The long-term stability of extrasolar system HD 37124. Numerical study of resonance effects

TL;DR

This paper develops numerical tools to analyze the long-term stability of the HD 37124 extrasolar system, revealing that resonance interactions can induce chaos and potential system self-destruction over millions of years.

Contribution

It introduces an efficient algorithm using the tangent map and MEGNO indicator for stability analysis of planetary systems, applied specifically to HD 37124.

Findings

System is in a dynamically active phase space region.

Long-term stability is influenced by low-order resonances.

Three-body resonances can cause chaos and system self-destruction.

Abstract

We describe numerical tools for the stability analysis of extrasolar planetary systems. In particular, we consider the relative Poincare variables and symplectic integration of the equations of motion. We apply the tangent map to derive a numerically efficient algorithm of the fast indicator MEGNO (a measure of the maximal Lyapunov exponent) that helps to distinguish chaotic and regular configurations. The results concerning the three-planet extrasolar system HD 37124 are presented and discussed. The best fit solutions found in earlier works are studied more closely. The system involves Jovian planets with similar masses. The orbits have moderate eccentricities, nevertheless the best fit solutions are found in dynamically active region of the phase space. The long term stability of the system is determined by a net of low-order two-body and three-body mean motion resonances. In particular, the three-body resonances may induce strong chaos that leads to self-destruction of the system after Myrs of apparently stable and bounded evolution. In such a case, numerically efficient dynamical maps are useful to resolve the fine structure of the phase space and to identify the sources of unstable behavior.