Solar Cycle Variability Induced by Tilt Angle Scatter in a Babcock--Leighton Solar Dynamo Model

We present results from a three-dimensional Babcock--Leighton dynamo model that is sustained by the explicit emergence and dispersal of bipolar magnetic regions (BMRs). On average, each BMR has a systematic tilt given by Joy's law. Randomness and nonlinearity in the BMR emergence of our model produce variable magnetic cycles. However, when we allow for a random scatter in the tilt angle to mimic the observed departures from Joy's law, we find more variability in the magnetic cycles. We find that the observed standard deviation in Joy's law of $\sigma_\delta = 15^\circ$ produces a variability comparable to observed solar cycle variability of $\sim $ 32%, as quantified by the sunspot number maxima between 1755--2008. We also find that tilt angle scatter can promote grand minima and grand maxima. The time spent in grand minima for $\sigma_\delta = 15^\circ$ is somewhat less than that inferred for the Sun from cosmogenic isotopes (about 9% compared to 17%). However, when we double the tilt scatter to $\sigma_\delta = 30^\circ$, the simulation statistics are comparable to the Sun ($\sim $18% of the time in grand minima and $\sim 10$% in grand maxima). Though the Babcock--Leighton mechanism is the only source of poloidal field, we find that our simulations always maintain magnetic cycles even at large fluctuations in the tilt angle. We also demonstrate that tilt quenching is a viable and efficient mechanism for dynamo saturation; a suppression of the tilt by only 1-2$^\circ$ is sufficient to limit the dynamo growth. Thus, any potential observational signatures of tilt quenching in the Sun may be subtle.