The observed relationships between some solar rotation parameters and the activity cycle

Several parameters of the solar rotation show variations which appear to relate to the phase of the solar-activity cycle. The latitude gradient of the differential rotation, as seen in the coefficients of the sin2 and sin4 terms in the latitude expansion, shows marked variations with the cycle. One of these variations may be described as a one-cycle-per-hemisphere torsional oscillation with a period of 11 years, where the high latitudes rotate faster at solar-activity maximum and slower at minimum, and the low latitudes rotate faster at solar-activity minimum and slower at maximum. Another variation is a periodic oscillation of the fractional difference in the low-latitude rotation between north and south hemispheres. The possibility of a variation in the absolute rotational velocity of the sun in phase with the solar cycle remains an open question. The two-cycle-per-hemisphere torsional waves in the solar rotation also represent an aspect of the rotation which varies with the cycle. It is shown that the amplitude of the fast flowing zone rises a year before the rise to activity maximum. The fast zone seems to be physically the more significant of the two zones.