Photometric Follow-up Transit (Primary Eclipse) Observations of WASP-43 b and TrES-3b and A Study on Their Transit Timing Variations

Abstract: Two photometric follow-up transit (primary eclipse) observations on WASP-43 b and four observations on TrES-3 b are performed using the Xuyi Near-Earth Object Survey Telescope. After differential photometry and light curve analysis, the physical parameters of the two systems are obtained and are in good match with the literature. Combining with transit data from a lot of literature, the residuals ($O-C$) of transit observations of both systems are fitted with the linear and quadratic functions. With the linear fitting, the periods and transit timing variations (TTVs) of the planets are obtained, and no obvious periodic TTV signal is found in both systems after an analysis. The maximum mass of a perturbing planet located at the 1:2 mean motion resonance (MMR) for WASP-43 b and TrES-3 b is estimated to be 1.826 and 1.504 Earth mass, respectively. By quadratic fitting, it is confirmed that WASP-43 b may have a long-term TTV which means an orbital decay. The decay rate is shown to be $\dot{P} =(-0.005248 \pm 0.001714)$~s$\cdot$yr$^{-1}$, and compared with the previous results. Based on this, the lower limit of the stellar tidal quality parameter of WASP-43 is calculated to be $Q'{\rm *} \ge 1.5\times10^5$, and the remaining lifetimes of the planets are presented for the different $Q'{\rm *}$ values of the two systems, correspondingly.