External Forcing of the Solar Dynamo

Abstract

In this paper I examine whether external forcing of the solar dynamo on long timescales can produce detectable signal in the form of long term modulation of the magnetic cycle. This task is motivated in part by some recent proposals (Abreu et al., 2012; Astron. Ap., 548, A88; Stefani et al., 2021; Solar Phys., 296, 88), whereby modulation of the solar activity cycle on centennial and millennial timescales, as recovered from the cosmogenic radioisotope record, is attributed to perturbation of the tachocline driven by planetary orbital motions. Working with a two-dimensional mean-field-like kinematic dynamo model of the Babcock-Leighton variety, I show that such an external forcing signal may be detectable in principle but is likely to be obliterated by other internal sources of fluctuations, in particular stochastic perturbations of the dynamo associated with convective turbulence, unless a very efficient amplification mechanism is at play. I also examine the ability of external tidal forcing to synchronize an otherwise autonomous, internal dynamo operating at a nearby frequency. Synchronization is readily achieved, and turns out to be very robust to the introduction of stochastic noise, but requires very high forcing amplitudes, again highlighting the critical need for a powerful amplification mechanism.