Over the course of the last two decades, traditional models of planet formation have been repeatedly challenged by the emerging census of extrasolar planets. Key among them is the orbital architecture problem: while standard models of orbital migration predict resonant orbits for short-period objects, most planets do not appear to lie in orbital resonances. Here, we show that the four-planet system Kepler-221, not previously recognized to have active orbital resonances, has a three-body commensurability relation unique within the Kepler sample. Using a suite of numerical experiments as well as a perturbative analysis, we demonstrate that this system likely began as a resonant chain and proceeded to undergo large-scale divergence away from resonance, under the action of tidal dissipation. Our results further indicate that obliquity tides, driven by a secular spin-orbit resonance and mutual inclination, are an excellent candidate for driving this orbital divergence, and that the high tidal luminosity may also explain the anomalous size of planet b, which lies within the Fulton radius gap. Unified Astronomy Thesaurus concepts: Exoplanet dynamics (490); Exoplanet tides (497); Exoplanet evolution (491); Orbital resonances (1181)

Compact nonresonant systems of sub-Jovian planets are the most common outcome of the planet formation process. Despite exhibiting broad overall diversity, these planets also display dramatic signatures of intrasystem uniformity in their masses, radii, and orbital spacings. Although the details of their formation and early evolution are poorly known, sub-Jovian planets are expected to emerge from their natal nebulae as multiresonant chains, owing to planet–disk interactions. Within the context of this scenario, the architectures of observed exoplanet systems can be broadly replicated if resonances are disrupted through postnebular dynamical instabilities. Here, we generate an ad hoc sample of resonant chains and use a suite of N-body simulations to show that instabilities can not only reproduce the observed period ratio distribution, but that the resulting collisions also modify the mass uniformity in a way that is consistent with the data. Furthermore, we demonstrate that primordial mass uniformity, motivated by the sample of resonant chains coupled with dynamical sculpting, naturally generates uniformity in orbital period spacing similar to what is observed. Finally, we find that almost all collisions lead to perfect mergers, but some form of postinstability damping is likely needed to fully account for the present-day dynamically cold architectures of sub-Jovian exoplanets.

In this paper we investigate systems previously identified to exhibit transit timing variations (TTVs) in Kepler data, with the goal of predicting the expected improvements to the mass and eccentricity constraints that will arise from combining Kepler data with future data from the TESS mission. We advocate for the use of the Kullback-Leibler (KL) divergence as a means to quantify improvements in the measured constraints. Compared to the original Kepler data, the TESS data will have a lower signal-tonoise ratio, rendering some of the planetary transits undetectable, and lowering the accuracy with which the transit mid-time can be estimated. Despite these difficulties, out of the 55 systems (containing 143 planets) investigated, we predict that the collection of short-cadence data by TESS will be of significant value (i.e. it will improve the mass uncertainty such that the KL divergence is > ∼ 0.1) for approximately 6 -14 planets during the nominal mission, with the range primarily driven by the uncertain precision with which transit mid-times will be recovered from TESS data. In an extended mission this would increase to a total of approximately 12 -25 planets.

Convergent disk migration has long been suspected to be responsible for forming planetary systems with a chain of mean-motion resonances (MMRs). Dynamical evolution over time could disrupt the delicate resonant configuration. We present TOI-1136, a 700 ± 150 Myr old G star hosting at least six transiting planets between ∼2 and 5 R ⊕. The orbital period ratios deviate from exact commensurability by only 10−4, smaller than the ∼10−2 deviations seen in typical Kepler near-resonant systems. A transit-timing analysis measured the masses of the planets (3–8M ⊕) and demonstrated that the planets in TOI-1136 are in true resonances with librating resonant angles. Based on a Rossiter–McLaughlin measurement of planet d, the star’s rotation appears to be aligned with the planetary orbital planes. The well-aligned planetary system and the lack of a detected binary companion together suggest that TOI-1136's resonant chain formed in an isolated, quiescent disk with no stellar flyby, disk warp, or significant axial asymmetry. With period ratios near 3:2, 2:1, 3:2, 7:5, and 3:2, TOI-1136 is the first known resonant chain involving a second-order MMR (7:5) between two first-order MMRs. The formation of the delicate 7:5 resonance places strong constraints on the system’s migration history. Short-scale (starting from ∼0.1 au) Type-I migration with an inner disk edge is most consistent with the formation of TOI-1136. A low disk surface density (Σ1 au ≲ 103g cm−2; lower than the minimum-mass solar nebula) and the resultant slower migration rate likely facilitated the formation of the 7:5 second-order MMR.

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