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Register a new userA Statistical Stability Analysis of Earth-like Planetary Orbits in Binary Systems
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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.
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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.
We considered the problem of stability for planets of finite mass in binary star systems. We selected a huge set of initial conditions for planetary orbits of the S-type, to perform high precision and very extended in time integrations. For our numerical integrations, we resorted to the use of a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term time integrations. We estimated the probability of different types of instability: planet collisions with the primary or secondary star or planet ejected away from the binary star system. We confirm and generalize to massive planets the dependence of the critical semi-major axis on eccentricity and mass ratio of the binary already found by Holman and Wiegert (1999). We were also able to pick a significant number of orbits that are only `marginally stable, according to the classification introduced by Musielak et al. (2005). A, natural, extension of this work has been the study of the effect of perturbations induced to circumbinary planet motion by a passing-by star, like it often happens in a star cluster. One of the targets of this analysis is the investigation of the possibility that a planet, formerly on a stable S-type orbit around one of the two stars, could transit to a stable P-type orbit (or viceversa). We performed a series of more than 4500 scattering experiments with different initial conditions typical of encounters in small star clusters. We found some interesting behaviors of the systems after perturbation and showed how a transition from an inner (S-type) stable orbit to a circumbinary (P-type) (and vice-versa) has a very low (but non null) probability.
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.
To date, more than 100 giant Jupiter-like planets have been discovered in Doppler surveys of solar-type stars. In this paper, we perform simulations to investigate three systems: GJ 876, HD 82943 and 55 Cnc. The former two systems both have a pair of planets in the 2:1 Mean Motion Resonance (MMR), while the inner two companions of the later is close to 3:1 MMR. By integrating hundreds of the planetary orbits of three systems for million years, we find that for GJ 876 and HD 82943, the critical argument $lambda_{1} - 2lambda_{2} + varpi_{1}$ and $lambda_{1} - 2lambda_{2} + varpi_{2}$ librate about $0^{circ}$ or $180^{circ}$, indicating 2:1 MMR can play an important role in stabilizing the motion of the planets so that they are protected from frequent close encounters. As for 55 Cnc, we further show the three resonant arguments for 3:1 MMR execute librations for millions of years respectively, which reveals the evidence of the resonance for this system. Additionally, we should emphasize another vital mechanism is the apsidal phase-locking between a couple of planets for a certain system. For GJ 876 and HD 82943, we discover the relative apsidal longitudes $varpi_{1} - varpi_{2}$ move about $0^{circ}$ or $180^{circ}$, respectively; but for 55 Cnc, we find that there exists an asymmetric apsidal libration between two inner planets. Finally, we made a brief discussion about the Habitable Zones in the exoplanetary systems.
The carbon-silicate cycle regulates the atmospheric $CO_2$ content of terrestrial planets on geological timescales through a balance between the rates of $CO_2$ volcanic outgassing and planetary intake from rock weathering. It is thought to act as an efficient climatic thermostat on Earth and, by extension, on other habitable planets. If, however, the weathering rate increases with the atmospheric $CO_2$ content, as expected on planets lacking land vascular plants, the carbon-silicate cycle feedback can become severely limited. Here we show that Earth-like planets receiving less sunlight than current Earth may no longer possess a stable warm climate but instead repeatedly cycle between unstable glaciated and deglaciated climatic states. This has implications for the search for life on exoplanets in the habitable zone of nearby stars.
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