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

## TL;DR

This study investigates the causes of transit timing variations in Kepler-410Ab, ruling out a stellar companion through radial velocity measurements and suggesting a small planet near a 2:3 mean-motion resonance as a plausible explanation.

## Contribution

The paper refutes the hypothesis of an additional stellar companion and proposes a small planet near a 2:3 resonance as the cause of TTVs, supported by numerical simulations.

## Key findings

- No periodic radial velocity variation observed, rejecting the stellar companion hypothesis.
- Transit timing variations may be caused by a small planet in 2:3 mean-motion resonance.
- The 2:3 resonance is stable over long timescales.

## Abstract

Transit timing variations of Kepler-410Ab were already reported in a few papers. Their semi-amplitude is about 14.5 minutes. In our previous paper, we found that the transit timing variations 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 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 a radial-velocity 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 transit timing variations 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.