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Abstract Systems with ultra-short-period (USP) planets tend to possess larger mutual inclinations compared to those with planets located farther from their host stars. This could be explained due to precession caused by stellar oblateness at early times when the host star was rapidly spinning. However, stellar oblateness reduces over time due to the decrease in the stellar rotation rate, and this may further shape the planetary mutual inclinations. In this work, we investigate in detail how the final mutual inclination varies under the effect of a decreasing J 2 . We find that different initial parameters (e.g., the magnitude of J 2 and planetary inclinations) will contribute to different final mutual inclinations, providing a constraint on the formation mechanisms of USP planets. In general, if the inner planets start in the same plane as the stellar equator (or coplanar while misaligned with the stellar spin axis), the mutual inclination decreases (or increases then decreases) over time due to the decay of the J 2 moment. This is because the inner orbit typically possesses less orbital angular momentum than the outer ones. However, if the outer planet is initially aligned with the stellar spin while the inner one is misaligned, the mutual inclination nearly stays the same. Overall, our results suggest that either USP planets formed early and acquired significant inclinations (e.g., ≳30° with its companion or ≳10° with its host star spin axis for Kepler-653 c) or they formed late (≳Gyr) when their host stars rotated slower.
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Sweeping secular resonances and giant planet inclinations in transition discs
ABSTRACT The orbits of some warm Jupiters are highly inclined (20°–50°) to those of their exterior companions. Comparable misalignments are inferred between the outer and inner portions of some transition discs. These large inclinations may originate from planet–planet and planet–disc secular resonances that sweep across interplanetary space as parent discs disperse. The maximum factor by which a seed mutual inclination can be amplified is of the order of the square root of the angular momentum ratio of the resonant pair. We identify those giant planet systems (e.g. Kepler-448 and Kepler-693) that may have crossed a secular resonance, and estimate the required planet masses and semimajor axes in transition discs needed to warp their innermost portions (e.g. in CQ Tau). Passage through an inclination secular resonance could also explain the hypothesized large mutual inclinations in apsidally-orthogonal warm Jupiter systems (e.g. HD 147018).
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- Award ID(s):
- 2205500
- PAR ID:
- 10479299
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 527
- Issue:
- 3
- ISSN:
- 0035-8711
- Format(s):
- Medium: X Size: p. 7203-7216
- Size(s):
- p. 7203-7216
- Sponsoring Org:
- National Science Foundation
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