Ultra-short-period Planets from Secular Chaos

Abstract

Over a hundred rocky planets orbiting Sun-like stars in very short orbital periods ( 1 day) have been discovered by the Kepler mission. These planets, known as ultra-short-period (USP) planets, are unlikely to have formed locally, or have attained their current orbits when their birth protoplanetary disks were still present. Instead, they must have migrated in later in life. Here we propose that these planets reach their current orbits by high-eccentricity migration. In a scaled-down version of the dynamics that may have been experienced by their high mass analog, the hot Jupiters, these planets reach high eccentricities via chaotic secular interactions with their companion planets and then undergo orbital circularization due to dissipation of tides raised on the planet. This proposal is motivated by the following observations: planetary systems observed by Kepler often contain several super-Earths with non-negligible eccentricities and inclinations, and possibly extending beyond ∼ AU distances; while only a small fraction of USP planets have known transiting companions, and none closely spaced, we argue that most of them should have companions at periods of ∼ 10 − 50 days. The outer sibling planets, through secular chaos, can remove angular momentum from the inner most planet, originally at periods of ∼ 5 − 10 days. When the latter reaches an eccentricity higher than 0.8, it is tidally captured by the central star and becomes an USP planet. This scenario naturally explains the observation that most USP planets have significantly more distant transiting companions compared to their counterparts at slightly longer periods (1 − 3 days), a feature un-accounted for in other proposed scenarios. Our model also predicts that USP planets should have: (i) spin-orbit angles, and inclinations relative to outer planets, in the range of ∼ 10 • − 50 • ; (ii) several outer planetary companions extending to beyond ∼ 1 AU distances, both of which may be tested by TESS and its follow-up observations. Subject headings: planets and satellites: dynamical evolution and stability

Mass determinations of the three mini-Neptunes transiting TOI-125

“…This is consistent with the observed trend that when one member of an adjacent pair of planets has an orbital period less than a day, the period ratio is unusually large (Steffen & Farr 2013;Sanchis-Ojeda et al 2014;Steffen & Coughlin 2016). The origin of the ultrashort-period planets remains unknown (Winn et al 2018) though a number of hypotheses have been proposed ranging from stripped cores of giant planets (Valsecchi et al 2014;Königl et al 2017) to various dynamical effects coupled with stellar tides (Muñoz et al 2016;Lee & Chiang 2017;Pu & Lai 2019;Petrovich et al 2019). The nearby presence of additional small planets would seem not to support the stripped-cores possibility, since hot Jupiter planets tend to be alone with few exceptions (Wright et al 2009;Steffen et al 2012;Becker et al 2015).…”

Kepler-78 and the Ultra-Short-Period planets

“…3. Petrovich et al investigated the possibility of eccentricity excitation from secular dynamical chaos in compact multiplanet systems [93]. They predicted that USP planets would often be accompanied by outer planets extending out to 1 AU.…”

Mutual Inclination Excitation by Stellar Oblateness

“…Dynamical migration mechanisms due to planetary interactions may also contribute to the large mutual inclinations of USPs close to the host stars (Petrovich et al 2019;Pu & Lai 2019). The J 2 precession timescales of the USPs are around 10 4 yrs, and thus, the transit duration variations are too small to be detected to distinguish the mechanisms.…”

“…Moreover, they showed that a large mutual inclination is also associated with a larger orbital period ratio between USP and its neighboring planets. It has been shown that dynamical hotter formation scenarios can generate orbital migration and mutual inclination of USPs simultaneously, and explain the observed signatures (Petrovich et al 2019;Pu & Lai 2019).…”