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Revista mexicana de astronomía y astrofísica

Print version ISSN 0185-1101

Rev. mex. astron. astrofis vol.55 n.1 México Apr. 2019

 

Articles

On the chromospheric activity nature of a low-mass close binary: KIC 12004834

E. Yoldaş1 

H. A. Dal1 

1 Department of Astronomy and Space Sciences, University of Ege, Bornova, İzmir, Turkey.

ABSTRACT:

We study the nature of the chromospheric activity of an eclipsing binary KIC 12004834, using Kepler data. We analyse the light curve of the system, the sinusoidal variations at out-of-eclipses and detected flare events. The secondary component’s temperature is found to be 4001±11 K, the mass ratio is 0.743±0.001, and the orbital inclination is 75º.89±0º.03. The analysis indicates a stellar spot effect on the variation. Moreover, the OPEA model has been derived over 149 flares. The saturation level called P lateau value, is found to be 2.093±0.236 s. The flare number per hour (known as flare frequency N1) is found to be 0.06644 h-1, while the flare-equivalent duration per hour (known as flare frequency N2) is found to be 0.59 second/hour. According to these results, KIC 12004834 is a very low-mass close binary system with high level of flare activity.

Key Words: binaries; eclipsing; methods; data analysis; stars; flare; stars; individual; KIC 12004834; stars; low-mass; techniques; photometric

RESUMEN:

Estudiamos la actividad cromosférica de la binaria eclipsante KIC 12004834 utilizando datos de Kepler. Analizamos la curva de luz y la variación sinusoidal fuera de eclipse, y detectamos ráfagas. Encontramos que la temperatura de la secundaria es de 4001±11 K, que el cociente de masas es 0.743±0.001 y la inclinación orbital es 75º.89±0º.03. El análisis indica que hay un efecto de manchas en la variabilidad. Obtenemos el modelo OPEA para 149 ráfagas. El nivel de saturación, llamado P lateau tiene un valor de 2.093±0.236 s. El número de ráfagas por hora, conocido como la frecuencia de ráfagas N1, es 0.06644 h-1, mientras que la duración de la emisión equivalente a las ráfagas, conocida como la frecuencia N2 es 0.59 s/hora. De acuerdo con estos resultados, KIC 12004834 es una binaria cerrada, de muy baja masa, y con frecuentes ráfagas.

1. Introduction

The nature of a low-mass eclipsing binary KIC 12004834 with 14m.7180 in Kepler band is studied here. KIC 12004834, whose nature is different from the classical UV Ceti type stars of spectral type dMe due to its being a binary system, was observed by Watson (2006) for the first time. Magnitudes of the system were given as J = 12m.007, H = 11m.407, K = 11m.170 by Cutri et al. (2003). Although there are no further studies in the literature, some estimated parameters of the system were given by Coughlin et al. (2011), using calibrations to derive the parameters. Taking Teff = 3576 K, the orbital inclination (i) was found to be 72◦.47, while the masses were found to be M1 = 0.48 M and M2 = 0.34 M. In addition, the radii were computed as R1 = 0.48 R and R2 = 0.35 R. Like Coughlin et al. (2011), taking Teff = 3576 K, Slawson et al. (2011) found log(g) as 4.217 cm/s2. There are several approaches to obtain the temperatures of its components. Coughlin et al. (2011) gave the temperatures as T1 =3620 K for the primary and T 2 =3468 K for the secondary. Armstrong et al. (2014) gave T 1 =3511 K for the primary and T 2 =3512 K for the secondary.

KIC 12004834 was mentioned as a chromospherically active system for the first time by Debosscher et al. (2011). In addition, a dominant flare activity was also reported by Balona (2015). Considering the estimated parameters of the system; KIC 12004834 is a low-mass close binary with a chromospherically active component. This makes the system an important object in the astrophysical sense. This is because the system exhibits not only spots, but also flare activity. A flaring star being a component of an eclipsing binary system is a rare phenomenon among the UV Ceti type stars. However, the red dwarf abundance is about 65% in our Galaxy, and seventy-five percent of them exhibit flare activity (Rodonó 1986). Thus, almost half of the stars in our galaxy should exhibit flare activity. The number of eclipsing binaries with a flaring component is nowadays increasing, thanks to space missions such the Kepler and Corot satellites.

Because of its effects on stellar evolution, flare activity is very important in astrophysics in terms of its sources and mechanism. Although the first flare was observed on the solar surface by R. C. Carrington and R. Hodgson on September 1, 1859 (Carrington 1859; Hodgson 1859), there are still unsolved problems, for instance, the different mass loss rate seen among stars of different spectral types, the different flare energy levels detected for stars of different spectral types (Gershberg & Shakhovskaya 1983; Haisch et al. 1991; Gershberg 2005; Benz 2008).

At this point, photometric data accumulated from the eclipsing binaries with a chromospherically active component can give some clues for these problems. Recently, several eclipsing binary stars, where one of the components is chromospherically active have been discovered by the Kepler Mission (Borucki et al. 2010; Koch et al. 2010; Caldwell et al. 2010). Most of them have an interesting nature. These chromospherically active components exhibit flare events and also rapidly evolving stellar spots (Balona 2015). Although the light variations due to the cool spots have remarkably small amplitudes, their shapes change over short time intervals, from one cycle to the next one (Yoldaş & Dal 2016, 2017; Özdarcan et al. 2017).

