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Register a new userThe Dynamics and Stability of Circumbinary Orbits
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We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a nodal libration mechanism in the longitude of the ascending node and in the inclination to the plane of the binary. We (i) analyse and quantify the behaviour of these orbits with reference to analytical work performed by Farago & Laskar (2010) and (ii) investigate the stability of these orbits over time. This work is the first dynamically aware analysis of the stability of circumbinary orbits across both binary mass fraction and binary eccentricity. This work also has implications for exoplanetary astronomy in the existence and determination of stable orbits around binary systems.
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The Kepler mission has detected a number of transiting circumbinary planets (CBPs). Although currently not detected, exomoons could be orbiting some of these CBPs, and they might be suitable for harboring life. A necessary condition for the existence of such exomoons is their long-term dynamical stability. Here, we investigate the stability of exomoons around the Kepler CBPs using numerical $N$-body integrations. We determine regions of stability and obtain stability maps in the (a_m,i_pm) plane, where a_m is the initial exolunar semimajor axis with respect to the CBP, and i_pm is the initial inclination of the orbit of the exomoon around the planet with respect to the orbit of the planet around the stellar binary. Ignoring any dependence on i_pm, for most Kepler CBPs the stability regions are well described by the location of the 1:1 mean motion commensurability of the binary orbit with the orbit of the moon around the CBP. This is related to a destabilizing effect of the binary compared to the case if the binary were replaced by a single body, and which is borne out by corresponding 3-body integrations. For high inclinations, the evolution is dominated by Lidov-Kozai oscillations, which can bring moons in dynamically stable orbits to close proximity within the CBP, triggering strong interactions such as tidal evolution, tidal disruption, or direct collisions. This suggests that there is a dearth of highly-inclined exomoons around the Kepler CBPs, whereas coplanar exomoons are dynamically allowed.
We analyze the stability of two charged conducting spheres orbiting each other. Due to charge polarization, the electrostatic force between the two spheres deviates significantly from $1/r^2$ as they come close to each other. As a consequence, there exists a critical angular momentum, $L_c$, with a corresponding critical radius $r_c$. For $L > L_c$ two circular orbits are possible: one at $r > r_c$ that is stable and the other at $r < r_c$ that is unstable. This critical behavior is analyzed as a function of the charge and the size ratios of the two spheres.
Ring galaxies are amazing objects exemplified by the famous case of the Hoags Object. Here the mass of the central galaxy may be comparable to the mass of the ring, making it a difficult case to model mechanically. In a previous paper, it was shown that the outer potential of a torus (ring) can be represented with good accuracy by the potential of a massive circle with the same mass. This approach allows us to simplify the problem of the particle motion in the gravitational field of a torus associated with a central mass by replacing the torus with a massive circle. In such a system there is a circle of unstable equilibrium that we call Lagrangian circle (LC). Stable circular orbits exist only in some region limited by the last possible circular orbit related to the disappearance of the extrema of the effective potential. We call this orbit the outermost stable circular orbit (OSCO) by analogy with the innermost stable circular orbit (ISCO) in the relativistic case of a black hole. Under these conditions, there is a region between OSCO and LC where the circular motion is not possible due to the competition between the gravitational forces by the central mass and the ring. As a result, a gap in the matter distribution can form in Hoag-like system with massive rings.
Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of its host stars and on the dynamical properties of the planetary orbit. The trajectory of a planet in a double star system can be determined, approximating stars and planets with point masses, by solving numerically the equations of motion of the classical three-body system. In this study, we analyze a large data set of planetary orbits, made up with high precision long integration at varying: the mass of the planet, its distance from the primary star, the mass ratio for the two stars in the binary system, and the eccentricity of the star motion. To simulate the gravitational dynamics, we use a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term integration. In our data analysis, we evaluate if an orbit is stable or not and also provide the statistics of different types of instability: collisions with the primary or secondary star and planets ejected away from the binary star system. Concerning the stability, we find a significant number of orbits that are only marginally stable, according to the classification introduced by Musielak et al. 2005. For planets of negligible mass, we estimate the critical semi-major axis $a_c$ as a function of the mass ratio and the eccentricity of the binary, in agreement with the results of Holman and Wiegert 1999. However, we find that for very massive planets (Super-Jupiters) the critical semi-major axis decrease in some cases by a few percent, compared to cases in which the mass of the planet is negligible.
Exoplanet detection in the past decade by efforts including NASAs Kepler and TESS missions has discovered many worlds that differ substantially from planets in our own Solar system, including more than 400 exoplanets orbiting binary or multi-star systems. This not only broadens our understanding of the diversity of exoplanets, but also promotes our study of exoplanets in the complex binary and multi-star systems and provides motivation to explore their habitability. In this study, we analyze orbital stability of exoplanets in non-coplanar circumbinary systems using a numerical simulation method, with which a large number of circumbinary planet samples are generated in order to quantify the effects of various orbital parameters on orbital stability. We also train a machine learning model that can quickly determine the stability of the circumbinary planetary systems. Our results indicate that larger inclinations of the planet tend to increase the stability of its orbit, but change in the planets mass range between Earth and Jupiter has little effect on the stability of the system. In addition, we find that Deep Neural Networks (DNNs) have higher accuracy and precision than other machine learning algorithms.
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