Transit timing variations, radial velocities, and long-term dynamical stability of the system Kepler-410

Transit timing variations (TTVs) of Kepler-410Ab were already reported in a few papers. Their semi-amplitude is about 14.5 min. In our previous paper, we found that the TTVs could be caused by the presence of a stellar companion in this system. Our main motivation for this paper was to investigate variation in a radial-velocity (RV) curve generated by this additional star in the system. We performed spectroscopic observation of Kepler-410 using three telescopes in Slovakia and Czech Republic. Using the cross-correlation function, we measured the radial velocities of the star Kepler-410A. We did not observe any periodic variation in an RV curve. Therefore, we rejected our previous hypothesis about additional stellar companion in the Kepler-410 system. We ran different numerical simulations to study mean-motion resonances with Kepler-410Ab. Observed TTVs could be also explained by the presence of a small planet near to mean-motion resonance 2:3 with Kepler-410Ab. This resonance is stable on a long time-scale. We also looked for stable regions in the Kepler-410 system where another planet could exist for a long time.