Nonlinear time-series analysis of Hyperion's lightcurves

TL;DR

This paper investigates the potential for detecting chaotic rotation of Hyperion through lightcurve analysis, emphasizing the need for long-term, well-sampled, and stationary time-series data to reliably estimate the maximal Lyapunov Exponent.

Contribution

It proposes observational strategies and conditions necessary for estimating chaos indicators in Hyperion's rotation using lightcurve data, highlighting limitations of current datasets.

Findings

Existing datasets are too short and undersampled to detect positive mLE.

Year-long observations from a single site are recommended for reliable detection.

Using multiple telescopes worldwide can improve data distribution without disrupting other projects.

Abstract

Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this aticle is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2---3 telescopes spread over the world to have observations distributed more uniformly. This may be achieved without disrupting other observational projects being conducted. The necessity of time-series to be stationary is highly stressed.