Dynamical Interactions in the Planetary System GJ4276

GJ4276 is an M4.0 dwarf star with an inferred Neptune mass planet from radial velocity (RV) observations. We reanalyse the RV data for this system and focus on the possibility of a second, super earth mass, planet. We compute the timescale for fast resonant librations in the eccentricity to be $\sim 2\,000\,\mathrm{days}$. Given that the observations were taken over $700\,\mathrm{days}$, we expect to see the effect of these librations in the observations. We perform a fully dynamical fit to test this hypothesis. Similar to previous results, we determine that the data could be fit by two planets in a 2:1 mean motion resonance. However, we also find solutions near the 5:4 mean motion resonance which are not present when planet-planet interactions are ignored. Using the MEGNO indicator, we analyze the stability of the system and find that our solutions lie in a stable region of parameter space. We also find that though out of resonance solutions are possible, the system favours a configuration which is in a first order mean motion resonance. The existence of mean motion resonances has important implications in many planet formation theories. Although we do not attempt to distinguish between the one and two planet models in this work, in either case, the predicted orbital parameters are interesting enough to merit further study. Future observations should be able to distinguish between the different scenarios within the next $5\,\mathrm{years}$.