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Description
For the determination of the individual times of transit we used short- cadence (sampled every 58.8 seconds) de-trended data (PDCSAP_FLUX) from quarters Q1 to Q17, provided by the NASA Exoplanet Archive. As a first step, we extracted parts of the LC around detected transits using the ephemeris given in Van Eylen et al. (2014ApJ...782...14V), where we took an interval 0.2 days around the computed transit time (the interval size is approximately double the transit duration). To remove additional residual trends caused by the stellar activity and instrumental long-term photometric variation, we fitted the out-of-transit part of LC by a second-order polynomial function. Then we subtracted 8% flux contamination from the wide companion Kepler-410B, according to calculations of Van Eylen et al. (2014ApJ...782...14V). All individual parts of the LC with transits were stacked together to obtain the template of the transit. The stacked LC was fitted by our software implementation of Mandel & Agol (2002ApJ...580L.117M) model, where we used theMarkov Chain Monte Carlo (MCMC) simulation method for the determination of transit parameters. This method takes into account individual errors of Kepler observations and gives a realistic and statistically significant estimate of parameter errors. As a starting point for the MCMC fitting, we used the physical parameters of the planet given in Van Eylen et al. (2014ApJ...782...14V). We have adopted a fixed value a=0.1226AU. We have used a quadratic model of limb darkening with starting values of coefficients from Sing (2010, Cat. J/A+A/510/A21). We ran the MCMC simulation with 10^6^ steps. We have repeated the MCMC simulation with the previous solution as the starting point on each of 70 individual transit intervals, and let only the time of transit to update. The new values were used to improve the linear ephemeris and to construct a new O-C diagram. The combined light curve stacked using a linear ephemeris is affected by relatively large amplitude of O-C time shifts. To correct this effect, we used iterative procedure that takes the best-fit O-C values into account. Afterwards, a new stacked light curve was constructed and a new MCMC transit solution was calculated, subsequently a new ephemeris and O-C values were determined. This process was repeated three times until a convergent solution was reached.
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