In this study, the variations of the times of minima are analysed (see § 2.1). The light curve of KIC 12004834 is studied (§ 2.2) for the first time in the literature in order to find the physical properties of the components. Then, the flares occurring on the chromospherically active component are used to model the nature of the magnetic activity of the system as described in § 2.3. The results obtained are given in § 3, comparing the active component with its analogue discovered in the Kepler Mission.

2. Data and analyses

The data analysed in this study are the detrended short cadence data from the Kepler Mission Database (Borucki et al. 2010; Koch et al. 2010; Caldwell et al. 2010; Slawson et al. 2011; Matijevič et al. 2012). In the analyses, the data of quarters Q10.1, Q10.2 and Q10.3 are used (Murphy 2012; Murphy et al. 2013), whose quality and sensitivity are the highest ones ever reached (Jenkins et al. 2010a,b).

After removing all the observations with large errors from the data, and using the ephemeris taken from the Kepler Mission database, the phases are computed for all data, and the obtained light curves are shown in Figure 1. Because of the study’s format, the detrended short cadence data were used in the analysis instead of those of the long cadence. The data were arranged in suitable formats for different analyses, such as the light curve analysis and the flare event calculations.

Fig. 1 Whole light curve of KIC 12004834 obtained from the data taken from the Kepler Mission database. In the bottom panel, the light curve is plotted along the orbital cycle with the flare activity, while it is plotted without the flare activity in the upper panel. 

2.1. Orbital Period Variation

The times of minima in the light curves were computed from short cadence data without any corrections. We used just short cadence data, because the system has a very short orbital period. The whole shape of the minima is not seen in the long cadence data. The minima times were computed with a script according to the method described by Kwee & van Woerden (1956). The (OC) I residuals were determined for each minimum time. Examining the times of minima indicated that some of them have very large errors. These errors are sometimes caused by scattered observations; while some of them are caused by the flare activity occurring during these minima. All the minima times with large errors were removed from the (OC) data. Finally, 688 minima times were determined in the analyses.

Using the epoch of 2455002.041 and the orbital period of 0.2623168 day given in the Kepler Eclipsing Binary Catalogue1 by Slawson et al. (2011), we computed the (OC) I residuals. Then, using the Least-Squares method, we applied a linear correction to these residuals. The linear correction revealed that the (OC) I residuals had a linear trend with a small slope; the distribution of the (OC) I residuals seems to be linear, needing just a zero point correction. After the linear correction, we obtained the new ephemerides given in equation (1) and the (OC) II residuals:

JD(Bary.)=2455002.04164(14)+0d.262317(1)×E. (1)

The (OC) I and (OC) II residuals are listed in Table 1. In the table, the minima times, cycles, the minima type, (OC)I and (OC) II residuals are listed, respectively. An interesting variation is seen in the (OC) II residuals plotted versus time in Figure 2.

Fig. 2 The variations of time of minimum residuals of (OC) I and (OC) II obtained by applying a linear correction. In the bottom panel, the filled blue circles represent the primary minima; the filled red circles represent the secondary minima. In the upper panel all the residuals are plotted with filled black circles, while the red line represents a linear fit. The color figure can be viewed online. 

According to the studies of Tran et al. (2013) on contact binaries, if one of the components of an eclipsing binary system exhibits stellar spot activity on its surface, there must be a separation between the (OC) II residuals of the primary and secondary minima. Debosscher et al. (2011) and Balona (2015) mentioned that the system exhibits chromospheric activity. In the case of KIC 12004834 considered as a very close binary, we firstly examined whether there was any separation in the primary and secondary minimum (OC) II residuals. As shown in the upper panel of Figure 2, there is an evident separation between the primary and secondary minima residuals. Secondly, the analysis indicates that the best fit is derived by a linear function for the distribution of (OC) I . The obtained fit is shown in the lower panel of is Figure 2.

2.2. Light Curve Analysis

The light curve of KIC 12004834 was analyzed by the PHOEBE V.0.32 software (Prša & Zwitter 2005) which depends on the 2003 version of the Wilson-Devinney Code (Wilson & Devinney 1971; Wilson 1990) to compute the physical parameters of each component. In the analyses, the averaged data were computed phase by phase with an interval of 0.001 to decrease the scattering. Although several modes were tried in the light curve analyses, astrophysically acceptable parameters were obtained only for the detached system mode.

The PHOEBE V.0.32, needs a temperature value for the primary component. We determined its temperature from the J HK brightness given by Cutri et al. (2003). The de-reddened colors were found to be (H − K)o = 0m.252 and (J − K)o = 0m.629. Then a temperature value of 4220±20 K corresponding to the de-reddened colours was obtained by using the calibrations given by Tokunaga (2000). We accepted this value as the primary component temperature. The temperature of the secondary component was taken as an adjustable free parameter. In the analyses, some coefficients, such as the albedos (A 1 and A 2), the gravity-darkening coefficients (g 1 and g 2) and the limb-darkening coefficients (x 1 and x 2), were taken from the tables given by Lucy (1967); Rucinski (1969); Van Hamme (1993), considering the possible temperatures of both components. The rest of the parameters, such as the dimensionless potentials (Ω1 and Ω2), the fractional luminosity (L 1) of the primary component, the inclination (i) and the mass ratio (q) of the system, were taken as adjustable free parameters.

The computed values of the free parameters are tabulated in Table 2, while the synthetic light curve derived by these parameters is shown in Figure 3. As the table shows, some errors are smaller than the expected values. However, the errors given in the table were computed by the PHOEBE V.0.32, depending on Taylor (1997). In fact the χ2 was computed as 3.15×10-3 from the Kepler short cadence data. The 3D model of Roche geometry obtained with these parameters is shown in Figure 4.

