Nonlinear Mechanisms that Regulate the Solar Cycle Amplitude

The solar magnetic activity cycle has an amplitude that varies within a wide but limited range of values. This implies that there are nonlinear mechanisms that prevent runaway solutions. The purpose of this paper is to propose observable nonlinear mechanisms in the framework of the Babcock-Leighton-type dynamo. Sunspot emergences show systematic properties that strong cycles tend to have higher mean latitudes and lower tilt angle coefficients. We use the surface flux transport model to investigate the effect of these systematic properties on the expected final total dipolar moment, i.e., cancellation plus generation of dipole moment by a whole solar cycle. We demonstrate that the systematic change in latitude has similar nonlinear feedback on the solar cycle (latitudinal quenching) as tilt does (tilt quenching). Both forms of quenching lead to the expected final total dipolar moment being enhanced for weak cycles and saturated to a nearly constant value for normal and strong cycles. This explains observed long-term solar cycle variability, e.g., the Gnevyshev-Ohl rule, which, in turn, justifies the nonlinear mechanisms inherent in the Babcock-Leighton-type dynamo.