The 55 Cancri Planetary System: Fully Self-Consistent N-body Constraints and a Dynamical Analysis

We present an updated study of the planets known to orbit 55 Cancri A using 1,418 high-precision radial velocity observations from four observatories (Lick, Keck, Hobby-Eberly Telescope, Harlan J. Smith Telescope) and transit time/durations for the inner-most planet, 55 Cancri "e" (Winn et al. 2011). We provide the first posterior sample for the masses and orbital parameters based on self-consistent n-body orbital solutions for the 55 Cancri planets, all of which are dynamically stable (for at least $10^8$ years). We apply a GPU version of Radial velocity Using N-body Differential evolution Markov Chain Monte Carlo (RUN DMC; B. Nelson et al. 2014) to perform a Bayesian analysis of the radial velocity and transit observations. Each of the planets in this remarkable system has unique characteristics. Our investigation of high-cadence radial velocities and priors based on space-based photometry yields an updated mass estimate for planet "e" ($8.09\pm0.26$ M$_\oplus$), which affects its density ($5.51\pm^{1.32}_{1.00}$ g cm$^{-3}$) and inferred bulk composition. Dynamical stability dictates that the orbital plane of planet "e" must be aligned to within $60^o$ of the orbital plane of the outer planets (which we assume to be coplanar). The mutual interactions between the planets "b" and "c" may develop an apsidal lock about $180^o$. We find 36-45% of all our model systems librate about the anti-aligned configuration with an amplitude of $51^o\pm^{6^o}_{10^o}$. Other cases showed short-term perturbations in the libration of $\varpi_b-\varpi_c$, circulation, and nodding, but we find the planets are not in a 3:1 mean-motion resonance. A revised orbital period and eccentricity for planet "d" pushes it further toward the closest known Jupiter analog in the exoplanet population.