Exciting the TTV Phases of Resonant Sub-Neptunes

TL;DR

This paper explains the observed period ratio excesses and non-zero TTV phases of sub-Neptunes near resonance by modeling their capture into resonance with a third body in a gas disc, highlighting the role of secular forcing.

Contribution

It introduces a new model where a third eccentric body causes non-zero TTV phases and explains the period ratio structure of sub-Neptunes near resonance.

Findings

Resonant pairs can have non-zero TTV phases due to secular forcing.

Gas disc migration leads to period ratios wide of resonance.

Resonant planets are predicted to be apsidally aligned with higher eccentricities.

Abstract

There are excesses of sub-Neptunes just wide of period commensurabilities like the 3:2 and 2:1, and corresponding deficits narrow of them. Any theory that explains this period ratio structure must also explain the strong transit timing variations (TTVs) observed near resonance. Besides an amplitude and a period, a sinusoidal TTV has a phase. Often overlooked, TTV phases are effectively integration constants, encoding information about initial conditions or the environment. Many TTVs near resonance exhibit non-zero phases. This observation is surprising because dissipative processes that capture planets into resonance also damp TTV phases to zero. We show how both the period ratio structure and the non-zero TTV phases can be reproduced if pairs of sub-Neptunes capture into resonance in a gas disc while accompanied by a third eccentric non-resonant body. Convergent migration and eccentricity damping by the disc drives pairs to orbital period ratios wide of commensurability; then, after the disc clears, secular forcing by the third body phase-shifts the TTVs. The scenario predicts that resonant planets are apsidally aligned and possess eccentricities up to an order of magnitude larger than previously thought.