9641031 has very high level spot activity unlike the flare activity. The variation due to rotational modulation is clearly revealed by the Kepler Mission with the highest quality sensitive observations (Jenkins et al. 2010a, b).

The distribution of these spots on the surface was modelled by SPOTMODEL program (Ribárik 2002, et al. 2003). The analyses of the pre-whitened light curves indicate two cool spots on the one component for all 92 sub-data sets. The derived parameters of both spots, such as latitude (), radius () and longitude () values, are listed in Table 3, while their variations versus time are shown in Figure 6. The latitudes of the spots are shown in the upper panel of the figure. As it can see, both spots are located between and in the latitude until HJD 24 56300. After this time, one of the spots is rapidly migrating to the latitude range from to , while the other one is stable in that latitude.

In the model, locating of the stellar spots close to one of the poles solves out a problematic behaviour of the flare activity. If the phase distribution of the detected flares is examined, it is seen that there are the flare activity patterns in each phase interval. Although it is normally expected that large number of the flares should be seen in the phase interval, in which the observers directly see the spotted areas on the surface of the star, but this expectation is not working in this system. However, considering both the orbital inclination of 86.3 and the spotted area latitudes close to the pole, it is easy to understand that the active regions on the star are always in front of the observers. This situation explains why the flare patterns are seen in each phase interval.

As it is seen from the middle panel of the Figure 6, the longitudes of the spotted areas are overlapped and changed their sides between each other around HJD 24 56300, when the spots changed their locations in the latitude range. There are about 180 longitudinal differences between two spots in the beginning, while the longitudinal differences are decreasing set by set, and finally, two spots changed sides in the longitudinal plane around HJD 24 56300. This is very interesting phenomenon in the astrophysical sense, because the spot with bigger radius is migrating towards the earlier longitudes, while the second spot with smaller radius is migrating towards the later longitudes. The migrations of both spots get more distinctive according to each other after HJD 24 56300. According to Fekel et al. (2002) and Berdyugina (2005), the behaviour of the spot migration on a star is very important to understand both the rotation of the star and also the dynamo process working its inside.

The variations of the spot radii are seen in the bottom panel of the Figure 6. As seen from the figure, the radii of both spots sometimes increase and sometimes decrease. However, the remarkable point is that the radii of the spots are synchronously varying in opposite directions relative to each other. The radius of one spot is increasing, on the contrary, the radius of the other one is decreasing in the moment. This phenomenon seems to be a recurrent behaviour.

Like the synchronous longitudinal variations of the spots, the synchronous variations of the spot radii demonstrate that the assumption of ”both spots are occurring on the same component” in the model is a right approach for this system. If the spots locate on the different components, it should not be expected any apparent synchronous variations like those.

Using the data obtained in the Kepler Mission, we demonstrated some clear variations with very short amplitudes in short time intervals. For example, the amplitude variations of the sinusoidal variation are lower than a few mmag, while it is clearly seen that this amplitude and light curve shapes are changing from one cycle to the next in short time intervals. However, in the case of observations made by the ground based telescopes, the variations of both the amplitude and the shape of the light curve due to the sinusoidal variations caused by rotational modulation can be perceived in a few months at least or generally from one season to the next (Dal et al. 2012).

Considering the studies of Tran et al. (2013) and Balaji et al. (2015), it is expected that the chromospheric activity affects the orbital period of the KIC 9641031. Therefore, all minima times were computed from the short cadence data given in the database. After the linear correction applied to residuals, residuals were obtained. It is seen that the residuals exhibit a variation as expected. The stellar spot activity occurring on the active component leads the residuals of both the primary and secondary minima to vary synchronously, but in opposite directions, due to the effects presented by Tran et al. (2013) and Balaji et al. (2015). The dominant effect is seen in the residuals of the secondary minima. Moreover, as it is seen in the cases of the spot longitudes and radii, the variation character of the residuals is changed around HJD 24 56300. After this time, there is nearly no separation between residuals of the primary and secondary minima.

In this study, although the secondary component was assumed as chromospherically active component, it is possible that the primary component could be chromospherically active star, too. In this point, considering the parameter variations of the models, it is certain that there are two spotted areas and both of them are located on the same component.

Consequently, these results in the general respect reveal that KIC 9641031 is an active binary, but not active as much as the eclipsing binaries such as UV Ceti, BY Dra or RS CVn type variables, though one of the components exhibits both the flare and the cool spot activities. Because, both the flare energy level and the flare frequency are saliently lower than those obtained from UV Ceti type flare stars from the spectral type dMe (Dal & Evren 2010, 2011). In addition, although both the minimum location and the shape of sinusoidal light variations due to the rotational modulation out-of-eclipses seem to be rapidly changing, but the amplitude of the variations is not large as much as that observed from other systems (Dal et al. 2012). Nonetheless, KIC 9641031 has one chromospherically active component at least.

In the future, the spectral observations of the system should be done to certainly understand which component is an active star. In addition, the system should be observed photometrically with high time resolution to easily detect flares in order to check the flare frequencies, and .

Acknowledgments

The authors thank Dr. 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.

Figure 1: All the light curves obtained from the data given in the Kepler Mission Database are shown together with the error bars. The full of the light curves are shown in the bottom panel, while the maxima of the curves are shown in the upper panel to reveal the variations out of eclipses, such as sinusoidal variation due to the rotational modulation and sudden variations due to the flares.
Figure 2: A slow flare example detected in the observations of the system. Filled circles show observations, while the dashed line represents the level of the quiescent state of the star for the observing night.
Figure 3: A fast flare example detected in the observations of the system. All the symbols are the same as in Figure 2.
Figure 4: The distributions of flare equivalent durations on the logarithmic scale versus flare total durations for detected 240 flares and the OPEA model derived for this distribution. Filled circles show observed flares, while the line represents the OPEA model.
Figure 5: Some examples selected among all the models of rotation modulations due to cool spots. In the left panels, filled circles show observations arranged as the pre-whitened light curve, while the line represents the synthetic fits derived by the SPOTMODEL. In the right panels, the spot distributions on the active component surface derived by the SPOTMODEL are shown as the 3D form. In the figure, the pre-whitened light curve fit and its 3D model are shown side by side for the same sub-data set.
Figure 6: The variations of the parameters found by SPOTMODEL are shown. In the figure, filled red circles represent the Spot 1; filled blue circles represent the Spot 2. In the middle panel, two linear lines are shown just as the representative fits to the trends of spot longitudes. In the bottom panel, the filled circles are also consolidated with the thin lines to reveal the asynchronous trends between two spots.
Figure 7: The variation of residuals obtained, after the linear correction on the . In the figure, the filled blue circles represent the primary minima, while the filled red circles represent the secondary minima.