Table 2 Parameters obtained from the light curve analysis of KIC 12004834 

Parameter Value
q 0.743 ± 0.001
i (º) 75.89 ± 0.03
T1 (K) 4220 (fixed)
T2 (K) 4001 ± 11
Ω1 4.308 ± 0.004
Ω2 5.485 ± 0.007
L1/L2 0.245 ± 0.067
g1, g2 0.32 (fixed)
A1, A2 0.32 (fixed)
x1,bol , x2,bol 0.377, 0.001 (fixed)
x1, x2 0.369, 0.001 (fixed)
< r1 > 0.287 ± 0.001
< r2 > 0.172 ± 0.001
Co-LatSpot(rad) 1.920 ± 0.004
LongSpot(rad) 1.710 ± 0.002
RSpot(rad) 0.244 ± 0.003
T f Spot 0.960 ± 0.001

Fig. 3 The light curve along the orbital cycle, from BJD 2455739.94 to 2455829.13. In the figure, the filled circles represent the observations, while the red smooth line represents the synthetic light curve. The color figure can be viewed online. 

Fig. 4 The 3D model of Roche geometry and spotted area distribution derived from the light curve analysis is shown for different phases, such as (a) 0.00, (b) 0.25, (c) 0.50, (d) 0.75. The color figure can be viewed online. 

It should be noted that we obtained a solution after some iterations in the detached system mode of the Wilson-Devinney Code (Wilson & Devinney 1971; Wilson 1990). Although the synthetic curve fitted the observations very well, it was revealed that it did not fit the observations around phase 0.27. To solve this mismatched part of synthetic light curve, we assumed that there is a spotted area on a component, considering the flare activity. We assumed that the spotted area was on the primary component. It could be assumed that the spotted star was the secondary component, which would lead to another acceptable solution.

The (BV) color indexes were computed as 1m.233 and 1m.329 for the primary and secondary components, respectively. The computed color indexes are in agreement with the values found by Walkowicz & Basri (2013). Considering these values, we determined the masses as 0.644M and 0.570M for primary and secondary components. Then, the semi-major axis of the system was found to be 1.84R (0.0086 AU) according to Kepler’s third law. With this value for the semi-major axis, the radius of the primary component was found to be 0.701R, while that of the secondary was 0.650R.

2.3. Flare Activity and the OPEA Model

The main subject of this paper is about flare activity in KIC 12004834. To demonstrate the nature of the flare activity occurring in a star with known photometric data, Dal & Evren (2010) and Dal (2012) described a simple way depending on the method mentioned by Gershberg (1972), which is just a smoothing out of the flares. However, apart from the flare activity, the light curve of KIC 12004834 exhibits other effects caused by both the geometrical nature of the components and the structures on them, such as eclipses and cool spots.

In order to determine and analyze the flares, first we removed the variations seen out-of-flares in the light curves. We follow the method of Dal & Evren (2010) for KIC 12004834. For this purpose, using the synthetic light curve derived from the light curve analyses described in the previous section, the residual data were obtained as a pre-whitened light curve, in which there was only flare activity variation. Following Dal (2012), 149 flares were detected from the available short cadence data. In the analyses, the synthetic light curve allowed us to fix the quiescent levels at the flare moment, which are shown in Figure 5.

Fig. 5 Four different samples for the flare light variations are shown. In the figure, the filled circles represent the observations, while the (red) lines represent the synthetic light curve obtained from the light curve analysis, which was taken as the quiescent levels for each flare. The color figure can be viewed online. 

Taking into account that the luminosity parameter enters in the energy calculations as described by Dal & Evren (2010, 2011), the equivalent duration parameter was computed for each flare, instead of its energy. According to the beginning and the end of a flare, the desired parameters, such as flare rise times (T r ), decay times (T d ), amplitudes of flare maxima, flare equivalent durations (P), were computed for each flare. The flare equivalent durations were computed by equation (2) taken from Gershberg (1972):

P=[(Iflare-I0)/I0]dt (2)

where I 0 is the flux of the star in the quiet state. As described above, the synthetic light curve derived by the light curve analysis was taken as I 0. I flare is the intensity observed at the moment of the flare. P is the flare-equivalent duration in the observing band. All the computed parameters are listed in Table 3 for these 149 flares. The general standard errors were computed by using the methods described by Taylor (1997) for the time scales such as flare rise and decay times.

Table 3 The flare parameters computed from KIC 12004834’s the available short cadence data in the Kepler mission database 

