  Power spectra of solar activity based on historical records of sunspot
numbers and on cosmogenic isotopes show peaks with enhanced power apart from
the dominant 11-year solar cycle, such as the 90-year Gleissberg cycle or the
210-year de Vries cycle. In a previous paper we have shown that the overall
shape of the power spectrum is well represented by the results of the generic
normal form model for a noisy and weakly nonlinear limit cycle, with parameters
all determined by observations. Using this model as a null case, we show here
that all local peaks with enhanced power, apart from the 11-year band, are
consistent with realisation noise. Even a $3\sigma$ peak is expected to occur
with a probability of about 0.25 at least once among the 216 period bins
resolved by the cosmogenic isotope data. This casts doubt upon interpretations
of such peaks in terms of intrinsic periodicities of the solar dynamo process.

Solar and Stellar Astrophysics