Flare Time Amplitude
(+24 00000) (s) (s) (s) (Intensity)
54964.828101 0.463112 353.111616 882.763488 0.00085
54966.495541 0.108480 58.857408 353.111616 0.00134
54968.531480 0.326691 176.556672 1118.158560 0.00072
54969.875376 0.182262 235.395936 529.658784 0.00081
54970.999262 0.077346 235.405440 235.395936 0.00046
54972.743670 0.530361 411.951744 941.610528 0.00073
54974.041928 0.070687 58.848768 58.858272 0.00092
54975.767943 0.095177 117.706176 176.547168 0.00051
54976.821670 0.175537 117.707040 588.515328 0.00062
54978.267735 0.269551 294.261985 647.346816 0.00044
54978.968630 0.308382 235.395936 941.608800 0.00064
54979.569397 0.083443 58.848768 117.706176 0.00121
54981.868930 0.060800 117.697536 117.706175 0.00087
54982.271484 16.122205 1412.416224 8180.233632 0.00536
54983.156286 53.681508 294.253344 588.505824 0.04729
54984.105115 0.718312 353.101247 2059.777728 0.74619
54984.142578 0.187637 235.403712 529.647552 0.00056
54985.149985 0.495380 294.252480 1177.010784 0.00084
54987.513541 0.000915 294.243840 1059.312384 0.00092
54988.077524 0.122731 235.403712 235.403712 0.00061
54991.675301 0.656824 294.243840 1235.864736 0.00113
54992.740602 0.643601 294.243840 1235.864736 0.00138
54993.979592 0.060850 58.848768 58.847904 0.00100
54996.189202 1.588175 353.108160 1059.300288 0.00308
55002.563290 0.837296 411.947424 1000.448064 0.00180
55005.208137 0.503817 235.401984 1118.152512 0.00073
55006.581304 2.036945 765.061632 2412.847872 0.00144
55006.703908 7.032545 1235.848320 3119.061600 0.00298
55006.703908 0.431862 235.409760 941.589792 0.00125
55008.479624 0.596772 235.401984 1588.944384 0.00063
55012.644069 0.838489 235.409760 1765.485504 0.00098
55013.727750 1.522967 176.553216 1706.636736 0.00222
55018.755856 0.301985 235.391616 529.648416 0.00078
55019.661758 0.464195 176.552352 1000.439424 0.00060
55019.853156 1.073934 470.791872 1000.448064 0.00164
55022.582439 9.673752 529.647552 5531.844672 0.00802
55031.746995 0.302319 235.398528 1294.686720 0.00061
55032.350471 0.122125 117.703584 294.245568 0.00060
55032.359326 0.268830 176.541984 529.644096 0.00084
55467.694308 1.885821 470.779776 5060.842848 0.00075
55468.036220 0.224123 58.853952 706.161024 0.00061
55468.036220 0.224123 58.853952 706.161024 0.00061
55476.468224 3.544130 588.476448 2706.943968 0.00257
55477.348883 1.760652 2059.647264 882.702144 0.00122
55478.400497 0.423655 235.380384 941.546592 0.00117
55478.657271 0.478065 176.543712 706.149791 0.00107
55484.085612 0.298814 58.853088 58.836672 0.00497
55486.315520 0.178004 58.845312 58.844448 0.00292
55487.200944 0.242768 176.552352 588.466944 0.00062
55488.744307 0.200370 117.698400 353.077920 0.00084
55496.947413 0.224043 58.844448 58.845312 0.00387
55497.324058 0.310694 117.689760 529.620768 0.00147
55497.409194 0.264936 235.379520 647.318304 0.00100
55502.361430 4.615213 764.999424 4001.565888 0.00307
55486.315520 0.178004 58.845312 58.844448 0.00292
55487.200944 0.242768 176.552352 588.466944 0.00062
55488.744307 0.200370 117.698400 353.077920 0.00084
55496.947413 0.224043 58.844448 58.845312 0.00387
55497.324058 0.310694 117.689760 529.620768 0.00147
55497.409194 0.264936 235.379520 647.318304 0.00100
55502.361430 4.615213 764.999424 4001.565888 0.00307
Table 1: Calculated Parameters of Flares Detected in the Observations of KIC 9641031.
Flare Time Amplitude
(+24 00000) (s) (s) (s) (Intensity)
55502.426134 0.105038 58.835808 58.844448 0.00146
55510.561799 0.243144 117.697536 294.223968 0.00140
55511.945101 0.118927 58.853952 470.765952 0.00041
55513.171751 0.225939 294.232608 411.922368 0.00092
55526.031492 37.460548 1706.544288 7650.056448 0.01375
55534.234607 0.386698 529.621632 529.622496 0.00080
55549.722099 0.601652 353.080512 1176.940800 0.00072
55551.038666 0.659278 117.699264 1412.331552 0.00116
55551.038666 0.953462 117.700128 1412.346240 0.00031
55569.559887 2.898580 353.083968 4060.501056 0.00178
55576.601875 0.909644 235.402848 1588.882176 0.00113
55582.646062 5.323281 353.078784 4472.468352 0.00574
55586.533182 0.648850 176.539392 823.869792 0.00165
55594.007077 0.183146 58.846176 58.855680 0.00309
55603.807709 5.780679 1765.470816 4060.584000 0.00210
55608.504741 1.975708 411.940512 2883.612960 0.00078
55611.104598 1.988434 1000.442880 2942.466048 0.00103
55614.553826 42.439277 529.638048 11416.792320 0.00962
55627.791601 0.233362 58.856544 58.847904 0.00394
55628.777201 0.153771 470.794464 294.249888 0.00043
55628.799678 0.174293 176.545440 411.945696 0.00051
55628.962469 0.679179 1471.257216 765.043488 0.00066
55629.928998 0.840648 353.097792 1824.339456 0.00089
55632.997510 0.804448 176.554080 2059.751808 0.00076
55633.814192 4.390032 353.107296 3530.997792 0.00593
55634.223554 0.628311 176.554080 1353.555360 0.00121
55634.564803 1.322826 235.393344 2707.121088 0.00151
56016.476472 0.168681 58.847904 58.848768 0.00268
56017.419168 65.836224 882.764352 26659.241856 0.02757
56019.800432 0.002725 235.412352 588.496320 0.00100
56021.131380 0.106976 58.848768 294.261120 0.00125
56021.204262 0.083883 58.848768 58.857408 0.00147
56022.705495 0.214953 58.857407 58.848768 0.00358
56022.742277 0.488879 58.848768 58.849632 0.00814
56026.543044 10.259427 1471.264992 6591.274560 0.00332
56030.632621 0.188793 176.555808 529.657920 0.00056
56030.681663 0.247377 235.404576 588.515328 0.00099
56033.568346 0.239645 235.404576 647.356320 0.00059
56033.717517 0.158799 58.848768 58.858272 0.00255
56033.992698 0.686340 117.706175 1059.308928 0.00167
56037.097350 0.097455 176.547168 411.952608 0.00034
56037.097350 0.199836 117.697536 529.650144 0.00070
56038.373132 0.343017 58.858272 1059.308928 0.00076
56039.407790 5.608481 529.667424 8768.766240 0.00147
56042.005674 0.000004 117.707040 647.357184 0.00132
56043.049187 3.516483 1118.168064 6885.547776 0.00086
56047.241632 40.052123 235.405440 8886.484512 0.02037
56048.921336 2.627696 529.660512 2000.932416 0.00241
56050.195758 0.260855 117.707040 470.802240 0.00109
56050.974307 0.291640 176.547168 765.065952 0.00072
56053.861001 6.842854 353.103840 5649.697728 0.00794
56054.345976 0.724180 176.555808 1177.019424 0.00106
56055.609501 1.368917 117.707040 2295.179712 0.00119
56056.725217 4.404903 353.103840 5355.434880 0.00289
56057.172730 1.029413 353.103840 1765.520064 0.00177
56057.934251 2.680671 470.810880 2824.841088 0.00175
56058.874231 15.620817 2824.849728 10652.029632 0.00267
56063.409979 1.136078 235.405440 1883.227104 0.00191
56069.179281 0.140559 117.707040 470.802240 0.00063
56069.447652 0.687776 353.103840 1412.432640 0.00081
56070.649873 0.716218 353.103840 1000.470528 0.00136
Table 1: Continued From Previous Page.