Tmax
(BJD-2450000)
P
(s)
Tr
(s)
Td
(s)
Tt
(s)
Amplitude
(Relative Flux)
55806.51506 0.762 58.846 ± 3.616 58.846 ± 3.616 117.692 ± 5.114 0.01180
55804.54459 0.471 58.846 ± 3.616 58.847 ± 3.616 117.693 ± 5.114 0.01221
55811.74873 0.896 58.847 ± 3.616 58.846 ± 3.616 117.693 ± 5.114 0.01720
55766.08239 0.745 58.848 ± 3.616 117.686 ± 5.114 176.534 ± 6.264 0.00989
55830.23880 1.240 58.845 ± 3.616 176.538 ± 6.264 235.383 ± 7.233 0.01713
55801.66075 1.066 117.702 ± 5.114 117.685 ± 5.114 235.386 ± 7.233 0.00827
55794.32581 1.117 58.855 ± 3.617 176.532 ± 6.263 235.387 ± 7.233 0.00929
55831.45798 1.880 117.700 ± 5.114 117.692 ± 5.114 235.392 ± 7.233 0.01391
55822.77794 1.137 58.846 ± 3.616 176.546 ± 6.264 235.392 ± 7.233 0.01338
55801.95704 2.098 58.846 ± 3.616 235.386 ± 7.233 294.233 ± 8.086 0.01416
55804.71215 1.290 117.684 ± 5.114 176.549 ± 6.264 294.233 ± 8.086 0.01001
55823.82889 1.051 58.846 ± 3.616 235.393 ± 7.233 294.240 ± 8.086 0.01032
55822.73912 1.633 117.692 ± 5.114 235.384 ± 7.233 353.076 ± 8.858 0.01343
55760.03465 0.632 58.848 ± 3.616 294.239 ± 8.086 353.087 ± 8.858 0.01071
55801.75679 2.621 58.838 ± 3.616 294.251 ± 8.087 353.088 ± 8.858 0.01381
55799.55611 1.312 117.702 ± 5.114 235.387 ± 7.233 353.089 ± 8.858 0.00642
55780.13399 1.711 117.703 ± 5.114 235.389 ± 7.233 353.092 ± 8.858 0.01102
55766.07149 0.848 117.704 ± 5.114 235.391 ± 7.233 353.094 ± 8.858 0.01050
55768.37983 2.922 58.857 ± 3.617 294.255 ± 8.087 353.112 ± 8.858 0.01705
55756.03029 1.168 117.687 ± 5.114 294.257 ± 8.087 411.944 ± 9.568 0.00935
55756.56293 1.245 117.696 ± 5.114 294.248 ± 8.086 411.944 ± 9.568 0.01079
55740.56791 2.973 117.696 ± 5.114 294.251 ± 8.087 411.947 ± 9.568 0.01556
55831.96472 4.468 58.846 ± 3.616 411.929 ± 9.568 470.775 ± 10.228 0.03456
55778.12332 2.165 117.694 ± 5.114 353.093 ± 8.858 470.787 ± 10.229 0.01238
55776.73927 1.898 117.695 ± 5.114 353.093 ± 8.858 470.788 ± 10.229 0.00963
55792.90704 6.883 117.694 ± 5.114 411.937 ± 9.568 529.631 ± 10.849 0.02718
55779.79002 9.266 117.694 ± 5.114 411.940 ± 9.568 529.634 ± 10.849 0.04237
55755.22928 3.861 176.552 ± 6.264 353.087 ± 8.858 529.640 ± 10.849 0.01210
55772.93588 0.849 117.704 ± 5.114 411.941 ± 9.568 529.644 ± 10.849 0.01032
55761.90026 1.219 117.704 ± 5.114 411.943 ± 9.568 529.648 ± 10.849 0.01217
55755.87908 1.132 294.248 ± 8.086 235.400 ± 7.233 529.648 ± 10.849 0.00573
55783.26307 0.793 58.856 ± 3.617 470.794 ± 10.229 529.650 ± 10.849 0.00322
55762.79935 1.244 117.704 ± 5.114 411.952 ± 9.568 529.655 ± 10.849 0.01132
55766.10282 2.214 294.247 ± 8.086 294.238 ± 8.086 588.485 ± 11.436 0.01453
55792.98265 2.377 117.693 ± 5.114 470.793 ± 10.229 588.486 ± 11.436 0.01164
55825.24424 2.172 117.700 ± 5.114 470.786 ± 10.229 588.486 ± 11.436 0.01260
55810.05753 1.166 176.557 ± 6.264 411.933 ± 9.568 588.489 ± 11.436 0.01357
55742.47985 1.287 176.545 ± 6.264 411.946 ± 9.568 588.490 ± 11.436 0.01300
55747.50593 1.506 117.696 ± 5.114 470.802 ± 10.229 588.498 ± 11.436 0.01536
55742.24282 3.543 294.241 ± 8.086 294.259 ± 8.087 588.500 ± 11.436 0.01447
55829.60128 2.781 117.692 ± 5.114 529.629 ± 10.849 647.322 ± 11.994 0.01256
55826.06293 3.057 176.546 ± 6.264 470.776 ± 10.228 647.323 ± 11.994 0.00379
55792.31311 1.336 176.540 ± 6.264 470.793 ± 10.229 647.333 ± 11.994 0.00897
55762.79186 3.297 117.686 ± 5.114 529.648 ± 10.849 647.334 ± 11.994 0.01830
55779.32482 2.116 117.703 ± 5.114 529.635 ± 10.849 647.337 ± 11.994 0.01469
55748.36688 1.896 235.392 ± 7.233 411.963 ± 9.568 647.355 ± 11.994 0.01075
55776.23933 3.682 117.694 ± 5.114 588.491 ± 11.436 706.185 ± 12.527 0.00924
55796.02792 3.817 117.703 ± 5.114 588.485 ± 11.436 706.188 ± 12.527 0.01597
55765.69482 5.587 235.408 ± 7.233 470.789 ± 10.229 706.197 ± 12.528 0.01827
55763.59627 1.525 117.704 ± 5.114 588.495 ± 11.436 706.199 ± 12.528 0.00532
