Polar Neptunes are Stable to Tides

There is an intriguing and growing population of Neptune-sized planets with stellar obliquities near $\sim90^{\circ}$. One previously proposed formation pathway is a disk-driven resonance, which can take place at the end stages of planet formation in a system containing an inner Neptune, outer cold Jupiter, and protoplanetary disk. This mechanism occurs within the first $\sim10$ Myr, but most of the polar Neptunes we see today are $\sim$Gyrs old. Up until now, there has not been an extensive analysis of whether the polar orbits are stable over $\sim$Gyr timescales. Tidal realignment mechanisms are known to operate in other systems, and if they are active here, this would cause theoretical tension with a primordial misalignment story. In this paper, we explore the effects of tidal evolution on the disk-driven resonance theory. We use both $N$-body and secular simulations to study tidal effects on both the initial resonant encounter and long-term evolution. We find that the polar orbits are remarkably stable on $\sim$Gyr timescales. Inclination damping does not occur for the polar cases, although we do identify sub-polar cases where it is important. We consider two case study polar Neptunes, WASP-107 b and HAT-P-11 b, and study them in the context of this theory, finding consistency with present-day properties if their tidal quality factors are $Q \gtrsim 10^4$ and $Q \gtrsim 10^5$, respectively.