Flare Time Amplitude
(+24 00000) (s) (s) (s) (Intensity)
56071.401857 0.179078 58.848768 58.858272 0.00269
56075.048026 0.624893 294.254208 1765.526976 0.00082
56075.977108 1.646454 235.396800 1177.026336 0.00269
56079.256818 0.118439 58.849632 58.857408 0.00212
56080.711061 2.236179 176.548032 2824.835040 0.00262
56083.697196 9.794873 5178.865248 7591.754592 0.00238
56087.183969 7.111719 411.951744 4060.711872 0.00842
56095.037541 7.523292 3354.481728 5767.365024 0.00221
56095.794289 0.278405 117.688896 588.515328 0.00131
56096.232263 1.446169 117.697536 1412.407584 0.00408
56100.370875 18.548503 941.606208 6708.960864 0.01059
56103.321574 0.341100 176.554944 647.344224 0.00075
56104.969250 0.509812 294.242976 941.613984 0.00078
56109.139853 0.485133 411.949152 1353.560544 0.00067
56109.785572 1.408311 706.191264 1294.720416 0.00194
56111.547675 1.376109 647.359776 2059.758720 0.00157
56112.440646 4.493970 353.099520 5237.672544 0.00194
56113.543407 0.595973 235.401984 1235.844000 0.00133
56114.803510 8.016312 1059.306336 9533.724192 0.00175
56115.800012 2.774649 882.760896 2471.701824 0.00178
56132.752056 1.486270 176.552352 2530.537632 0.00156
56132.927787 1.091035 411.952608 1942.042176 0.00117
56135.367594 4.004825 1588.943520 4119.468192 0.00167
56136.515296 1.663035 647.334720 2471.684544 0.00112
56143.088859 0.413005 176.560129 823.883616 0.00106
56144.216803 3.457132 765.035712 5826.078144 0.00111
56147.055052 0.639562 294.245568 1000.441152 0.00094
56151.409477 2.444966 470.795328 4590.217728 0.00122
56155.667171 1.478003 529.641504 2353.945536 0.00117
56157.949606 4.405529 470.793600 4237.108704 0.00378
56158.279950 0.902990 117.702720 1235.831040 0.00239
56164.405252 2.045450 647.340767 2295.086400 0.00172
56170.504648 0.294271 353.088288 176.548896 0.00099
56172.716909 0.241851 470.789280 235.395072 0.00062
56173.721552 0.495333 117.701856 1412.359200 0.00092
56187.947916 0.521143 176.538528 1118.108448 0.00064
56188.426054 0.598732 294.230016 1118.116224 0.00108
56188.966173 0.631781 235.392480 1059.253632 0.00107
56190.499346 1.260252 765.014976 1706.574528 0.00098
56194.364625 3.822607 706.166208 4119.327360 0.00184
56195.547706 1.025324 176.554944 1824.261696 0.00124
56197.199385 2.376246 1059.257088 2648.134944 0.00100
56199.549877 0.392141 117.700128 765.010656 0.00114
56199.675200 0.541799 353.082240 941.564736 0.00140
56201.810459 0.345300 235.382976 588.472992 0.00087
56202.508590 1.289982 235.382112 3118.909536 0.00092
56211.433042 0.253313 235.381248 470.771136 0.00091
56212.912391 0.398212 117.699264 882.704736 0.00165
56212.984587 0.636392 117.690624 765.005472 0.00138
56219.273174 1.744263 235.397664 2353.874688 0.00374
56221.997566 0.332327 235.380384 1118.091168 0.00068
56227.370058 0.532126 235.389024 1530.012672 0.00084
56228.156724 1.002638 353.086560 2236.169376 0.00142
56228.538819 0.771124 117.699264 1706.546880 0.00137
56230.928104 0.291106 117.698400 823.846464 0.00064
56231.936807 0.781827 411.922368 1883.098368 0.00074
56232.299149 1.096483 176.542848 1235.777472 0.00220
56232.446266 0.497900 117.689760 1530.010944 0.00078
56233.019067 0.477360 294.223968 1294.640064 0.00074
56235.193123 0.918914 470.776320 2236.165920 0.00078
56238.375199 2.646142 176.542848 2177.328384 0.00512
Table 1: Continued From Previous Page.
Flare Time Amplitude
(+24 00000) (s) (s) (s) (Intensity)
56240.689558 1.698398 235.396800 1118.085984 0.00343
56253.134493 0.579830 235.387296 1118.076480 0.00077
56253.270712 3.909380 235.396800 4472.339616 0.00261
56253.708655 0.577834 235.387296 1118.085120 0.00088
56253.764505 0.333632 235.378656 470.775456 0.00092
56259.634853 0.519913 588.456575 823.862016 0.00058
56263.408795 4.314619 764.999424 4236.946272 0.00161
56265.192581 0.829487 117.698400 1235.775744 0.00145
56266.091626 5.000047 235.379520 3766.171680 0.00566
56266.690989 1.376481 353.077056 2412.707040 0.00102
56268.161472 0.762166 117.698400 941.543136 0.00208
56272.319556 0.697019 294.241248 1294.621920 0.00087
56279.123704 1.220712 176.543712 2295.023328 0.00140
56279.983247 0.739083 117.689760 2000.790720 0.00085
56280.433452 0.821007 176.543712 1235.771424 0.00179
56286.625990 1.469311 117.699264 1588.853664 0.00354
56291.777822 2.093364 58.845312 3177.730657 0.00129
56296.087824 0.969906 294.236064 1294.640928 0.00194
56301.549580 4.504331 353.082240 3589.690177 0.00438
56305.497216 3.824587 588.482496 3883.926240 0.00293
56307.391368 1.230758 235.391616 1647.732672 0.00208
56327.035909 0.719264 353.096064 1588.889088 0.00087
56327.035909 25.439798 353.096928 4825.556640 0.01881
56336.668926 2.989529 353.090016 2707.022592 0.00263
56339.221077 1.136775 235.387296 2530.496160 0.00131
56339.541884 1.604309 411.937056 1118.126592 0.00270
56345.040568 0.477432 411.938784 882.724608 0.00092
56345.307568 0.392422 176.549760 941.589792 0.00070
56349.715794 0.163734 235.406304 470.787552 0.00058
56352.338123 0.323102 117.703584 1000.432512 0.00072
56353.343464 1.210804 529.644960 2707.070976 0.00094
56353.736473 0.690799 117.686304 1294.697088 0.00102
56354.213942 0.993478 529.636320 1412.392032 0.00111
56354.931168 0.406601 235.398528 823.882752 0.00080
56359.817574 1.007938 294.255936 2765.921472 0.00070
56360.278698 0.597696 235.399392 765.038304 0.00161
56360.297769 0.760295 294.239520 1412.388576 0.00112
56360.603596 4.503978 647.342496 3884.073984 0.00295
56361.760834 0.596414 117.704448 1353.533760 0.00116
56361.861641 0.459723 235.390752 529.647552 0.00122
56361.882075 0.506702 117.695808 647.343360 0.00218
56384.711629 8.440221 294.259392 5237.676864 0.00740
56386.072543 0.471606 176.554944 1530.105984 0.00075
56386.759811 1.334255 176.554080 1942.064640 0.00178
56387.568322 0.682612 176.554944 1765.510560 0.00112
56390.454308 0.212132 235.395072 529.655328 0.00062
56392.943840 0.316764 117.706176 647.361504 0.00079
56393.122299 1.295137 529.656192 2295.162432 0.00098
56393.208804 0.890257 235.412352 1942.061184 0.00103
56395.091476 0.310735 176.546304 529.657056 0.00110
56397.452991 0.451218 353.110752 823.910400 0.00085
56397.766998 2.049632 353.102112 4708.047456 0.00086
56403.314898 0.769157 117.698400 1235.871648 0.00257
56405.543598 0.848409 411.951744 1353.561408 0.00087
56408.559018 0.398574 117.707040 1412.420544 0.00051
56410.992064 0.928899 176.565312 941.601888 0.00205
56423.590507 3.395311 411.969888 3531.047040 0.00240
Table 1: Continued From Previous Page.
