Predicting frequency changes of global-scale solar Rossby modes due to solar cycle changes in internal rotation

Context. Large-scale equatorial Rossby modes have been observed on the Sun over the last two solar cycles.
Aims: We investigate the impact of the time-varying zonal flows on the frequencies of Rossby modes.
Methods: A first-order perturbation theory approach is used to obtain an expression for the expected shift in the mode frequencies due to perturbations in the internal rotation rate.
Results: Using the time-varying rotation from helioseismic inversions we predict the changes in Rossby mode frequencies with azimuthal orders from m = 1 to m = 15 over the last two solar cycles. The peak-to-peak frequency change is less than 1 nHz for the m = 1 mode, grows with m, and reaches 25 nHz for m = 15.
Conclusions: Given the observational uncertainties on mode frequencies due to the finite mode lifetimes, we find that the predicted frequency shifts are near the limit of detectability.