Modelling the rotation dependence of cycle variability in sun-like stars: Answering why only slowly rotating stars produce grand minima

Abstract: The Sun and solar-type stars exhibit irregular cyclic variations in their magnetic activity over long time scales. To understand this irregularity, we employed the flux transport dynamo models to investigate the behavior of one solar mass star at various rotation rates. To achieve this, we have utilized a mean-field hydrodynamic model to specify differential rotation and meridional circulation, and we have incorporated stochastic fluctuations in the Babcock-Leighton source of the poloidal field to capture inherent fluctuations in the stellar convection. Our simulations successfully demonstrated consistency with the observational data, revealing that rapidly rotating stars exhibit highly irregular cycles with strong magnetic fields and no Maunder-like grand minima. On the other hand, slow rotators produce smoother cycles with weaker magnetic fields, long-term amplitude modulation, and occasional extended grand minima. We observed that the frequency and duration of grand minima increase with the decreasing rotation rate. These results can be understood as the tendency of a less supercritical dynamo in slow rotators to be more prone to produce extended grand minima. We further explore the possible existence of the dynamo in the subcritical regime in a Babcock-Leighton-type framework and in the presence of a small-scale dynamo.