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EPIC 202843107 : A Close Eclipsing Binary Containing a {\delta} Scuti Variable

This paper reports on the discovery that an eclipsing binary system, EPIC 202843107 , has a {\delta} Scuti variable component. The phased light curve from Kepler space telescope presents a detached configuration. The binary modelling indicates that the two component stars have almost the same radius and may have experienced orbital circularization. Frequency analyses are performed for the residual light curve after subtracting the binary variations. The frequency spectrum reveals that one component star is a {\delta} Scuti variable. A large frequency separation is cross-identified with the histogram graph, the Fourier transform, and the echelle diagram method. The mean density of the {\delta} Scuti component is estimated to be 0.09 g/cm3 based on the large separation and density relation. Systems like EPIC 202843107 are helpful to study the stellar evolution and physical state for binary stars.


INTRODUCTION
The delta Scuti (δ Sct) variables represent a class of asteroseismic objects which locate at the bottom of the Cepheid instability strip on the Hertzsprung-Russell (HR) diagram. Their typical brightness fluctuations range from 0.003 to 0.9 magnitudes with pulsating periods between about 0.3 and 8 hours (Aerts et al. 2010). Their intrinsic pulsations is driven by the κ mechanism, which originates from the partial ionization zone of helium.
The eclipsing binary with a δ Sct component is valuable for testing the stellar theoretical models and the interactions between stars. For example, some researchers (Liakos et  Continuous photometric data with high precision were acquired thanks to the NASA's Kepler space telescope (Borucki et al. 2008). The data of Kepler are quite valuable for the study of time-domain astronomy, e.g. investigating eclipsing binaries (Prša et al. 2011;Borkovits et al. 2016;Kirk et al. 2016) and δ Sct stars (Balona & Dziembowski 2011;Guo et al. 2016;Bowman & Kurtz 2018). The K2 mission (Howell et al. 2014) took the place of the Kepler mission when two of the four reaction wheels failed in May 2013. The K2 mission observed the fields along the ecliptic plane. Each K2 campaign lasted for about 80 days with a photometric precision ∼80 ppm over 6 hours (Howell et al. 2014). In order to distinguish each target, a new input catalogue, the Ecliptic Plane Input Catalogue (EPIC), has been used for the K2 mission. EPIC 202843107 (RA=16:22:11.469, Dec=-28:09:42.56) falls in the second campaign field of the K2 mission. The observation of EPIC 202843107 lasted for 77.29 days from August 23 to November 10, 2014. EPIC 202843107 was first identified as an exoplanet candidate by Vanderburg & Johnson (2014).
However, Armstrong et al. (2016) classified EPIC 202843107 as an eclipsing binary using the machine learning technique. Barros et al. (2016) also pointed out its binary nature by analysing the de-correlated flux-position of the photometric pixel file.
In this paper, we discover that EPIC 202843107 is a short-period eclipsing binary system with a δ Sct variable. The structure of this paper is as follows. Section 2 describes the observational data. Section 3 solves the light curve with binary modelling and obtains the binary parameters. Section 4 analyses the stellar pulsations and confirms that one component star is a δ Sct variable. Regular frequency spacing is described in section 4.1, and the mean density of the δ Sct component is estimated in section 4.2. Finally, section 5 presents the results and conclusions.

OBSERVATIONS
The data of EPIC 202843107 come from the Mikulski Archive for Space Telescopes (MAST; https://archive.stsci.edu/). The raw data contain some instrumental noises, which should be removed before data analysis. Three types of data processing techniques have been applied. Vanderburg & Johnson (2014) corrected the K2 data using the centroid position of the stellar images. Armstrong et al. (2016) adopted a similar method and developed an analytical procedure specifically for variable stars. Luger et al. (2016) applied pixel level de-correlation to remove instrumental noise. However, the long-term trends, which means continuous rise or fall, still exist in the light curves. The trends can be removed by a low-order polynomial fitting. We adopt a third-order polynomial function to remove the trends in the data of Luger et al. (2016). There is an obvious jump around 2104 as shown in the top panel of Figure 1. Thus the light curve of EPIC 202843107 are divided into two segments. For each segment, we only use the out-of-eclipse part to fit the long-term trend. Then the fitting function is extended to the global segment (including eclipses).
The detrended light curve is shown in the bottom panel of Figure 1.