Parameter Values 95 Confidence Intervals
-1.0520.037 -1.1255 to -0.979
1.2320.069 1.097 to 1.368
0.00030.0001 0.0003 to 0.0003
3306.2 2904.7 to 3836.5
2291.7 2013.4 to 2659.3
2.2850.061 2.165 to 2.405
Goodness of Fit Method Values
0.9010
(D’Agostino-Pearson) 0.0010
(Shapiro-Wilk) 0.0005
(Kolmogorov-Smirnov) 0.0007
Table 2: The OPEA model parameters by using the least-squares method.
HJD Average
(+24 00000) (degree) (degree) (degree) (degree) (degree) (degree)
54966.748617 79.9901.342 85.2490.731 16.0271.850 30.3790.971 12.6931.401 161.6911.850
54971.548427 79.0171.211 84.8990.691 16.6791.837 29.3420.992 17.0081.682 153.1931.872
54975.579032 82.6000.455 81.5360.925 23.8290.674 21.2871.410 23.7551.304 176.0011.927
54981.174707 82.3240.477 87.3511.216 16.9950.695 30.0321.431 23.1481.325 134.4701.948
54986.814506 83.5590.498 94.0280.012 5.1780.135 31.8690.016 7.7530.163 280.8380.447
54991.711822 84.7930.519 94.3650.012 7.2370.999 31.9940.011 10.9580.163 264.4160.298
54996.265208 86.0280.540 95.0180.020 4.3690.155 31.8630.030 -2.0150.320 262.7980.653
55005.446506 87.2621.692 96.6810.033 7.0790.223 30.6200.027 -31.3740.249 281.1650.295
55011.432468 85.5780.016 97.9150.695 25.9650.015 10.2820.151 23.5490.293 140.6820.111
55020.696339 85.3500.051 83.3810.717 27.6330.070 11.5160.172 58.2421.070 120.9860.132
55028.344387 79.0461.578 89.0110.420 18.3440.091 12.7510.193 43.6441.058 120.1050.154
55031.989276 83.0001.599 87.1350.441 22.8890.113 25.2570.214 22.5901.079 163.2230.175
55464.747687 85.3190.020 88.3690.462 27.9580.011 6.7790.191 -40.9000.125 162.9240.172
55487.675251 85.3360.040 62.3941.065 26.9810.023 10.1790.277 -20.3000.177 177.7450.175
55497.802773 83.5900.024 63.6291.086 26.2070.013 11.4130.170 -7.4180.087 187.4340.221
55504.991926 75.4620.659 88.4840.458 16.7440.896 29.5560.477 -7.5090.140 200.1880.242
55512.008636 71.0050.387 85.0270.163 15.5060.284 30.1050.122 -0.7560.089 200.4670.684
55526.123227 106.5930.466 103.5310.208 14.9890.294 25.9880.159 6.9030.399 152.2670.455
55531.947550 108.4800.538 98.1600.059 10.6540.241 29.7570.052 4.6510.249 136.1960.405
55540.150265 74.7580.722 82.2780.297 16.4410.771 28.3480.430 0.5260.984 241.6130.426
55550.120846 78.7700.105 109.4500.322 17.6760.109 18.9820.262 -10.6840.551 47.3130.421
55570.653552 67.2270.163 117.9380.272 -16.4530.073 17.4090.106 -22.1000.167 34.8130.203
55577.332141 75.5370.106 69.8930.261 20.3830.087 18.8100.176 -23.8980.330 210.4530.345
55582.640857 118.3860.582 102.0930.049 21.6170.147 28.1440.036 17.5830.137 146.6210.193
55589.146197 81.1380.248 74.8000.631 24.5930.252 19.5830.665 -27.2371.014 553.0750.781
55598.882642 79.5240.948 83.2580.917 19.5671.416 27.1301.225 -9.0821.471 203.2900.802
55606.616321 80.7590.969 91.6960.021 4.5820.166 32.8700.016 15.9100.229 145.1930.786
55612.337192 104.6011.503 94.8910.211 10.7250.936 32.6370.172 21.5850.514 173.8701.225
55620.453150 105.8361.524 92.8350.021 6.4290.055 31.8460.015 18.5410.081 65.1270.406
55626.068455 107.0701.563 88.1340.017 6.8110.119 32.5320.015 11.1920.098 248.8590.726
55632.806400 109.5780.657 102.3300.163 13.6800.321 30.9200.101 7.3390.100 188.0910.062
56019.935539 110.8130.679 87.4680.040 5.8750.160 31.5420.020 25.7910.140 191.1370.401
56026.670560 96.4990.017 88.7030.061 27.3980.009 5.5851.298 9.2900.072 170.8180.215
56032.419541 104.9360.810 95.5510.739 19.1460.981 29.1780.701 7.0020.312 169.8420.237
56036.438862 103.3851.923 92.7101.387 17.1351.002 31.1511.376 8.3420.251 189.9971.131
56039.995372 83.2160.700 77.8670.603 21.7480.845 27.6080.872 8.4560.609 180.9110.249
56051.904498 88.9230.455 74.1710.983 24.7500.510 18.9391.463 26.0780.630 170.8350.216
56058.709566 83.9740.420 78.6390.424 21.4340.530 25.0990.645 11.7550.962 174.4310.374
56063.740465 72.3750.414 82.9750.089 12.5570.232 30.9030.063 17.4890.102 182.5730.189
56067.478165 67.3090.410 83.8420.030 9.6870.124 32.3780.018 14.1970.091 184.6180.067
56072.319884 68.5430.432 87.3190.018 10.9220.203 34.3170.010 27.1570.341 179.4320.203
56076.369572 91.5260.453 87.8170.039 19.4780.224 31.2330.031 14.7910.362 171.2710.225
56083.175187 91.1411.752 81.7160.060 26.6390.245 16.5000.053 3.4130.383 129.0740.246
56090.021171 81.3681.642 84.6910.309 11.3260.266 32.0920.436 23.9590.404 162.9360.267
56098.945279 90.5610.568 77.1971.733 26.3591.467 20.2930.458 31.0630.425 149.6490.593
56106.238782 87.3550.028 78.4321.194 27.6310.021 9.1730.284 137.0260.619 182.4680.170
56110.914339 86.7400.315 78.7441.574 25.3081.389 19.9600.305 90.4030.641 191.2170.191
56119.146386 83.9480.484 79.4241.212 24.7180.699 19.4491.888 65.1740.662 204.8090.213
56133.285043 85.1821.012 88.6290.029 7.6690.130 32.2150.019 29.5210.101 190.0220.544
56142.330996 86.4171.574 91.7670.015 6.8150.183 31.3890.021 15.9460.164 117.7581.230
56148.859429 67.8270.564 96.1400.044 12.5290.268 29.4210.079 19.2330.230 94.4631.031
56155.366816 69.0610.585 103.8710.047 6.4170.015 27.9360.032 44.7800.142 163.4710.155
56160.755894 108.0420.521 109.3930.298 16.0440.358 23.3550.280 56.4831.097 168.9320.895
56167.279388 107.2980.052 122.0430.292 20.4170.041 15.7730.107 67.8210.178 173.1400.161
56174.646136 112.9200.229 126.2880.482 15.8990.106 15.5240.148 55.3230.321 157.7130.263
56180.652267 112.1270.310 119.1250.469 17.1340.150 17.5680.201 48.5330.459 157.7710.412
56184.967399 115.9870.589 121.5740.802 14.9960.225 16.4670.288 47.1250.558 154.3970.572
56193.553737 102.6350.165 111.5700.587 20.2180.163 17.2510.383 38.1120.877 151.7830.691
56200.757825 76.5030.837 82.0360.489 16.4950.937 25.9720.631 -47.1791.390 186.4760.712
Table 3: The spot parameters obtained from the SPOTMODEL program.