55811.84817 9.222 176.539 ± 6.264 588.481 ± 11.436 765.020 ± 13.039 0.02482
55808.84242 3.326 176.548 ± 6.264 588.472 ± 11.436 765.020 ± 13.039 0.01629
55806.89444 2.641 294.241 ± 8.086 470.781 ± 10.229 765.022 ± 13.039 0.04012
55810.38923 3.032 176.548 ± 6.264 588.481 ± 11.436 765.029 ± 13.039 0.00910
55779.65108 6.755 176.551 ± 6.264 588.481 ± 11.436 765.031 ± 13.039 0.02747
55777.26170 2.436 58.847 ± 3.616 706.185 ± 12.527 765.032 ± 13.039 0.01427
55800.70583 1.053 176.549 ± 6.264 588.483 ± 11.436 765.032 ± 13.039 0.01235
55773.50393 2.461 235.407 ± 7.233 529.627 ± 10.849 765.034 ± 13.039 0.04477
55762.69582 2.510 58.839 ± 3.616 706.199 ± 12.528 765.038 ± 13.039 0.01041
55748.38868 3.771 117.704 ± 5.114 647.337 ± 11.994 765.042 ± 13.039 0.01522
55746.66405 1.236 117.704 ± 5.114 647.338 ± 11.994 765.043 ± 13.039 0.01060
55743.15553 2.308 353.098 ± 8.858 411.946 ± 9.568 765.043 ± 13.039 0.01575
55745.65597 2.618 117.705 ± 5.114 647.347 ± 11.994 765.052 ± 13.039 0.01126
55821.60644 2.042 294.230 ± 8.086 529.632 ± 10.849 823.862 ± 13.531 0.00904
55798.75171 4.518 58.838 ± 3.616 765.032 ± 13.039 823.871 ± 13.531 0.02078
55794.34352 4.924 58.856 ± 3.617 765.026 ± 13.039 823.882 ± 13.531 0.01618
55783.25353 3.925 235.388 ± 7.233 588.498 ± 11.436 823.886 ± 13.531 0.01514
55763.58673 4.125 176.551 ± 6.264 647.342 ± 11.994 823.893 ± 13.531 0.01013
55775.11139 3.272 117.704 ± 5.114 706.194 ± 12.528 823.897 ± 13.531 0.01310
55740.48481 2.590 294.250 ± 8.087 529.652 ± 10.849 823.902 ± 13.531 0.01744
55747.88464 3.972 58.857 ± 3.617 765.051 ± 13.039 823.908 ± 13.531 0.02227
55820.70669 11.448 176.546 ± 6.264 706.171 ± 12.527 882.717 ± 14.006 0.02987
55812.88346 5.447 58.855 ± 3.617 823.865 ± 13.531 882.720 ± 14.006 0.02041
55792.81781 3.461 411.937 ± 9.568 470.783 ± 10.229 882.720 ± 14.006 0.01339
55809.54465 3.030 117.693 ± 5.114 765.029 ± 13.039 882.722 ± 14.006 0.01444
55807.14032 3.450 411.934 ± 9.568 470.789 ± 10.229 882.723 ± 14.006 0.01147
55815.95868 2.639 58.856 ± 3.617 823.872 ± 13.531 882.728 ± 14.006 0.01146
55744.32436 4.279 176.553 ± 6.264 706.196 ± 12.528 882.749 ± 14.006 0.01569
55742.23055 5.768 117.705 ± 5.114 765.052 ± 13.039 882.757 ± 14.006 0.01393
55817.51569 6.776 117.701 ± 5.114 823.864 ± 13.531 941.565 ± 14.465 0.02661
55792.21979 1.686 176.541 ± 6.264 765.026 ± 13.039 941.567 ± 14.465 0.00954
55806.74527 3.401 176.548 ± 6.264 765.021 ± 13.039 941.569 ± 14.465 0.01014
55804.56094 2.295 176.539 ± 6.264 765.031 ± 13.039 941.571 ± 14.465 0.00944
55743.93339 1.965 176.553 ± 6.264 765.043 ± 13.039 941.597 ± 14.466 0.00956
55818.95147 5.622 58.846 ± 3.616 941.564 ± 14.465 1000.410 ± 14.911 0.02512
55820.43834 4.285 117.701 ± 5.114 882.718 ± 14.006 1000.419 ± 14.911 0.00997
55800.59413 2.617 117.702 ± 5.114 882.725 ± 14.006 1000.427 ± 14.911 0.01204
55773.99094 2.775 58.848 ± 3.616 941.585 ± 14.465 1000.433 ± 14.911 0.01211
55760.96984 3.584 117.696 ± 5.114 882.743 ± 14.006 1000.439 ± 14.911 0.01461
55777.94827 9.265 176.542 ± 6.264 823.897 ± 13.531 1000.439 ± 14.911 0.02508
55756.66238 4.502 176.552 ± 6.264 823.888 ± 13.531 1000.440 ± 14.911 0.01090
55755.86341 3.832 176.552 ± 6.264 823.897 ± 13.531 1000.449 ± 14.911 0.00772
55752.17713 3.504 176.553 ± 6.264 823.897 ± 13.531 1000.451 ± 14.911 0.01063
55803.99153 3.654 294.233 ± 8.086 765.022 ± 13.039 1059.254 ± 15.343 0.01084
55826.07315 3.786 176.546 ± 6.264 882.715 ± 14.006 1059.261 ± 15.343 0.00801
55741.05083 10.207 58.849 ± 3.616 1000.455 ± 14.911 1059.304 ± 15.343 0.03355
55805.48113 6.780 235.386 ± 7.233 882.724 ± 14.006 1118.109 ± 15.763 0.01629
55792.62642 8.534 353.090 ± 8.858 765.027 ± 13.039 1118.117 ± 15.763 0.02378
55751.93397 6.862 117.696 ± 5.114 1000.442 ± 14.911 1118.138 ± 15.763 0.03174
55765.32020 4.999 176.551 ± 6.264 941.589 ± 14.466 1118.140 ± 15.763 0.01279