LIGHT CURVE SOLUTIONS
In order to determine reliable parameters for this eclipsing binary system, we analyse the light curve of EPIC 202843107 using the JKTEBOP code (Southworth et al. 2004(Southworth et al. , 2005(Southworth et al. , 2009  is widely used for fitting Kepler data (Bognár et al. 2015;Gaulme et al. 2016;Mancini et al. 2016). This code can find appropriate parameters for a global minimum that best reproduces the observational data. The fitting parameters include the surface brightness ratio S 2 /S 1 , the ratio of the radii R 2 /R 1 , the sum of radii over the semi-major axis (R 1 + R 2 )/a, the orbital inclination i, the eccentricity e, and the orbital period The best-fit parameters of the binary modelling are listed in Table 1, with the modelled light curve and residuals presented in Figure 2. The residuals all concentrate around zero. Therefore, the fitting results are reliable. We can see that the two component stars have almost identical radius. The orbital eccentricity is very small, which means this system may have experienced the process of circularization. Notes: Parameters are surface brightness ratio (S 2 /S 1 ), ratio of the radii (R 2 /R 1 ), the sum of radii over the semi-major axis ((R 1 + R 2 )/a), orbital inclination (i), eccentricity (e), and orbital period (P orb ).  frequencies, amplitudes, and signal-to-noise ratios (S/N). To ensure the robustness of the extracted pulsation frequencies, we only retain the frequencies with a signal-to-noise ratio larger than 4. As a result, a total of 16 frequencies are found and are listed in Table 2. The frequency spectrum is shown in Figure 3. The main pulsations lie in the frequency region between 120 µHz and 270 µHz , with the dominant peak at f 12 = 208.769 µHz . According to the pulsation periods, amplitudes, and the profile, we confirm that EPIC 202843107 has a δ Sct component star.

FREQUENCY ANALYSIS
Mode identification --the determining of pulsation mode values l --is difficult in the analysis of pulsating variable stars. Generally, pulsation modes can be identified by comparing the phase lags between the light curves at different wavelength (Breger et al. 1999;Paparó et al. 2018  stars. The large separation presents a regular spacing and is related with the physical state of the star. In the following we will describe the regular spacing study of EPIC 202843107 .  Table 2, and the open circle is the 63-order harmonic of the orbital frequency.

Regular frequency spacing
There are several well-developed methods to search for regular spacing in δ Sct stars, including the histogram graph (Breger et al. 1999

The histogram graph
The frequency differences between every two of the 16 extracted frequencies are calculated. The left panel of Figure 4 illustrates the distribution of the frequency differences. The bin size is 4 µHz . The histogram graph can be used to examine the regular frequency spacing. For EPIC 202843107 , there are two obvious peaks around 4 µHz and 28 µHz , respectively. The first peak may be caused by close frequencies and potential rotational splitting frequencies. The significant second peak can be explained by the large separation which is caused by frequencies with the same degree l of different radial orders.

The Fourier transform
The Fourier transform is another method widely used to find the regular spacing. We follow the descriptions

The echelle diagram
An echelle diagram (Grec et al. 1983;Bedding et al. 2010;Mosser et al. 2012) can directly show the regular patterns of the frequency spectrum. The histogram and Fourier transform method indicate the best regular spacing ranges from 28 µHz to 29.8 µHz . Therefore, the pulsation frequencies are modulated by a series of values between 28 µHz and 29.8 µHz . When the spacing is equal to around 28.6 µHz , the EPIC 202843107 : A Close Eclipsing Binary Containing a δ Scuti Variable 7 diagram. Hambleton et al. (2013) speculate that the frequencies in a vertical ridge are the coupling of the self excited frequencies and the tidally induced frequencies. Liakos & Niarchos (2017) proposed that there is a threshold in the binary period of about 13 days. The pulsation properties can be affected for short-period binaries because of tidal interactions. The orbital period of EPIC 202843107 is 4.398 days, which is below the 13-day threshold. Therefore, the tidal effects may play an important role to the pulsation frequency for EPIC 202843107 . µHz . There are two obvious vertical ridges (solid line), and two potential vertical ridges (dashed line).

RESULTS AND CONCLUSIONS
In this paper, we confirm that EPIC 202843107 is a short-period eclipsing binary containing a δ Sct variable. This system may have experienced orbital circularization because the orbital eccentricity is very close to zero.
After removing the eclipsing variations, the residual light curve shows 16 pulsating frequencies between 120 µHz and 270 µHz with a signal-to-noise ratio larger than 4. The dominant peak has a pulsation amplitude of ∼0.5 mmag at f 12 = 208.769 µHz . A regular frequency spacing is cross-identified with the histogram graph, the Fourier transform, and the echelle diagram method. The regular spacing is about 28.6 µHz , which is approximately 11 times of the orbital frequency (28.95 µHz ). It implies that the pulsations of the δ Sct star may have been influenced by the companion's tidal forces. Using the scale relation between the mean stellar density and the large frequency separation, we obtained a mean density of 0.09 g·cm −3 for the δ Sct component of EPIC 202843107 .
Although Kepler has accomplished its mission, there are still a large amount of data waiting to be analysed. EPIC 202843107 was first recognized as an exoplanet, but then corrected to be an eclipsing binary system. In our work, by analyzing the Kepler data we are able to confirm that this system contains a δ Sct component. In the future, more systems like EPIC 202843107 can help scientists study the differences in evolutionary and physical status between single δ Sct stars and those in binary systems.