# Magneto-Rossby waves in the solar tachocline and the annual variations in solar activity

## TL;DR

This paper investigates the role of magneto-Rossby and magneto-Kelvin waves in the solar tachocline as a possible explanation for observed annual and multi-year oscillations in solar activity, combining theoretical analysis with observational data.

## Contribution

It provides a theoretical framework for understanding how global magneto-Rossby and Kelvin waves can produce observed solar periodicities, linking wave dynamics with solar activity oscillations.

## Key findings

- Magneto-Rossby waves match observed 1-year oscillations in solar activity.
- Multiple periodicities in sunspot data are explained by harmonics of magneto-Rossby waves.
- Theoretical dispersion relations align with observed wave phase speeds.

## Abstract

Annual oscillations have been detected in many indices of solar activity during many cycles. Recent multi spacecraft observations of coronal bright points revealed slow retrograde toroidal phase drift (with the speed of 3 m/s of 1 yr oscillations, which naturally suggested their connection with Rossby-type waves in the interior. We have studied from a theoretical point of view the dynamics of global magneto-Kelvin and magneto-Rossby waves in the solar tachocline with toroidal magnetic field. Using spherical coordinates, the dispersion relations of the waves and latitudinal structure of solutions were obtained analytically. We have also obtained the spectrum of unstable magneto-Rossby wave harmonics in the presence of the latitudinal differential rotation. Estimated periods and phase speeds show that the magneto-Rossby waves rather than the Kelvin waves match with the observations of 1 yr oscillations. On the other hand, Morlet wavelet analysis of Greenwich Royal Observatory sunspot areas for the solar cycle 23 has revealed multiple periodicities with periods of 450-460 days, 370-380 days, 310-320 days, 240-270 days, and 150-175 days in hemispheric and full disk data. Comparison of theoretical results with the observations allow us to conclude that the global magneto-Kelvin waves in the upper overshoot tachocline may be responsible for the periodicity of 450-460 days (1.3 yrs), while the remaining periods can be connected with different harmonics of global fast magneto-Rossby waves.