Statistical analysis of the ambiguities in the asteroid period determinations

TL;DR

This study uses extensive simulations of asteroid lightcurves to statistically analyze ambiguities in rotation period determinations caused by observational constraints and asteroid shape effects.

Contribution

It introduces a comprehensive simulation approach to identify characteristic lightcurve features that influence period ambiguity in asteroid observations.

Findings

Lightcurves at phase angles <30° with amplitudes >0.2 mag are typically bimodal.

The first harmonic is most frequently dominant in the Fourier analysis.

For low amplitude lightcurves, the 4th harmonic can dominate in a small percentage.

Abstract

Among asteroids there exist ambiguities in their rotation period determinations. They are due to incomplete coverage of the rotation, noise and/or aliases resulting from gaps between separate lightcurves. To help to remove such uncertainties, basic characteristic of the lightcurves resulting from constraints imposed by the asteroid shapes and geometries of observations should be identified. We simulated light variations of asteroids which shapes were modelled as Gaussian random spheres, with random orientations of spin vectors and phase angles changed every $5^\circ$ from $0^\circ$ to $65^\circ$. This produced 1.4 mln lightcurves. For each simulated lightcurve Fourier analysis has been made and the harmonic of the highest amplitude was recorded. From the statistical point of view, all lightcurves observed at phase angles $\alpha < 30^\circ$, with peak-to-peak amplitudes $A>0.2$ mag are bimodal. Second most frequently dominating harmonic is the first one, with the 3rd harmonic following right after. For 1% of lightcurves with amplitudes $A < 0.1$ mag and phase angles $\alpha < 40^\circ$ 4th harmonic dominates.