  In order to explain the significant orbital eccentricity of the short-period
transiting Neptune-mass planet GJ 436b and at the same time satisfy various
observational constraints and anomalies, Ribas, Font-Ribera and Beaulieu have
proposed the existence of an eccentric low-mass companion planet at the
position of the outer 2:1 resonance. The authors demonstrate the viability of
their proposal using point-mass three-body integrations, arguing that as long
as the system appears to be dynamically stable, the short-term secular
variations ought to dominate the long-term dissipative evolution. Here we
demonstrate that if one includes tidal dissipation, both orbits circularize
after a few times the circularization timescale of the inner planet. We
conclude that with or without a nearby companion planet, in or out of the 2:1
resonance, the Q-value of GJ 436b must be near the upper bound estimate for
Neptune if the system is as young as 1 Gyr, and an order of magnitude higher if
the system is as old as 10 Gyr. We show detail of passage through resonance and
conclude that even out of resonance, a companion planet should still be
detectable through transit timing variations.
