A Statistical Stability Analysis of Earth‐like Planetary Orbits in Binary Systems

Abstract

ABSTRACTThis 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 MC, the companion eccentricity e, the companion periastron p, and the planet’s inclination angle i relative to the stellar binary plane. Specifically, we generate a large sample of survival times (τs) 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 μs≡log τs (where τs 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 orbital configurations that, 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 μs distribution and look for general features that may aid further understanding and numerical exploration of these chaotic systems. To leading order, most distributions are nearly Gaussian, with a width of σ∼0.5, although the longest‐lived systems display substantial (non‐Gaussian) tails. As a result, many independent realizations of these systems must be considered in order to characterize the survival time. The situation is more complicated for orbital configurations with longer mean survival times, owing in part to the increasing importance of resonances.