Role of observable nonlinearities in solar cycle modulation

Context. Two candidate mechanisms have recently been considered with regard to the nonlinear modulation of solar cycle amplitudes. Tilt quenching (TQ) comprises the negative feedback between the cycle amplitude and the mean tilt angle of bipolar active regions relative to the azimuthal direction. Latitude quenching (LQ) consists of a positive correlation between the cycle amplitude and average emergence latitude of active regions. Aims. Here, we explore the relative importance and the determining factors behind the LQ and TQ effects. Methods. We systematically probed the degree of nonlinearity induced by TQ and LQ, as well as a combination of both using a grid based on surface flux transport (SFT) models. The roles played by TQ and LQ are also explored in the successful 2x2D dynamo model, which has been optimized to reproduce the statistical behaviour of real solar cycles. Results. The relative importance of LQ versus TQ is found to correlate with the ratio u(0)/eta in the SFT model grid, where u(0) is the meridional flow amplitude and eta is the diffusivity. An analytical interpretation of this result is given, further demonstrating that the main underlying parameter is the dynamo effectivity range, lambda(R), which is, in turn, determined by the ratio of equatorial flow divergence to diffusivity. The relative importance of LQ versus TQ is shown to scale as C-1 + C-2/lambda(R). The presence of a latitude quenching effect is seen in the 2x2D dynamo, contributing to the nonlinear modulation by an amount that is comparable to TQ. For other dynamo and SFT models considered in the literature, the contribution of LQ to the modulation covers a broad range - from entirely insignificant to serving as a dominant source of feedback. On the other hand, the contribution of a TQ effect (with the usually assumed amplitude) is never shown to be negligible.