  Predictions of solar cycle 24 obtained from advection-dominated and
diffusion-dominated kinematic dynamo models are different if the
Babcock-Leighton mechanism is the only source of the poloidal field. Yeates et
al. (2008) argue that the discrepancy arises due to different memories of the
solar dynamo for advection- and diffusion-dominated solar convection zones. We
aim to investigate the differences in solar cycle memory obtained from
advection-dominated and diffusion-dominated kinematic solar dynamo models.
Specifically, we explore whether the inclusion of Parker's mean-field $\alpha$
effect, in addition to the Babcock-Leighton mechanism, has any impact on the
memory of the solar cycle. We used a kinematic flux transport solar dynamo
model where poloidal field generation takes place due to both the
Babcock-Leighton mechanism and the mean-field $\alpha$ effect. We additionally
considered stochastic fluctuations in this model and explored cycle-to-cycle
correlations between the polar field at the minima and toroidal field at cycle
maxima. Solar dynamo memory is always limited to only one cycle in
diffusion-dominated dynamo regimes while in advection-dominated regimes the
memory is distributed over a few solar cycles. However, the addition of a
mean-field alpha effect reduces the memory of the solar dynamo to within one
cycle in the advection-dominated dynamo regime when there are no fluctuations
in the mean-field $\alpha$ effect. When fluctuations are introduced in the
mean-field poloidal source a more complex scenario is evident, with very weak
but significant correlations emerging across a few cycles. Our results imply
that inclusion of a mean-field alpha effect in the framework of a flux
transport Babcock-Leighton dynamo model leads to additional complexities that
may impact memory and predictability of predictive dynamo models of the solar
cycle.
