Properties of Solar Rossby Waves and Their Correlation with Solar Cycles: Helioseismic Observations and Theoretical Explanations

Solar Rossby waves, also known as r-modes, are large-scale global oscillations driven by the Sun’s rotation and play a significant role in solar interior dynamics. In recent years, helioseismic observations have enabled the detection and characterization of these waves, revealing their potential connection with long-term solar activity variations. This study investigates the physical properties of solar Rossby waves and examines their correlation with solar cycle indicators using helioseismic data and statistical analysis techniques. I analyze several low-order azimuthal modes of Rossby waves, focusing on their frequencies, amplitudes, and temporal evolution. Correlation analysis is performed between the extracted Rossby wave parameters and established solar activity indices, including sunspot numbers and magnetic activity proxies. Both Pearson and Spearman correlation coefficients are employed to assess the robustness of linear and monotonic relationships. The results demonstrate that low azimuthal wave number modes exhibit statistically significant correlations with solar activity, with certain modes showing stronger associations during specific phases of the solar cycle. These findings support the hypothesis that solar Rossby waves are dynamically linked to the solar magnetic cycle and may contribute to the modulation of large-scale solar activity. The study provides observational and theoretical insights into the role of Rossby waves in solar dynamics and offers a framework for future investigations of solar cycle variability.