Rotation of Halley's comet

Abstract

The two distinct periodicities of 2.2 days and 7.4 days inferred from the coma structure and lightcurves of Halley's comet together with the irregular shape of its nucleus suggest that the nucleus is not in a state of principal axis rotation. We model this situation using numerical simulations supported by analytic calculations. It is easy to numerically generate lightcurves from modulated jets of material which exhibit both periodicities if we choose initial conditions for a representative nucleus such that the shorter period is the rotation period and the longer period is that of precession of the spin vector in the body frame of reference. The dominant spectral power in such curves most often corresponds to the 7.4 day period unless the amplitude of precession is very small. Although curves similar to those observed over short time intervals are obtained for precession about either of the axes with extreme moments of inertia, the observed marked seasonal changes in the lightcurve are only produced for precession about the axis of maximum moment of inertia. The generation and stability of a wobble-type rotation state is investigated by numerically solving Euler's equations for the reaction torque from a jet of ejected material. A nonprincipal axis rotation is easy to excite from an initial rotation about the axis of maximum moment of inertia (minimum energy) only if the nucleus is nearly axisymmetric. Except for almost perfect axial symmetry, excitation of a precession about the axis of minimum moment of inertia is always frustrated by an initial precession about the axis of maximum moment of inertia. In the more probable case of significant triaxiality, even a precession of the spin about the axis of maximum moment of inertia is difficult to excite from an initial minimum energy state, and it can change only slowly from the jet-induced torques. However, this slow change could suffice to generate a substantial amplitude wobble from the cumulative effects of many apparitions. The damping time for the wobble is O(10 6 t 10 8) years, which rules out a primordial origin of a wobble but allows a gradual excitation. Significant changes in the spin angular momentum can occur in a single apparition, but the stability of the amplitude of precession about the axis of maximum moment of inertia means that a rotation state which is relatively stable over many apparitions is not unreasonable. The improbability of exciting a spin precession about the axis of minimum moment of inertia, the relative instability of this state to the jet-induced torques, and the smaller probability of observing significant seasonal changes in the lightcurve in this state all favor the model in which Halley's nucleus precesses about the axis of maximum moment of inertia.