HJD Average
(+24 00000) (degree) (degree) (degree) (degree) (degree) (degree)
56211.056479 109.4170.645 95.8090.082 11.2780.289 31.2340.062 -40.9070.174 110.0140.396
56217.956451 90.5330.667 91.9140.103 11.8580.310 33.0400.083 51.0110.195 63.8430.417
56226.753235 136.3890.688 87.4930.039 5.5170.328 32.1160.032 66.0050.302 206.7600.955
56234.493888 98.7790.482 78.8801.577 25.6980.496 17.8901.707 23.8920.485 34.2330.905
56240.418359 103.9241.839 103.2620.524 26.9321.149 29.4760.381 177.0010.509 5.8030.294
56244.159299 105.1591.860 78.4510.023 5.8540.857 31.5480.012 2.3990.126 179.1820.050
56254.131126 83.5510.057 67.2020.411 23.3660.207 20.8780.441 102.1510.147 195.0640.410
56263.188537 84.0220.115 68.8950.371 22.6820.285 22.6260.483 79.9980.168 180.9250.454
56271.454008 109.8870.588 81.3090.048 23.9160.613 26.3470.414 0.1810.790 100.8570.475
56277.288435 111.1220.610 79.4970.045 0.0200.634 32.4910.046 -136.9980.811 -194.2500.405
56282.783429 112.3560.631 98.3660.029 8.8531.224 30.1350.033 128.8270.166 26.0350.352
56286.913227 73.0660.979 105.1930.221 10.0870.528 28.7280.180 -72.3270.885 -29.5050.576
56292.187548 109.4871.006 95.0710.077 15.5140.845 28.4340.415 -42.8210.564 46.9740.597
56297.298298 84.8280.017 -22.4760.099 25.7970.019 8.1751.224 190.7680.353 105.5610.125
56301.917977 84.5730.034 66.5990.434 24.8650.074 16.5950.289 209.7081.092 109.3780.204
56308.021249 85.1080.017 -45.0130.455 25.3220.025 9.0391.696 180.8590.485 104.7220.182
56326.631702 77.6490.291 -77.3720.284 20.5390.273 31.3590.304 220.9830.354 63.3630.366
56331.357357 81.0060.231 -73.6620.324 22.3260.190 26.8860.364 208.1290.490 48.2900.256
56336.183459 81.7310.096 -70.9810.198 23.3030.067 23.4460.197 198.2380.202 37.1700.109
56341.198233 79.8380.062 -69.1680.183 23.8650.039 22.0240.150 207.1090.090 41.9060.087
56345.884105 82.5070.040 -67.5210.229 25.7960.024 18.5560.164 212.9470.069 33.6730.105
56353.018823 85.3510.055 -64.8090.385 26.4210.034 17.9060.263 220.3140.401 8.9330.117
56360.668713 86.4360.029 -60.4610.215 26.8800.017 18.3620.125 197.6210.196 -4.5600.045
56365.601473 87.5270.019 -57.7680.296 26.4430.013 16.6130.132 133.6220.300 -17.2670.049
56369.951021 85.3610.029 -60.5480.152 25.4210.018 20.1820.093 146.5360.106 -24.4660.045
56375.100519 82.6300.101 -67.9480.150 24.1830.066 26.1100.155 154.4210.102 -23.3940.050
56380.272754 77.9110.246 -72.5380.222 20.5100.183 31.2180.206 158.4920.122 -25.7270.081
56387.350166 82.6010.104 -68.5870.161 23.5190.070 25.5170.164 140.1320.147 -30.3620.062
56394.302243 73.6430.854 -78.8540.394 15.9560.568 33.4150.319 139.1200.196 -36.2860.202
56402.891002 85.0660.498 -73.7590.544 24.5700.454 29.2880.849 116.9640.324 -62.4680.154
56410.718694 79.5381.771 -81.0520.377 12.3991.618 38.0900.421 140.4461.752 -68.6131.076
56421.983368 113.0740.592 -77.7560.051 10.2770.181 34.1870.041 204.2340.224 -110.2440.177
Table 3: Continued From Previous Page.
HJD E Type HJD E Type
(+24 00000) (day) (day) (+24 00000) (day) (day)
54965.02435 5.0 I 0.00087 0.00010 56094.39675 523.5 II 0.00026 -0.00052
54966.11283 5.5 II 0.00027 -0.00049 56095.48623 524.0 I 0.00066 -0.00012
54967.20248 6.0 I 0.00084 0.00008 56096.57528 524.5 II 0.00064 -0.00015
54968.29097 6.5 II 0.00025 -0.00051 56097.66474 525.0 I 0.00102 0.00023
54969.38064 7.0 I 0.00085 0.00009 56098.75353 525.5 II 0.00073 -0.00005
54970.46903 7.5 II 0.00016 -0.00060 56099.84287 526.0 I 0.00100 0.00021
54971.55879 8.0 I 0.00084 0.00008 56100.93176 526.5 II 0.00081 0.00002
54972.64723 8.5 II 0.00020 -0.00056 56103.10961 527.5 II 0.00050 -0.00029
54973.73698 9.0 I 0.00088 0.00012 56104.19889 528.0 I 0.00071 -0.00008
54974.82533 9.5 II 0.00015 -0.00061 56105.28786 528.5 II 0.00059 -0.00019
54975.91504 10.0 I 0.00078 0.00002 56107.46594 529.5 II 0.00052 -0.00027
54977.00355 10.5 II 0.00022 -0.00055 56108.55525 530.0 I 0.00076 -0.00003
54978.09316 11.0 I 0.00075 -0.00002 56109.64387 530.5 II 0.00030 -0.00048
54979.18175 11.5 II 0.00026 -0.00050 56110.73329 531.0 I 0.00064 -0.00014
54980.27132 12.0 I 0.00076 -0.00001 56111.82235 531.5 II 0.00063 -0.00016
54981.35952 12.5 II -0.00013 -0.00089 56112.91161 532.0 I 0.00081 0.00002
54982.44953 13.0 I 0.00082 0.00005 56114.00021 532.5 II 0.00033 -0.00046
54983.53796 13.5 II 0.00016 -0.00060 56115.08982 533.0 I 0.00087 0.00008
54984.62767 14.0 I 0.00080 0.00003 56116.17843 533.5 II 0.00040 -0.00039
54985.71626 14.5 II 0.00031 -0.00045 56117.26792 534.0 I 0.00081 0.00003
54986.80584 15.0 I 0.00081 0.00005 56118.35633 534.5 II 0.00014 -0.00065
54987.89440 15.5 II 0.00030 -0.00047 56119.44608 535.0 I 0.00082 0.00003
54988.98392 16.0 I 0.00074 -0.00003 56120.53446 535.5 II 0.00012 -0.00066
54990.07264 16.5 II 0.00038 -0.00039 56121.62441 536.0 I 0.00099 0.00020
54991.16211 17.0 I 0.00077 0.00001 56130.33682 540.0 I 0.00078 -0.00001
54992.25093 17.5 II 0.00052 -0.00024 56131.42608 540.5 II 0.00097 0.00018
