Nonlinear time series analysis of Hyperion's rotation: photometric observations and numerical simulations

TL;DR

This paper analyzes Hyperion's chaotic rotation using time series analysis and numerical simulations, estimating persistence and chaos indicators, and highlights the need for longer observations to better understand its dynamics.

Contribution

It applies nonlinear time series analysis to Hyperion's photometric data and compares results with numerical simulations, providing new insights into its chaotic rotational behavior.

Findings

Hurst exponent indicates persistent behavior (H≈0.87-0.88)

Chaotic zone characterized by a Lyapunov time of about 30 days

Short dataset limits reliable Lyapunov exponent estimation

Abstract

The case of Hyperion has been studied excesively due to the fact it is the largest known celestial body of a highly aspherical shape. It also has a low mass density and remains in a 4:3 orbital resonance with Titan. Its lightcurve, obtained through photometric observations by (Klavetter 1989a,b), was initialy used to show that Hyperion's rotation exhibits no periodicity. Herein it is analyzed in the means of time series analysis. The Hurst Exponent was estimated to be H=0.87, indicating a persistent behaviour. The largest Lyapunov Exponent $\lambda_{max}$ unfortunately could not be given a reliable estimate because of the shortness of the dataset, consisting 38 observational points. These results are compared with numerical simulations, which gave a value H=0.88 for the chaotic zone of the phase space. The Lyapunov time $T_{Lyap}=1/\lambda_{max}$ is about 30 days, which is roughly 1.5 times greater than the orbital period. By conducting observations over a longer period an insight in the dynamical features of the present rotational state is possible.