The high multiplicity systems Gliese 667C and KOI 3158

High multiplicity extra-solar systems display a wealth of planetary interactions which can constrain the orbital properties of the system as well as the physical nature of the planets (e.g, rocky vs. volatile rich). These systems may also serve as analogues for our own high-multiplicity solar system. One example is KOI 3158, a metal-poor, high-proper-motion star for which has been identified in the Kepler data set evidence for five small planets. Given the probable stellar type, K0V (Wilson 1962), we infer that the planets range in size from 0.3 to 0.5 Earth radii. The star's high proper motion and radial velocity are compatible with membership in the Milky Way's thick disk. The orbital architecture of this system includes proximity to several mean motion resonances, which allow us to constrain the mass and eccentricities of the planets. Gliese 667C, another metal poor star, hosts a system of 6 or 7 planets, 3 of which are potentially in the habitable zone. Classical secular theory of non-resonant interactions, coupled with standard tidal evolution theory, can constrain the tidal dissipation parameters Q for each of the planets. The eccentricities and pericenter longitudes from Anglada-Escude et al.’s (2013) currently-most-stable 6-planet solution (S⁶, their Table 6) imply that the one of the two large-amplitude secular eigenmodes is controlled by the innermost planet. Therefore, if the innermost planet's Q is < 10₄, going backwards in time the amplitude of this already high-amplitude mode increases, so < 2 Gyr ago (the minimum age of the star) the planets would have been too close for stability. Tides on the other planets only affect eigenmodes that are currently of low amplitude. As a result, the Qs of these planets could be very low and still be consistent with the past stability of the system. Thus, the orbital solution that is currently the most stable indicates that the inner planet cannot be rocky, while the other planets can be. In particular, the dynamics permit the planets in the habitable zone to be rocky, and thus does not exclude any of those planets from having a solid surface and being habitable.