The stability limit for circumbinary planets (CBPs) is not well defined and can depend on initial parameters defining either the planetary orbit or the inner binary orbit. We expand on the work of Holman & Wiegert (1999, AJ 117, 621) to develop numerical tools for quick, easy, and accurate determination of the stability limit. The results of our simulations, as well as our numerical tools, are available to the community through Zenodo and GitHub, respectively. We employ a grid interpolation method based on ∼150 million full N-body simulations of initially circular, coplanar systems and compare to the 9 known Kepler CBP systems. Using a formalism from planet packing studies, we find that 55% of the Kepler CBP systems allow for an additional equal-mass planet to potentially exist on an interior orbit relative to the observed planet. Therefore, we do not find strong evidence for a pile-up in the Kepler CBP systems and more detections are needed to adequately characterize the formation mechanisms for the CBP population. Observations from the Transiting Exoplanet Survey Satellite are expected to substantially increase the number of detections using the unique geometry of CBP systems, where multiple transits can occur during a single conjunction.
Of the nine confirmed transiting circumbinary planet systems, only Kepler-47 is known to contain more than one planet. Kepler-47 b (the "inner planet") has an orbital period of 49.5 days and a radius of about 3 R ⊕ . Kepler-47 c (the "outer planet") has an orbital period of 303.2 days and a radius of about 4.7 R ⊕ . Here we report the discovery of a third planet, Kepler-47 d (the "middle planet"), which has an orbital period of 187.4 days and a radius of about 7 R ⊕ . The presence of the middle planet allows us to place much better constraints on the masses of all three planets, where the 1σ ranges are less than 26 M ⊕ , between 7 − 43 M ⊕ , and between 2 − 5 M ⊕ for the inner, middle, and outer planets, respectively. The middle and outer planets have low bulk densities,
In the Jupiter-Io system, the moon's motion produces currents along the field lines that connect it to Jupiter's polar regions. The currents generate, and modulate radio emissions along their paths via the electron-cyclotron maser instability. Based on this process, we suggest that such modulation of planetary radio emissions may reveal the presence of exomoons around giant planets in exoplanetary systems. A model explaining the modulation mechanism in the Jupiter-Io system is extrapolated, and used to define criteria for exomoon detectability. A cautiously optimistic scenario of possible detection of such exomoons around Epsilon Eridani b, and Gliese 876 b is provided.
The orbits of two individual planets in two known binary star systems, γ Cephei and HD 196885 are numerically integrated using various numerical techniques to assess the chaotic or quasi-periodic nature of the dynamical system considered. The Hill stability (HS) function which measures the orbital perturbation of a planet around the primary star due to the secondary star is calculated for each system. The maximum Lyapunov exponent (MLE) time series are generated to measure the divergence/convergence rate of stable manifolds, which are used to differentiate between chaotic and nonchaotic orbits. Then, we calculate dynamical Mean Exponential Growth factor of Nearby Orbits (MEGNO) maps from solving the variational equations along with the equations of motion. These maps allow us to accurately differentiate between stable and unstable dynamical systems. The results obtained from the analysis of HS, MLE, and MEGNO maps are analysed for their dynamical variations and resemblance. The HS test for the planets shows stability and quasi-periodicity for at least ten million years. The MLE and the MEGNO maps have also indicated the local quasi-periodicity and global stability in a relatively short integration period. The orbital stability of the systems is tested using each indicator for various values of planet inclinations (i pl 25 • ) and binary eccentricities. The reliability of HS criterion is also discussed based on its stability results compared with the MLE and MEGNO maps.
The idea of single exomoon detection due to the radio emissions caused by its interaction with the host exoplanet is extended to multiple-exomoon systems. The characteristic radio emissions are made possible in part by plasma from the exomoon's own ionosphere. In this work, it is demonstrated that neighboring exomoons and the exoplanetary magnetosphere could also provide enough plasma to generate a detectable signal. In particular, the plasma-torus-sharing phenomenon is found to be particularly well suited to facilitate the radio detection of plasmadeficient exomoons. The efficiency of this process is evaluated, and the predicted power and frequency of the resulting radio signals are presented.
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