Von Zeipel – Lidov – Kozai cycles in action: <i>Kepler</i> triples with eclipse depth variations: KICs 6964043, 5653126, 5731312, and 8023317

ABSTRACT 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.

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