Creating Pileups of Eccentric Planet Pairs Wide of MMRs Through Divergent Migration

A widely discussed feature in the distribution of orbital period ratios between adjacent exoplanets in multiplanet systems are the significant pileups of planet pairs wide of mean motion resonances (MMRs) at integer ratios. Previous models have argued that significant eccentricity damping would tend to push planet pairs wide of MMRs, and can explain the observed period ratio distribution. These models would naturally also predict low eccentricities for these planet pairs, but such measurements were not available at the time. However, precise eccentricities inferred from transit-timing variations (TTVs) over the last decade have revealed that most of these planet pairs wide of MMRs exhibit significant eccentricities, presenting an important observational tension for previous models.

We present an alternate model, considering divergent orbital migration. In such a scenario, capture into resonance is forbidden, so planet pairs interior to the resonance are forced to jump over wide of resonance, and in the process receive a kick to their eccentricity. In this way, one can evacuate the planet pairs narrow of resonance, and naturally create a pileup of eccentric planet pairs wide of resonance as observed.

We will present numerical integrations of this process using the REBOUND N-body package for observed planet pairs near the main 3:2 and 2:1 MMRs. We additionally use an analytical MMR model to rescale variables so that the predictions for our MMR-jumping model and previous eccentricity damping models each fall onto 1-D lines, independent of the planetary masses and particular MMR. This facilitates the comparison of observed planet pairs spanning a range of masses and MMRs, and alleviates mass-eccentricity degeneracies intrinsic to TTV analyses. We show that our MMR-jumping model provides a significantly better match to observations than previous eccentricity-damping models. While our model is agnostic to the source of divergent migration, we discuss various candidate mechanisms.