Orbital Dynamics of Multi-Planet Systems with Eccentricity Diversity
  Since exoplanets were detected using the radial velocity method, they have revealed a diverse distribution of orbital configurations. Amongst these are planets in highly eccentric orbits (e > 0.5). Most of these systems consist of a single planet but several have been found to also contain a longer period planet in a near-circular orbit. Here we use the latest Keplerian orbital solutions to investigate four known systems which exhibit this extreme eccentricity diversity; HD 37605, HD 74156, HD 163607, and HD 168443. We place limits on the presence of additional planets in these systems based on the radial velocity residuals. We show that the two known planets in each system exchange angular momentum through secular oscillations of their eccentricities. We calculate the amplitude and timescale for these eccentricity oscillations and associated periastron precession. We further demonstrate the effect of mutual orbital inclinations on the amplitude of high-frequency eccentricity oscillations. Finally, we discuss the implications of these oscillations in the context of possible origin scenarios for unequal eccentricities. 
Stephen R. Kane, Sean N. Raymond
astro-ph.EP