55807.98013 4.321 117.702 ± 5.114 1059.261 ± 15.343 1176.963 ± 16.173 0.01249
55792.84574 5.480 176.549 ± 6.264 1000.423 ± 14.911 1176.972 ± 16.173 0.02244
55804.36682 5.572 235.386 ± 7.233 1000.417 ± 14.911 1235.803 ± 16.572 0.01366
55818.06535 18.899 117.692 ± 5.114 1118.111 ± 15.763 1235.803 ± 16.572 0.04024
55763.74271 5.420 235.399 ± 7.233 1000.445 ± 14.911 1235.845 ± 16.572 0.01580
55808.48143 6.886 294.241 ± 8.086 1000.415 ± 14.911 1294.656 ± 16.962 0.01014
55752.86099 2.487 470.793 ± 10.229 823.897 ± 13.531 1294.690 ± 16.962 0.01033
55748.43023 6.680 176.536 ± 6.264 1118.157 ± 15.764 1294.693 ± 16.962 0.01774
55757.40209 13.431 235.400 ± 7.233 1059.296 ± 15.343 1294.696 ± 16.962 0.02852
55740.24641 5.290 176.554 ± 6.264 1118.152 ± 15.764 1294.706 ± 16.962 0.01038
55755.23405 7.243 58.857 ± 3.617 1235.850 ± 16.572 1294.707 ± 16.962 0.02040
55799.53567 5.955 58.847 ± 3.616 1294.670 ± 16.962 1353.517 ± 17.343 0.02091
55759.69340 8.248 235.400 ± 7.233 1118.134 ± 15.763 1353.535 ± 17.344 0.01900
55748.56237 5.839 235.400 ± 7.233 1118.140 ± 15.763 1353.540 ± 17.344 0.01245
55746.72876 6.982 294.240 ± 8.086 1059.301 ± 15.343 1353.542 ± 17.344 0.01395
55759.69340 2.293 235.391 ± 7.233 1118.152 ± 15.764 1353.542 ± 17.344 0.00198
55820.42199 10.170 176.539 ± 6.264 1235.811 ± 16.572 1412.350 ± 17.716 0.01346
55797.44873 4.053 235.396 ± 7.233 1176.969 ± 16.173 1412.365 ± 17.716 0.01008
55807.03611 20.538 294.241 ± 8.086 1176.964 ± 16.173 1471.205 ± 18.082 0.03700
55791.63812 11.512 294.243 ± 8.086 1176.973 ± 16.173 1471.216 ± 18.082 0.02267
55746.15729 4.354 117.697 ± 5.114 1353.550 ± 17.344 1471.247 ± 18.082 0.01144
55806.00150 11.359 176.540 ± 6.264 1412.367 ± 17.716 1588.907 ± 18.791 0.02162
55787.89945 7.928 58.847 ± 3.616 1530.075 ± 18.440 1588.922 ± 18.791 0.00838
55768.84435 5.401 235.391 ± 7.233 1353.537 ± 17.344 1588.928 ± 18.791 0.01316
55833.09059 25.717 117.700 ± 5.114 1530.033 ± 18.440 1647.734 ± 19.136 0.07710
55819.06454 16.793 588.478 ± 11.436 1059.265 ± 15.343 1647.743 ± 19.136 0.02017
55766.87590 18.093 235.391 ± 7.233 1412.386 ± 17.717 1647.777 ± 19.136 0.03545
55773.95416 4.012 176.543 ± 6.264 1471.237 ± 18.082 1647.780 ± 19.136 0.01109
55790.05588 38.271 411.947 ± 9.568 1294.676 ± 16.962 1706.623 ± 19.475 0.16402
55816.58802 7.120 176.547 ± 6.264 1588.891 ± 18.791 1765.438 ± 19.807 0.01858
55793.88104 24.987 117.702 ± 5.114 1647.764 ± 19.136 1765.466 ± 19.808 0.11313
55826.02002 6.115 117.691 ± 5.114 1706.585 ± 19.475 1824.276 ± 20.135 0.01318
55827.89170 10.892 117.691 ± 5.114 1765.429 ± 19.807 1883.121 ± 20.457 0.02212
55819.08497 46.875 176.547 ± 6.264 1765.435 ± 19.807 1941.983 ± 20.774 0.14180
55780.39486 10.869 588.489 ± 11.436 1471.224 ± 18.082 2059.714 ± 21.395 0.01187
55765.45575 21.704 176.544 ± 6.264 1883.185 ± 20.457 2059.728 ± 21.395 0.04175
55822.75342 10.331 353.085 ± 8.858 2000.826 ± 21.087 2353.911 ± 22.872 0.01707
55828.63411 32.706 117.700 ± 5.114 2412.751 ± 23.156 2530.451 ± 23.714 0.04817
55821.43071 23.129 294.240 ± 8.086 2589.304 ± 23.988 2883.544 ± 25.314 0.01867
55756.89805 22.867 117.704 ± 5.114 2765.928 ± 24.793 2883.633 ± 25.315 0.03313
55763.10313 119.328 117.704 ± 5.114 2942.472 ± 25.572 3060.177 ± 26.078 1.31184
55764.80868 19.131 1059.301 ± 15.343 2059.729 ± 21.395 3119.030 ± 26.328 0.01630
55810.14130 28.083 176.548 ± 6.264 3118.961 ± 26.327 3295.509 ± 27.062 0.02015
55795.62606 59.471 117.703 ± 5.114 3236.660 ± 26.820 3354.362 ± 27.303 0.05526
55822.11727 32.769 235.392 ± 7.233 3177.782 ± 26.575 3413.175 ± 27.541 0.02822
55795.07436 37.409 353.089 ± 8.858 3589.768 ± 28.245 3942.857 ± 29.601 0.04263
55792.70202 36.928 176.541 ± 6.264 3766.321 ± 28.931 3942.862 ± 29.601 0.04881
55766.71856 117.197 235.391 ± 7.233 4119.463 ± 30.257 4354.854 ± 31.109 0.11637
55741.94107 52.968 1059.303 ± 15.343 4296.050 ± 30.899 5355.353 ± 34.498 0.02498

