Orbital stability study and transit-timing variations of the extrasolar planetary system: K2-3

We investigated the dynamical properties of the K2-3 multi-planet system. Recently three transiting planets are discovered using the extended Kepler2 (K2) mission (Crossfield et al. 2015). We extended their preliminary stability study by considering a substantial longer integration time. Since planet mass is not known from photometry we calculated exoplanets masses using empirical mass-radius relations (Weiss & Marcy 2014). Forward numerical integration was done using the MERCURY integration package (Chambers 1999). Our results demonstrate that this system is stable over a time scale of $10^8years$. Furthermore, we investigated the dynamical effects of a hypothetical planet in the semi-major axis vs eccentricity space. For stable orbits of the hypothetical planet we calculated transit-timing variation (TTV) and radial velocity signals. We find that for a hypothetical perturber with mass 1-13 Mjup, semi-major axis 0.2 - 0.8 AU and eccentricity 0.00-0.47 the following timing signals for the planet K2-3 b is ~ 5 sec, K2-3 c is ~ 130 sec and for K2-3 d is ~ 190 sec. The radial velocity signal of the hypothetical planet is ~ 4 m/s. Using typical transit-timing errors from the K2 mission, we find that the above hypothetical planet would not be detectable. Its radial velocity signal, however, would be detectable using the APF 2.4m telescope or HARPS at the ESO/La Silla Observatory in Chile.