Statistical analysis of the ambiguities in the asteroid period determinations

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 $\alpha 0.2$ 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.