Sub-Neptune formation: the view from resonant planets

Abstract

ABSTRACT The orbital period ratios of neighbouring sub-Neptunes are distributed asymmetrically near first-order resonances. There are deficits of systems – ‘troughs’ in the period ratio histogram – just short of commensurability, and excesses – ‘peaks’ – just wide of it. We reproduce quantitatively the strongest peak-trough asymmetries, near the 3:2 and 2:1 resonances, using dissipative interactions between planets and their natal discs. Disc eccentricity damping captures bodies into resonance and clears the trough, and when combined with disc-driven convergent migration, draws planets initially wide of commensurability into the peak. The migration implied by the magnitude of the peak is modest; reductions in orbital period are ∼10 per cent, supporting the view that sub-Neptunes complete their formation more-or-less in situ. Once captured into resonance, sub-Neptunes of typical mass $\sim \,$5–15M⊕ stay captured (contrary to an earlier claim), as they are immune to the overstability that afflicts lower mass planets. Driving the limited, short-scale migration is a gas disc depleted in mass relative to a solar-composition disc by three to five orders of magnitude. Such gas-poor but not gas-empty environments are quantitatively consistent with sub-Neptune core formation by giant impacts (and not, e.g. pebble accretion). While disc-planet interactions at the close of the planet formation era adequately explain the 3:2 and 2:1 asymmetries at periods $\gtrsim \, $5–15 d, subsequent modification by stellar tides appears necessary at shorter periods, particularly for the 2:1.