Evidence of persistence of weak magnetic cycles driven by meridional plasma flows during solar grand minima phases

Long-term sunspot observations and solar activity reconstructions reveal that the Sun occasionally slips into quiescent phases known as solar grand minima, the dynamics during which is not well understood. We use a flux transport dynamo model with stochastic fluctuations in the mean-field and Babcock-Leighton poloidal field source terms to simulate solar cycle variability. Our long-term simulations detect a gradual decay of the polar field during solar grand minima episodes. Although regular active region emergence stops, compromising the Babcock-Leighton mechanism, weak magnetic activity continues during minima phases sustained by a mean-field $\alpha$-effect; surprisingly, periodic polar field amplitude modulation persist during these phases. A spectral analysis of the simulated polar flux time series shows that the 11-year cycle becomes less prominent while high frequency periods and periods around 22 years manifest during grand minima episodes. Analysis of long-term solar open flux observations appears to be consistent with this finding. Through numerical experimentation we demonstrate that the persistence of periodic amplitude modulation in the polar field and the dominant frequencies during grand minima episodes are governed by the speed of the meridional plasma flow -- which appears to act as a clock.