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Sub-Neptune Formation: The View from Resonant Planets

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 $\sim$10\%, 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$--$15 M_{\oplus}$ 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 3--5 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 $\gtrsim$ $5$--$15$ days, subsequent modification by stellar tides appears necessary at shorter periods, particularly for the 2:1.