On the maximum amplitude of harmonics of an asteroid lightcurve

Most asteroid lightcurves are dominated by the second harmonic of the rotation period, caused by elongated shape. However, if the shape is not very elongate, other harmonics may dominate, leading to ambiguity of which is the true rotation period. We argue from geometry that at low phase angle, harmonics other than the second with amplitude exceeding ∼0.4 magnitude are nearly impossible, so lightcurves with larger amplitude than that suggest a unique period dominated by the second harmonic, unless the spin is complex, non-principal axis rotation. On the other hand, lightcurves with amplitude less than 0.2-0.3 magnitudes can be dominated by other harmonics, especially the 4th and 6th, so the period may be ambiguous unless odd harmonics can be found to identify the true rotation period. We present examples of each, low and high amplitude ambiguities.