54993.34034 18.0 I 0.00084 0.00008 56132.51494 541.0 I 0.00076 -0.00003
54994.42910 18.5 II 0.00054 -0.00023 56133.60463 541.5 II 0.00136 0.00057
54995.51851 19.0 I 0.00087 0.00010 56134.69317 542.0 I 0.00083 0.00004
54996.60731 19.5 II 0.00059 -0.00018 56135.78257 542.5 II 0.00115 0.00036
54997.69664 20.0 I 0.00084 0.00007 56136.87132 543.0 I 0.00082 0.00003
55003.14196 22.5 II 0.00077 0.00001 56137.96091 543.5 II 0.00133 0.00055
55004.23107 23.0 I 0.00081 0.00004 56140.13881 544.5 II 0.00108 0.00030
55005.32020 23.5 II 0.00086 0.00010 56141.22765 545.0 I 0.00084 0.00006
55006.40914 24.0 I 0.00072 -0.00004 56142.31718 545.5 II 0.00130 0.00051
55007.49835 24.5 II 0.00085 0.00009 56143.40575 546.0 I 0.00079 0.00000
55008.58741 25.0 I 0.00084 0.00008 56144.49537 546.5 II 0.00133 0.00055
55009.67650 25.5 II 0.00085 0.00009 56145.58397 547.0 I 0.00085 0.00007
55010.76541 26.0 I 0.00069 -0.00008 56146.67353 547.5 II 0.00134 0.00055
55011.85469 26.5 II 0.00089 0.00012 56147.76212 548.0 I 0.00085 0.00007
55012.94375 27.0 I 0.00087 0.00011 56148.85144 548.5 II 0.00110 0.00031
55014.03282 27.5 II 0.00087 0.00010 56149.94004 549.0 I 0.00061 -0.00017
55017.30026 29.0 I 0.00107 0.00031 56151.02955 549.5 II 0.00105 0.00026
55018.38930 29.5 II 0.00103 0.00027 56152.11832 550.0 I 0.00075 -0.00004
55019.47810 30.0 I 0.00076 -0.00001 56153.20745 550.5 II 0.00080 0.00001
55020.56717 30.5 II 0.00075 -0.00002 56154.29642 551.0 I 0.00069 -0.00010
55021.65630 31.0 I 0.00080 0.00004 56155.38562 551.5 II 0.00081 0.00002
55022.74570 31.5 II 0.00113 0.00036 56156.47451 552.0 I 0.00062 -0.00016
55023.83455 32.0 I 0.00089 0.00013 56157.56410 552.5 II 0.00114 0.00035
55024.92399 32.5 II 0.00127 0.00050 56158.65273 553.0 I 0.00069 -0.00010
55026.01283 33.0 I 0.00103 0.00026 56159.74244 553.5 II 0.00132 0.00053
55027.10204 33.5 II 0.00116 0.00040 56160.83105 554.0 I 0.00085 0.00006
55028.19091 34.0 I 0.00095 0.00019 56161.92067 554.5 II 0.00140 0.00062
55029.28016 34.5 II 0.00112 0.00036 56163.00923 555.0 I 0.00088 0.00009
55030.36898 35.0 I 0.00087 0.00010 56164.09944 555.5 II 0.00201 0.00122
55031.45871 35.5 II 0.00151 0.00075 56165.18740 556.0 I 0.00090 0.00011
55032.54732 36.0 I 0.00105 0.00029 56166.27785 556.5 II 0.00227 0.00129
55463.82153 234.0 I 0.00072 -0.00006 56167.36551 557.0 I 0.00085 0.00007
55464.91111 234.5 II 0.00121 0.00044 56168.45620 557.5 II 0.00247 0.00118
Table 4: Minima times and and residuals.
HJD E Type HJD E Type
(+24 00000) (day) (day) (+24 00000) (day) (day)
55465.99971 235.0 I 0.00073 -0.00004 56170.63419 558.5 II 0.00230 0.00121
55467.08912 235.5 II 0.00107 0.00029 56171.72156 559.0 I 0.00059 -0.00020
55468.17804 236.0 I 0.00091 0.00014 56172.81225 559.5 II 0.00220 0.00112
55469.26714 236.5 II 0.00093 0.00016 56173.89971 560.0 I 0.00058 -0.00020
55470.35608 237.0 I 0.00079 0.00002 56174.99024 560.5 II 0.00204 0.00125
55471.44513 237.5 II 0.00077 0.00000 56176.07788 561.0 I 0.00061 -0.00018
55472.53418 238.0 I 0.00075 -0.00003 56177.16833 561.5 II 0.00198 0.00119
55473.62329 238.5 II 0.00078 0.00000 56178.25612 562.0 I 0.00069 -0.00010
55474.71230 239.0 I 0.00071 -0.00006 56179.34637 562.5 II 0.00186 0.00107
55475.80135 239.5 II 0.00068 -0.00009 56180.43428 563.0 I 0.00070 -0.00009
55476.89046 240.0 I 0.00071 -0.00006 56181.52434 563.5 II 0.00168 0.00090
55477.97947 240.5 II 0.00065 -0.00013 56182.61245 564.0 I 0.00072 -0.00007
55479.06863 241.0 I 0.00073 -0.00005 56183.70257 564.5 II 0.00176 0.00097
55480.15761 241.5 II 0.00064 -0.00014 56184.79061 565.0 I 0.00072 -0.00007
55481.24674 242.0 I 0.00069 -0.00008 56185.88092 565.5 II 0.00196 0.00117
55482.33599 242.5 II 0.00086 0.00009 56186.96877 566.0 I 0.00072 -0.00007
55483.42492 243.0 I 0.00072 -0.00006 56188.05913 566.5 II 0.00201 0.00122
55484.51395 243.5 II 0.00067 -0.00011 56189.14684 567.0 I 0.00064 -0.00015
55485.60292 244.0 I 0.00056 -0.00021 56190.23745 567.5 II 0.00218 0.00139
55486.69209 244.5 II 0.00065 -0.00012 56191.32501 568.0 I 0.00065 -0.00014
55487.78109 245.0 I 0.00057 -0.00021 56192.41549 568.5 II 0.00205 0.00127
55488.87019 245.5 II 0.00060 -0.00018 56193.50316 569.0 I 0.00065 -0.00014
55489.95926 246.0 I 0.00059 -0.00019 56194.59356 569.5 II 0.00198 0.00119
55491.04833 246.5 II 0.00058 -0.00019 56195.68133 570.0 I 0.00067 -0.00012
55492.13740 247.0 I 0.00058 -0.00020 56196.77145 570.5 II 0.00170 0.00092
55493.22685 247.5 II 0.00095 0.00018 56197.85947 571.0 I 0.00065 -0.00014
55494.31591 248.0 I 0.00093 0.00016 56198.94932 571.5 II 0.00143 0.00064
55495.40462 248.5 II 0.00056 -0.00021 56200.03761 572.0 I 0.00064 -0.00015
55496.49414 249.0 I 0.00101 0.00024 56201.12734 572.5 II 0.00129 0.00051
55497.58276 249.5 II 0.00055 -0.00023 56202.21555 573.0 I 0.00042 -0.00037
55498.67235 250.0 I 0.00106 0.00029 56203.30550 573.5 II 0.00129 0.00051
55499.76086 250.5 II 0.00049 -0.00028 56206.57202 575.0 I 0.00059 -0.00020
