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Register a new userRelativistic Dynamical Stability Criterion of Multi-Planet Systems with a Distant Companion
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Multi-planetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai-Lidov mechanism. However, the star-planet and the planet-planet interactions can help stabilize the system. Here, we extend the previous stability criterion that considered only the companion-planet and planet-planet interactions by also accounting for short-range forces or effects, specifically, relativistic precession induced by the host star. A general analytical stability criterion is developed for planetary systems with $N$ inner planets and a far-away inclined perturber by comparing precession rates of relevant dynamical effects. Furthermore, we demonstrate as examples that in systems with $2$ and $3$ planets, the analytical criterion is consistent with numerical simulations using a combination of Gausss averaging method and direct N-body integration. This new stability criterion extends the parameter space in which inclined companions of multi-planet systems can inhabit.
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To date, 17 circumbinary planets have been discovered. In this paper, we focus our attention on the stability of the Kepler circumbinary planetary systems with only one planet, i.e. Kepler-16, Kepler-34, Kepler-35, Kepler-38, Kepler-64 and Kepler-413. In addition to their intrinsic interest, the study of such systems is an opportunity to test our understanding of planetary system formation and evolution around binaries. The investigation is done by means of numerical simulations. We perform numerical integrations of the full equations of motion of each system with the aim of checking the stability of the planetary orbit. The investigation of the stability of the above systems consists of three numerical experiments. In the first one we perform a long term (1Gyr) numerical integration of the nominal solution of the six Kepler systems under investigation. In the second experiment, we look for the critical semimajor axis of the six planetary orbits, and finally, in the third experiment, we construct two dimensional stability maps on the eccentricity-pericentre distance plane. Additionally, using numerical integrations of the nominal solutions we checked if this solutions were close to the exact resonance.
The SIM Lite mission will undertake several planet surveys. One of them, the Deep Planet Survey, is designed to detect Earth-mass exoplanets in the habitable zones of nearby main sequence stars. A double blind study has been conducted to assess the capability of SIM to detect such small planets in a multi-planet system where several giant planets might be present. One of the tools which helped in deciding if the detected planets were actual was an orbit integrator using the publicly available HNBody code so that the orbit solutions could be analyzed in terms of temporal stability over many orbits. In this contribution, we describe the implementation of this integrator and analyze the different blind test solutions. We discuss also the usefulness of this method given that some planets might be not detected but still affect the overall stability of the system.
Transit surveys have revealed a significant population of compact multi-planet systems, containing several sub-Neptune-mass planets on close-in, tightly-packed orbits. These systems are thought to have formed through a final phase of giant impacts, which would tend to leave systems close to the edge of stability. Here, we assess this hypothesis, comparing observed eccentricities in systems exhibiting transit-timing variations (TTVs), with the maximum eccentricities compatible with long-term stability. We use the machine-learning classifier SPOCK (Tamayo et al. 2020) to rapidly classify the stability of numerous initial configurations and hence determine these stability limits. While previous studies have argued that multi-planet systems are often maximally packed, in the sense that they could not host any additional planets, we find that the existing planets in these systems have measured eccentricities below the limits allowed by stability by a factor of 2--10. We compare these results against predictions from the giant impact theory of planet formation, derived from both $N$-body integrations and theoretical expectations that in the absence of dissipation, the orbits of such planets should be distributed uniformly throughout the phase space volume allowed by stability. We find that the observed systems have systematically lower eccentricities than this scenario predicts, with a median eccentricity about 4 times lower than predicted. These findings suggest that if such systems formed through giant impacts, then some dissipation must occur to damp their eccentricities. This may take place during formation, perhaps through interactions with the natal gas disk or a leftover population of planetesimals, or over longer timescales through the coupling of tidal and secular processes.
We study the excitation of planet inclination by a novel secular-orbital resonance in multiplanet systems perturbed by binary companions which we call ivection. Ivection resonance happens when the nodal precession rate of the planet matches a multiple of the orbital frequency of the binary, and its physical nature is similar to the previously-studied evection resonance. Capture into an ivection resonance requires the nodal precession rate to slowly increase passed the resonant value during planet migration, and will excite the mutual inclination of the planets without affecting their eccentricities. If the system encounters another resonance (e.g., a mean-motion resonance) after being captured into an ivection resonance, resonance overlap can make the system dynamically unstable, ejecting the smaller planet. Using ivection resonance, we are able to explain why planets in Kepler-108 have significant mutual inclination but modest eccentricity. We also find a deficit of multiplanet systems which would have nodal precession period comparable to binary orbital period, suggesting that ivection resonance may inhibit the formation or destablize multiplanet systems with external binary companion.
Kepler-454 (KOI-273) is a relatively bright (V = 11.69 mag), Sun-like starthat hosts a transiting planet candidate in a 10.6 d orbit. From spectroscopy, we estimate the stellar temperature to be 5687 +/- 50 K, its metallicity to be [m/H] = 0.32 +/- 0.08, and the projected rotational velocity to be v sin i <2.4 km s-1. We combine these values with a study of the asteroseismic frequencies from short cadence Kepler data to estimate the stellar mass to be 1.028+0:04-0:03 M_Sun, the radius to be 1.066 +/- 0.012 R_Sun and the age to be 5.25+1:41-1:39 Gyr. We estimate the radius of the 10.6 d planet as 2.37 +/- 0.13 R_Earth. Using 63 radial velocity observations obtained with the HARPS-N spectrograph on the Telescopio Nazionale Galileo and 36 observations made with the HIRES spectrograph at Keck Observatory, we measure the mass of this planet to be 6.8 +/- 1.4M_Earth. We also detect two additional non-transiting companions, a planet with a minimum mass of 4.46 +/- 0.12 M_J in a nearly circular 524 d orbit and a massive companion with a period >10 years and mass >12.1M_J . The twelve exoplanets with radii <2.7 R_Earth and precise mass measurements appear to fall into two populations, with those <1.6 R_Earth following an Earth-like composition curve and larger planets requiring a significant fraction of volatiles. With a density of 2.76 +/- 0.73 g cm-3, Kepler-454b lies near the mass transition between these two populations and requires the presence of volatiles and/or H/He gas.
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