Structural Tilting and Depth-Dependent Behavior of Equatorial Rossby Waves

TL;DR

The paper investigates the depth-dependent structure of equatorial Rossby waves in the solar interior using ~14.5 years of ring-diagram and time-distance helioseismology data. By performing sectoral spherical-harmonic decomposition of radial vorticity and applying Fourier-space filtering to isolate the Rossby ridge, it quantifies how the wave tilt and power vary with depth and over the solar cycle. The main findings show a robust retrograde tilt, with deeper layers leading shallower ones (negative normalized phase differences) that grow in magnitude with depth, and a cross-power that correlates positively with solar activity, while the tilt itself remains largely cycle-independent. These results have implications for angular-momentum and energy transport in the solar interior and motivate integrated analyses with magnetohydrodynamic simulations to understand magnetic and differential-rotation coupling to Rossby modes.

Abstract

Over the past decade, solar equatorial Rossby waves have been unambiguously identified and are considered potential diagnostics of solar interior dynamics. We investigate their inclined structure and temporal evolution in the solar interior across multiple depths using approximately 14.5 yr of ring-diagram (RD) and time-distance (TD) helioseismology data from SDO/HMI. Normalized phase differences and cross power are computed from filtered spherical harmonic coefficients of radial vorticity to probe the structural tilt and power of Rossby waves. We find a systematic and robust depth-dependent phase behavior that shows no clear significant correlation with the solar cycle, while the depth-dependent cross power exhibits a positive correlation with the solar cycle for both datasets. Our results show that deeper depths lead in phase over shallower ones, with increasing negative phases with depth. We infer that Rossby waves exhibit a retrograde tilt relative to the Sun's rotation that is stable throughout the solar cycle. Analogous small tilts have been noted in planetary atmospheres and in magnetohydrodynamic simulations of the Sun, indicating that this behavior is not uncommon in rotating, stratified bodies and has implications for angular momentum and energy transport in the solar interior.

Figures (8)

• Figure 1: Sectoral power $\mathcal{P}_m(\nu, d)$, cross power $\mathcal{S}_m(\nu, d_{0i})$, and coherence $\mathcal{C}_{m}(\nu, d_{0i})$ spectra of the decomposed RD radial vorticity, focusing on azimuthal orders $3\,\leq\,m\,\leq\,16$. The tracking frequency is $\Omega/(2\pi) = 424.3$ nHz. Top row: $\mathcal{P}_m(\nu, d)$ for multiple depths from 1.4 Mm to 16.0 Mm. Middle row: $\mathcal{S}_m(\nu, d_{0i})$ between 1.4 Mm and successive depths indicated in the top row. Bottom row: $\mathcal{C}_{m}(\nu, d_{0i})$ between 1.4 Mm and successive depths. The Rossby wave ridge is indicated by the black dashed lines drawn $\pm$ 30 nHz around the peak frequencies for each $m$.
• Figure 2: Normalized phase differences $\Delta\varphi_m(t, d_{0i})/m$ derived from the filtered complex coefficients of the decomposed RD radial vorticity between the near-surface reference depth (1.4 Mm) and several subsurface depths, averaged over approximately 14.5 yr. (a): $\Delta\varphi_m(t, d_{0i})/m$ versus $\ell=m$, focusing on $6\,\leq\,m\,\leq\,14$. (b): $\Delta\varphi_m(t, d_{0i})/m$ versus depth below the near-surface reference depth for $m$ = $8$, $10$, and $12$. Error bars represent the standard error across time for $\Delta\varphi_m(t, d_{0i})/m$ at each depth and $m$.
• Figure 3: Temporal evolution of the normalized cross power $\mathcal{S}_m(t, d_{0i})$ for $6\,\leq\,m\,\leq\,11$ between the near-surface reference depth (1.4 Mm) and select subsurface depths for the RD data. For all depths, the dataset is segmented into 3 yr moving windows with a 0.5 yr step size. Error bars represent standard errors across time segments. The SSN (gray) is overplotted for comparison with the solar cycle.
• Figure 4: Temporal evolution of the normalized phase differences $\Delta\varphi_m(t, d_{0i})/m$ for $6\,\leq\,m\,\leq\,11$ between the near-surface reference depth (1.4 Mm) and select subsurface depths for the RD data. For all depths, the dataset is segmented into 3 yr moving windows with a 0.5 yr step size. Error bars represent standard errors across time segments. The SSN (gray) is overplotted for comparison with the solar cycle.
• Figure 5: Sectoral power $\mathcal{P}_m(\nu, d)$, cross power $\mathcal{S}_m(\nu, d_{0i})$, and coherence $\mathcal{C}_{m}(\nu, d_{0i})$ spectra of the decomposed TD radial vorticity data, focusing on azimuthal orders $3\,\leq\,m\,\leq\,16$. The TD data is tracked at the Carrington rotation rate. The figure is the same as Fig. \ref{['fig:RD_Fourier_Maps']}.