No Arabic abstract
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.
Large dips in the brightness for a number of stars have been observed, for which the tentative explanation is occultation of the star by a transiting circumplanetary disk or ring system. In order for the circumplanetary disk/rings to block the host stars light, the disk must be tilted out of the planets orbital plane, which poses stability problems due to the radial extent of the disk required to explain the brightness dip durations. This work uses N-body integrations to study the structure and stability of circumplanetary disk/ring systems tilted out of the planets orbital plane by the spinning planets mass quadrupole. Simulating the disk as a collection of test particles with orbits initialized near the Laplace surface (equilibrium between tidal force from host star and force from planets mass quadrupole), we find that many extended, inclined circumplanetary disks remain stable over the duration of the integrations (~3-16 Myr). Two dynamical resonances/instabilities excite the particle eccentricities and inclinations: the Lidov-Kozai effect which occurs in the disks outer regions, and ivection resonance which occurs in the disks inner regions. Our work places constraints on the maximum radial extent of inclined circumplanetary disk/ring systems, and shows that gaps present in circumplanetary disks do not necessarily imply the presence of exomoons.
This paper explores the stability of an Earth-like planet orbiting a solar-mass star in the presence of a stellar companion using ~ 400,000 numerical integrations. Given the chaotic nature of the systems being considered, we perform a statistical analysis of the ensuing dynamics for ~500 orbital configurations defined by the following set of orbital parameters: the companion mass; the companion eccentricity; the companion periastron; and the planets inclination angle relative to the stellar binary plane. Specifically, we generate a large sample of survival times for each orbital configuration through the numerical integration of N >> 1 equivalent experiments (e.g., with the same orbital parameters but randomly selected initial orbital phases). We then construct distributions of survival time using the variable mu_s = log tau_s (where tau_s is in years) for each orbital configuration. The primary objective of this work is twofold. First, we use the mean of the distributions to gain a better understanding of what orbital configurations, while unstable, have sufficiently long survival times to make them interesting to the study of planet habitability. Second, we calculate the width, skew, and kurtosis of each mu_s distribution and look for general features that may aid further understanding and numerical exploration of these chaotic systems.
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.
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.
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.