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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Von Zeipel – Lidov – Kozai cycles in action: Kepler triples with eclipse depth variations: KICs 6964043, 5653126, 5731312, and 8023317
We report the results of the photodynamical analyses of four compact, tight triple stellar systems, KICs 6964043, 5653126, 5731312, and 8023317, based largely on Kepler and TESS data. All systems display remarkable eclipse timing and eclipse depth variations, the latter implying a non-aligned outer orbit. Moreover, KIC 6964043 is also a triply eclipsing system. We combined photometry, ETV curves, and archival spectral energy distribution data to obtain the astrophysical parameters of the constituent stars and the orbital elements with substantial precision. KICs 6964043 and 5653126 were found to be nearly flat with mutual inclinations imut = 4${_{.}^{\circ}}$1 and 12${_{.}^{\circ}}$3, respectively, while KICs 5731312 and 8023317 (imut = 39${_{.}^{\circ}}$4 and 55${_{.}^{\circ}}$7, respectively) are found to lie in the high imut regime of the von Zeipel-Kozai-Lidov (ZKL) theorem. We show that, currently, both high inclination triples exhibit observable unusual retrograde apsidal motion. Moreover, the eclipses will disappear in all but one of the four systems within a few decades. Short-term numerical integrations of the dynamical evolution reveal that both high inclination triples are currently subject to ongoing, large amplitude (Δe ∼ 0.3) inner eccentricity variations on centuries-long time-scales, in accord with the ZKL theorem. Longer-term integrations predict that two of the four systems may become dynamically unstable on ∼ Gyr time-scales, while in the other two triples common envelope phases and stellar mergers may occur. Finally, we investigate the dynamical properties of a sample of 71 KIC/TIC triples statistically, and find that the mutual inclinations and outer mass ratios are anticorrelated at the 4σ level. We discuss the implications for the formation mechanisms of compact triples.
more » « less- NSF-PAR ID:
- 10369205
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 515
- Issue:
- 3
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 3773-3795
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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