Monday, November 19, 2012

1211.3956 (S. Satyal et al.)

Assessment of Hill stability versus known chaos indicators: application to the dynamics of S-type extrasolar planets    [PDF]

S. Satyal, B. Quarles, T. C. Hinse
The efficacy of the Hill stability (HS) criterion is compared to other known chaos indicators such as the maximum Lyapunov exponent (MLE) and Mean Exponential Growth factor of Nearby Orbits (MEGNO) maps. The orbits of four individual planets in four known binary star systems, \gamma Cephei, Gliese 86, HD 41004, and HD 196885, are numerically integrated using various numerical techniques to assess the chaotic or quasi-periodic nature of the dynamical system considered. The Hill stability which measures the orbital perturbation of a planet around the primary star due to the secondary star is calculated for each system. The maximum Lyapunov exponent time series are generated to measure the divergence/convergence rate of stable manifolds, which are used to differentiate between chaotic and non-chaotic orbits. Then, we calculate dynamical MEGNO maps from solving the variational equations along with the equations of motion. These maps allow us to accurately differentiate between stable and unstable dynamical systems. The results obtained from the analysis of HS, MLE, and MEGNO maps are analysed for their dynamical variations and resemblance. The qualitative efficiency of each indicator is analysed which demonstrates that HS can be used as an alternative to MLE. The HS test for the planets shows stability and quasi-periodicity for at least ten million years. The MLE and the MEGNO maps have also indicated the local quasi-periodicity and global stability in relatively short integration period. Based on our discussion, the HS criterion is found to be a comparably efficient tool to measure the stability of planetary orbits with respect to different simulation timespans.
View original: http://arxiv.org/abs/1211.3956

No comments:

Post a Comment