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We investigate the possibility that the large orbital eccentricity of thetransiting Neptune-mass planet Gliese 436b is maintained in the face of tidaldissipation by a second planet in the system. We find that the currentlyobserved configuration can be understood if Gliese 436b and a putativecompanion have evolved to a quasi-stationary fixed point in which the planets'orbital apses are co-linear and in which secular variations in the orbitaleccentricities of the two planets have been almost entirely damped out. Weadopt an octopole-order secular theory based on a Legendre expansion in thesemi-major axis ratio to delineate well-defined regions of (P_c, M_c, e_c)space that can be occupied by a perturbing companion. We incorporate theevolutionary effect of tidal dissipation into our secular model of the system,and solve the resulting initial value problems for a large sample of theallowed configurations. We then polish the stationary configurations derivedfrom secular theory with full numerical integrations. We present our results inthe form of candidate companion planets to Gliese 436b. For these candidates,radial velocity half-amplitudes, K_c, are of order 3 m/s, and the maximumamplitude of orbit-to-orbit transit timing variations are of order Delta t=1 sto Delta t=5s. For the particular example case of a perturber with orbitalperiod, P_c=40 d, mass, M_c=8.5 M_Earth, and eccentricity, e_c=0.58, we confirmour semi-analytic calculations with a full numerical 3-body integration of theorbital decay that includes tidal damping and spin evolution. Additionally, wediscuss the possibility of many-perturber stationary configurations, utilizingmodified Laplace-Lagrange secular theory.

A Quasi-Stationary Solution to Gliese 436b's Eccentricity