The distributions of flare equivalent durations on a logarithmic scale versus flare total durations were modelled by the One Phase Exponential Association (hereafter OPEA) defined by equation (3), using the SPSS V17.0 (Green et al. 1999) and GrahpPad Prism V5.02 (Dawson & Trapp 2004) software:

y=y0+(Plateau-y0)×(1-e-k×x) (3)

where y is the flare equivalent duration, x is the flare total duration. According to the description of Dal & Evren (2010), the most important parameter in this equation is the P lateau term to reveal the flare behavior of a star. Following three different methods described by D’Agostino & Stephens (1986), the probability values (p − value) were calculated to test the quality of the fit. The p − value was found to be < 0.001 in all the methods. The derived OPEA model is shown in Figure 6 together with the observed flare equivalent durations. The parameters computed from the model are listed in Table 4.

Fig. 6 The OPEA model derived from 149 flares detected in the available short cadence data of KIC 12004834 is shown. In the figure, the filled circles represent the calculated log(P) values from observations, while the red line represents the OPEA model. The color figure can be viewed online. 

Table 4 The OPEA model parameters derived by using the least-squares method 

Parameter Value
Y 0 −0.197 ± 0.081
Plateau 2.093 ± 0.236
K 0.00048 ± 0.00010
Tau 2098.68
Half − life 1454.7
95% Confidence Intervals
Y 0 −0.355 to −0.038
Plateau 1.630 to 2.556
K 0.00029 to 0.00067
Tau 1497.65 to 3505.49
Half − life 1038.09 to 2429.82
Goodness of Fit
R 2 0.7628
p − value (D’Agostino-Pearson) 0.0001
p − value (Shapiro-Wilk) 0.0001
p − value (Kolmogorov-Smirnov) 0.0005

In contrast to the known UV Ceti flare stars, KIC 12004834 is a binary system. It is well known that the flare events are generally random phenomena. To test this situation for a close binary like KIC 12004834, we calculated the phase distribution of the flares, depending on the orbital period of the system. The phase distribution is shown in Figure 7. In the figure, the distribution of the total number of flares computed in phase intervals of 0.05, for all 149 flares is shown.

Fig. 7 The distribution of flare total number in each phase interval of 0.05, plotted versus phase for 149 flares. The color figure can be viewed online. 

We also derived the flare energy spectrum (Gershberg 1972) for KIC 12004834. Like for the OPEA model, we again used the flare equivalent duration instead of the flare energy. To derive the flare energy spectrum, the cumulative flare frequencies were computed for 149 flares, and then, its distribution was derived in order to compare KIC 12004834 to its analogues. The obtained cumulative flare frequency distribution and its models are shown in Figure 8.

Fig. 8 Cumulative flare frequencies and model computed for 149 flares obtained from KIC 12004834. In the upper panel, the variation of the flare equivalent durations versus the cumulative flare frequency is shown, while the residuals obtained from the model are shown in the middle panel. The bottom panel shows the linear part of the flare energy spectrum and its linear representation. The color figure can be viewed online. 

In the literature there are two other flare frequency descriptions. Contrary to Gershberg (1972), Ishida et al. (1991) described the flare frequencies N 1 and N 2, a flare number and a total flare-equivalent duration emitting per hour, respectively. In this study, we detected 149 flares from the available observations lasting 89.19 days. We computed the frequencies by equations (4) and (5) (Ishida et al. 1991):

N1=Σnf/ΣDT (4)

N2=ΣP/ΣDT (5)

where Σnf is the total flare number, ΣDT is the total observing duration, and ΣP is the total equivalent duration. We found that the N 1 frequency is 0.070 h-1, while the N 2 frequency is 0.62 second/hour for KIC 12004834. It should be noted that the N 2 frequency is a unitless parameter, because the unit of ΣDT is time as well as the unit of ΣDT. However, the N 2 frequency is given in units of second/hour to facilitate the reading of the manuscript.

3. Results and discussion

We analysed the light curve and (OC) residuals of the system for the first time in the literature. The mass ratio of the system (q) was found to be 0.743 ± 0.001, while the inclination (i) was found to be 75º.89 ± 0.03. This inclination (i) value is in agreement with the inclination (i) value of 72º.47 given by Coughlin et al. (2011). The mass of the primary component was found to be 0.64M with a radius of 0.70R, while it was found to be 0.57M for the secondary component with a radius of 0.65R. Although these parameters are a bit larger than those found by Coughlin et al. (2011), it can be assumed that they are in agreement. In addition, these values indicate that KIC 12004834 is a simple close binary system. Indeed, the possible semi-major axis was found to be as small as 1.84R (≈ 0.0086 AU), which indicates that there must be a distance of 0.49R between the surfaces of the components. In this case, it is possible that each component can trigger the magnetic activity of the other.