55500.85058 251.0 I 0.00114 0.00036 56207.66137 575.5 II 0.00086 0.00007
55501.93904 251.5 II 0.00052 -0.00026 56208.75022 576.0 I 0.00063 -0.00016
55503.02849 252.0 I 0.00090 0.00012 56209.83947 576.5 II 0.00080 0.00001
55504.11689 252.5 II 0.00021 -0.00056 56210.92835 577.0 I 0.00060 -0.00019
55505.20659 253.0 I 0.00084 0.00007 56212.01750 577.5 II 0.00068 -0.00011
55506.29519 253.5 II 0.00037 -0.00041 56213.10657 578.0 I 0.00067 -0.00012
55507.38477 254.0 I 0.00087 0.00010 56214.19565 578.5 II 0.00068 -0.00011
55508.47340 254.5 II 0.00042 -0.00036 56215.28471 579.0 I 0.00065 -0.00014
55509.56292 255.0 I 0.00086 0.00009 56216.37392 579.5 II 0.00079 0.00000
55510.65152 255.5 II 0.00038 -0.00040 56217.46297 580.0 I 0.00076 -0.00003
55511.74103 256.0 I 0.00081 0.00004 56218.55226 580.5 II 0.00097 0.00019
55512.82957 256.5 II 0.00028 -0.00049 56219.64109 581.0 I 0.00073 -0.00006
55513.91917 257.0 I 0.00080 0.00003 56220.73113 581.5 II 0.00169 0.00091
55515.00805 257.5 II 0.00060 -0.00017 56221.81938 582.0 I 0.00086 0.00007
55516.09758 258.0 I 0.00106 0.00029 56222.90953 582.5 II 0.00194 0.00115
55517.18634 258.5 II 0.00074 -0.00004 56223.99735 583.0 I 0.00068 -0.00011
55518.27576 259.0 I 0.00108 0.00030 56225.08749 583.5 II 0.00175 0.00096
55519.36441 259.5 II 0.00066 -0.00012 56226.17567 584.0 I 0.00084 0.00005
55520.45386 260.0 I 0.00102 0.00025 56227.26570 584.5 II 0.00180 0.00101
55521.54259 260.5 II 0.00068 -0.00009 56228.35365 585.0 I 0.00067 -0.00012
55522.63202 261.0 I 0.00104 0.00026 56229.44406 585.5 II 0.00200 0.00122
55524.81008 262.0 I 0.00094 0.00016 56230.53187 586.0 I 0.00073 -0.00006
55525.89886 262.5 II 0.00064 -0.00013 56231.62219 586.5 II 0.00198 0.00120
55526.98821 263.0 I 0.00091 0.00014 56232.71007 587.0 I 0.00079 0.00000
55528.07694 263.5 II 0.00057 -0.00021 56233.80040 587.5 II 0.00203 0.00124
55529.16618 264.0 I 0.00074 -0.00004 56234.88819 588.0 I 0.00075 -0.00004
55530.25517 264.5 II 0.00065 -0.00013 56235.97836 588.5 II 0.00184 0.00105
Table 4: Continued From Previous Page.
HJD E Type HJD E Type
(+24 00000) (day) (day) (+24 00000) (day) (day)
55531.34426 265.0 I 0.00066 -0.00011 56237.06635 589.0 I 0.00075 -0.00004
55532.43367 265.5 II 0.00099 0.00021 56239.24456 590.0 I 0.00081 0.00002
55533.52250 266.0 I 0.00075 -0.00003 56240.33416 590.5 II 0.00133 0.00054
55534.61189 266.5 II 0.00105 0.00028 56241.42267 591.0 I 0.00077 -0.00002
55535.70051 267.0 I 0.00060 -0.00017 56242.51185 591.5 II 0.00087 0.00008
55536.79010 267.5 II 0.00111 0.00033 56243.60086 592.0 I 0.00080 0.00001
55537.87868 268.0 I 0.00061 -0.00016 56244.69066 592.5 II 0.00152 0.00074
55538.96820 268.5 II 0.00105 0.00028 56245.77906 593.0 I 0.00085 0.00006
55540.05691 269.0 I 0.00069 -0.00009 56252.31346 596.0 I 0.00078 -0.00001
55541.14646 269.5 II 0.00116 0.00039 56253.40336 596.5 II 0.00161 0.00082
55542.23516 270.0 I 0.00079 0.00002 56254.49177 597.0 I 0.00094 0.00015
55543.32464 270.5 II 0.00119 0.00041 56255.58137 597.5 II 0.00147 0.00068
55545.50269 271.5 II 0.00108 0.00031 56256.66998 598.0 I 0.00100 0.00021
55546.59151 272.0 I 0.00082 0.00005 56257.75957 598.5 II 0.00151 0.00072
55547.68109 272.5 II 0.00133 0.00056 56258.84814 599.0 I 0.00100 0.00021
55548.76952 273.0 I 0.00069 -0.00009 56259.93743 599.5 II 0.00122 0.00043
55549.85912 273.5 II 0.00121 0.00043 56261.02635 600.0 I 0.00106 0.00027
55550.94780 274.0 I 0.00080 0.00003 56262.11576 600.5 II 0.00139 0.00060
55552.03744 274.5 II 0.00137 0.00060 56263.20444 601.0 I 0.00099 0.00020
55568.37258 282.0 I 0.00035 -0.00043 56264.29344 601.5 II 0.00091 0.00013
55569.46246 282.5 II 0.00115 0.00038 56265.38255 602.0 I 0.00095 0.00016
55570.55098 283.0 I 0.00060 -0.00017 56266.47120 602.5 II 0.00052 -0.00027
55571.64050 283.5 II 0.00104 0.00027 56267.56037 603.0 I 0.00061 -0.00018
55572.72924 284.0 I 0.00070 -0.00007 56269.73890 604.0 I 0.00099 0.00020
55573.81852 284.5 II 0.00091 0.00014 56270.82777 604.5 II 0.00079 0.00000
55574.90753 285.0 I 0.00084 0.00007 56271.91699 605.0 I 0.00092 0.00013
55575.99651 285.5 II 0.00075 -0.00003 56273.00502 605.5 II -0.00012 -0.00091
55577.08546 286.0 I 0.00062 -0.00016 56274.09503 606.0 I 0.00081 0.00002
55578.17461 286.5 II 0.00069 -0.00009 56275.18293 606.5 II -0.00037 -0.00116
55579.26374 287.0 I 0.00075 -0.00003 56276.27301 607.0 I 0.00064 -0.00016
55580.35269 287.5 II 0.00061 -0.00016 56277.36075 607.5 II -0.00070 -0.00120
55581.44198 288.0 I 0.00083 0.00005 56278.45114 608.0 I 0.00062 -0.00017
55582.53087 288.5 II 0.00064 -0.00013 56279.53911 608.5 II -0.00050 -0.00119
55583.62008 289.0 I 0.00078 0.00000 56280.62913 609.0 I 0.00045 -0.00034
55584.70916 289.5 II 0.00078 0.00000 56281.71735 609.5 II -0.00041 -0.00110
55585.79818 290.0 I 0.00072 -0.00006 56282.80722 610.0 I 0.00039 -0.00040
55586.88733 290.5 II 0.00080 0.00002 56283.89567 610.5 II -0.00025 -0.00104
55587.97639 291.0 I 0.00077 -0.00001 56284.98542 611.0 I 0.00043 -0.00036