If being in a very close binary affects the chromospheric patterns of the active component, we should see an effect: an increase of the flare frequency or of the Plateau value. KIC 12004834 was continuously observed over 89.19 days from JD 24 55739.83568694 to JD 24 55833.27789066, and we detected 149 flare events. The flare frequency N1, the general flare number per an hour, was found to be 0.070 h -1, while the flare frequency N2, the averaged flare energy per an hour, was computed as 0.62 second/hour. However, according to these results, KIC 12004834 did not show a high magnetic activity, not at the expected level.

Comparing the target to similar systems, we can easily notice that like KIC 12004834, both FL Lyr and KIC 9761199 are binary systems, but with high level chromospheric activity. Indeed, the flare frequencies of FL Lyr were recently found to be N1 = 0.41632 h−1 and N2 = 0.00027 by (Yoldaş & Dal 2016). However, the radii of the FL Lyr components were given as R1=1.283R, R2=0.963R with a semi-major axis of a=9.17R by Eker et al. (2014). In the case of KIC 9761199, Yoldaş & Dal (2017) found the P lateau value as 1.951 s, while the flare frequencies, N1 and N2, were found to be 0.01351 h -1 and 0.00006, respectively. The authors computed the masses of the primary and secondary components as 0.57M, 0.39M, and the radii of the components as 0.62R and 0.56R with a semi-major axis of a=5.16R. According to these results, if being a close binary affects the surface magnetic activity, KIC 12004834 should exhibit more frequent or more powerful flares than FL Lyr. On the other hand, according to Dal & Evren (2011); Dal (2012), it is a controversial topic whether the flare frequencies are an indicator of flare activity level, or not. There is one more parameter that may be taken an indicator for the flare activity level, which is the Plateau value. The Plateau value was found to be 2.093±0.236 s from the OPEA model of KIC 12004834. However, Yoldaş & Dal (2016) found the Plateau value as 1.232±0.069 s for FL Lyr. According to these results, the activity level of KIC 12004834 is nearly two times higher than FL Lyr, as expected. With an increasing number of eclipsing binaries with a flaring component, we may determine which parameter is real indicator for the flare activity level.

Using the regression calculations, the half−life value was found to be 1454.7 s from the OPEA model for KIC 12004834. In the case of FL Lyr, it is 2291.7 s (Yoldaş & Dal 2016). This means that a flare occurring on FL Lyr can reach the maximum energy level when the flare total duration reaches 38 minutes, while it takes 24.245 minutes for KIC 12004834. Moreover, the maximum flare rise time (T r ) obtained from the flares of KIC 12004834 was found to be 1059.303 s, while the maximum flare total time (T t ) was found to be 5355.050 s. However, these values are T r = 5179.00 s and T t = 12770.62 s for FL Lyr. As a result, the FL Lyr flare time scales are obviously larger than those obtained from KIC 12004834, which is in agreement with the results found by Dal & Evren (2011); Dal (2012) for single flare stars of type dMe.

However, there is one more controversial feature of KIC 12004834, which is stellar spot activity. During the analysis process, we recognised that the synthetic curve derived without any stellar spot does not fit the observations around phase 0.27. Because of this, the results of the light curve analysis point to the presence of stellar spot activity on one of the components. Considering the temperatures of the components we assumed that the flare activity is a sinusoidal variation caused by the rotational modulation due to the stellar cool spots. Indeed, this sinusoidal variation could be easily modelled with a cool spot on the primary component as seen in the 3D model of Roche geometry shown in Figure 4. However, the analyses indicated that the location of the spot is not changed on the primary component along 89.19 day despite the presence of high level flare activity. Considering the rapid variation in the flare behaviour, a stable spotted area on the component is very interesting. According to Hall et al. (1989) and Gershberg (2005), it is well known that the spotted areas on the active components of some RS CVn binaries can keep their shapes and locations for as long as two years. Therefore, the behavior of the cool spot activity observed for KIC 12004834 is not inconsistent with the stellar spot activity phenomenon.

In addition, considering the distribution of the total flare number in each phase interval of 0.05, it is noticed that the flares tend to occur in two specific phases, 0.25 and 0.75, as seen in Figure 7. Since the spotted area is seen around phase 0.27, the behavior of the flare activity of this close binary system KIC 12004834 can be understood.

At this point, one can question whether the sinusoidal variation out-of-eclipses is really caused by the stellar spots. In the literature, Tran et al. (2013) found a way to obtain the sign of the spot activity. They demonstrated that the spot activity remarkably affects the variations of the (O − C) residuals, especially for the (O − C)II residuals. Tran et al. (2013) reported that the stellar spot activity occurring on the active component causes the (O − C)II residuals of both the primary and secondary minima to vary synchronously in a sinusoidal manner, but in opposite directions. We could not determine the minima times from the Kepler long cadence data because the orbital period of KIC 12004834 is short, 0d.262317. However, we determined all the minima times from the available short cadence data. In the Kepler Mission Database, the short cadence data of observations are covered over 100 days. Because of this, the sinusoidal variation cannot be properly seen. On the other hand, we determined that the minima times computed from the primary and the secondary minima are separated from each other. This is enough evidence for the spot presence on one component.

We wish to thank the Turkish Scientific and Technical Research Council for supporting this work through grant No. 116F213. We thank the referee for useful comments that have contributed to the improvement of the paper. We also thank Dr. O. Özdarcan for the useful scripts that have supported us, providing an easy way to solve hard calculations.

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Received: June 10, 2018; Accepted: January 17, 2019

H. A. Dal and E. Yoldaş: Department of Astronomy and Space Sciences, University of Ege, Bornova, 35100 İzmir, Turkey (ezgiyoldas@gmail.com).

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