55589.06548 291.5 II 0.00078 0.00001 56286.07420 611.5 II 0.00014 -0.00065
55590.15453 292.0 I 0.00076 -0.00002 56287.16371 612.0 I 0.00057 -0.00022
55591.24364 292.5 II 0.00079 0.00002 56288.25230 612.5 II 0.00008 -0.00071
55592.33269 293.0 I 0.00076 -0.00001 56289.34188 613.0 I 0.00059 -0.00020
55593.42162 293.5 II 0.00062 -0.00015 56290.43065 613.5 II 0.00027 -0.00052
55597.77804 295.5 II 0.00073 -0.00005 56291.52004 614.0 I 0.00059 -0.00020
55598.86729 296.0 I 0.00091 0.00013 56292.60883 614.5 II 0.00030 -0.00049
55599.95600 296.5 II 0.00053 -0.00025 56293.69826 615.0 I 0.00066 -0.00013
55601.04512 297.0 I 0.00058 -0.00019 56294.78707 615.5 II 0.00038 -0.00041
55602.13419 297.5 II 0.00057 -0.00020 56295.87649 616.0 I 0.00072 -0.00007
55603.22334 298.0 I 0.00065 -0.00013 56296.96556 616.5 II 0.00072 -0.00007
55604.31254 298.5 II 0.00077 -0.00001 56298.05474 617.0 I 0.00082 0.00003
55605.40170 299.0 I 0.00085 0.00008 56299.14364 617.5 II 0.00064 -0.00015
55606.49095 299.5 II 0.00103 0.00025 56300.23284 618.0 I 0.00077 -0.00003
55607.57990 300.0 I 0.00090 0.00012 56301.32203 618.5 II 0.00088 0.00009
55608.66880 300.5 II 0.00072 -0.00006 56302.41106 619.0 I 0.00083 0.00004
55609.75798 301.0 I 0.00082 0.00004 56303.50006 619.5 II 0.00075 -0.00004
55610.84706 301.5 II 0.00082 0.00005 56305.67817 620.5 II 0.00071 -0.00008
55611.93610 302.0 I 0.00079 0.00001 56306.76724 621.0 I 0.00071 -0.00008
55613.02544 302.5 II 0.00105 0.00028 56307.85628 621.5 II 0.00067 -0.00012
55614.11450 303.0 I 0.00103 0.00025 56308.94545 622.0 I 0.00076 -0.00003
Table 4: Continued From Previous Page.
HJD E Type HJD E Type
(+24 00000) (day) (day) (+24 00000) (day) (day)
55615.20329 303.5 II 0.00075 -0.00003 56310.03424 622.5 II 0.00048 -0.00031
55616.29270 304.0 I 0.00108 0.00031 56322.01451 628.0 I 0.00089 0.00010
55617.38160 304.5 II 0.00090 0.00013 56323.10328 628.5 II 0.00059 -0.00020
55618.47086 305.0 I 0.00109 0.00031 56324.19265 629.0 I 0.00088 0.00009
55619.55956 305.5 II 0.00071 -0.00006 56325.28146 629.5 II 0.00062 -0.00017
55620.64880 306.0 I 0.00087 0.00010 56326.37083 630.0 I 0.00091 0.00012
55621.73779 306.5 II 0.00078 0.00001 56327.45948 630.5 II 0.00048 -0.00031
55622.82702 307.0 I 0.00093 0.00016 56328.54903 631.0 I 0.00096 0.00017
55623.91617 307.5 II 0.00100 0.00023 56329.63763 631.5 II 0.00048 -0.00031
55625.00496 308.0 I 0.00072 -0.00006 56330.72720 632.0 I 0.00097 0.00018
55626.09425 308.5 II 0.00093 0.00016 56331.81633 632.5 II 0.00102 0.00023
55627.18316 309.0 I 0.00077 -0.00001 56332.90532 633.0 I 0.00093 0.00014
55628.27267 309.5 II 0.00120 0.00043 56333.99389 633.5 II 0.00043 -0.00036
55629.36126 310.0 I 0.00071 -0.00007 56335.08329 634.0 I 0.00075 -0.00004
55630.45087 310.5 II 0.00125 0.00047 56336.17220 634.5 II 0.00058 -0.00021
55631.53952 311.0 I 0.00082 0.00004 56337.26140 635.0 I 0.00071 -0.00008
55632.62923 311.5 II 0.00145 0.00067 56338.35037 635.5 II 0.00059 -0.00020
55633.71768 312.0 I 0.00082 0.00004 56339.43967 636.0 I 0.00083 0.00004
55634.80743 312.5 II 0.00150 0.00072 56340.52819 636.5 II 0.00026 -0.00053
56015.98447 487.5 II 0.00154 0.00075 56341.61783 637.0 I 0.00083 0.00003
56017.07249 488.0 I 0.00048 -0.00031 56342.70668 637.5 II 0.00060 -0.00019
56018.16265 488.5 II 0.00156 0.00078 56343.79597 638.0 I 0.00081 0.00002
56019.25054 489.0 I 0.00037 -0.00042 56344.88476 638.5 II 0.00053 -0.00026
56020.34079 489.5 II 0.00155 0.00076 56345.97409 639.0 I 0.00078 -0.00001
56021.42873 490.0 I 0.00041 -0.00038 56347.06295 639.5 II 0.00056 -0.00023
56022.51873 490.5 II 0.00133 0.00054 56348.15228 640.0 I 0.00081 0.00002
56023.60686 491.0 I 0.00039 -0.00040 56349.24112 640.5 II 0.00058 -0.00021
56024.69676 491.5 II 0.00121 0.00042 56350.33040 641.0 I 0.00078 -0.00001
56025.78520 492.0 I 0.00057 -0.00021 56351.41928 641.5 II 0.00059 -0.00020
56026.87496 492.5 II 0.00125 0.00047 56352.50856 642.0 I 0.00078 -0.00001
56027.96337 493.0 I 0.00059 -0.00020 56353.59744 642.5 II 0.00059 -0.00020
56029.05319 493.5 II 0.00133 0.00054 56354.68667 643.0 I 0.00074 -0.00005
56030.14102 494.0 I 0.00009 -0.00070 56355.77550 643.5 II 0.00050 -0.00029
56031.23087 494.5 II 0.00086 0.00008 56356.86478 644.0 I 0.00070 -0.00009
56032.31969 495.0 I 0.00060 -0.00018 56357.95469 644.5 II 0.00153 0.00074
56033.40903 495.5 II 0.00086 0.00008 56360.13205 645.5 II 0.00073 -0.00006
56034.49794 496.0 I 0.00070 -0.00009 56361.22130 646.0 I 0.00091 0.00012
56035.58742 496.5 II 0.00109 0.00031 56362.31014 646.5 II 0.00067 -0.00012
56036.67622 497.0 I 0.00082 0.00003 56363.39936 647.0 I 0.00081 0.00002
56037.76534 497.5 II 0.00086 0.00007 56364.48817 647.5 II 0.00054 -0.00025
56038.85417 498.0 I 0.00061 -0.00017 56365.57750 648.0 I 0.00080 0.00001
56039.94305 498.5 II 0.00042 -0.00036 56366.66574 648.5 II -0.00004 -0.00083
56041.03229 499.0 I 0.00059 -0.00020 56367.75564 649.0 I 0.00078 -0.00001
56042.12093 499.5 <