Probing Depth Variations of Solar Inertial Modes through Normal Mode Coupling

Abstract: Recently discovered inertial waves, observed on the solar surface, likely extend to the deeper layers of the Sun. Utilizing helioseismic techniques, we explore these motions, allowing us to discern inertial-mode eigenfunctions in both radial and latitudinal orientations. We analyze $8$ years of space-based observations ($2010 - 2017$) taken by the Helioseismic and Magnetic Imager (HMI) onboard the Solar dynamic observatory (SDO) using normal-mode coupling. Coupling between same and different-degree acoustic modes and different frequency bins are measured in order to capture the various length scales of inertial modes. We detect inertial modes at high latitude with azimuthal order $t=1$ and frequency $\sim -80$ nHz. This mode is present in the entire convection zone. The presence of Rossby modes may be seen down to a depth of $\sim 0.83R_\odot$ and the Rossby signal is indistinguishable from noise below that depth for high azimuthal order. We find that the amplitudes of these modes increase with depth down to around $0.92 R_\odot$ and decrease below that depth. We find that the latitudinal eigenfunctions of Rossby modes deviate from sectoral spherical harmonics if we use a similar approach as adopted in earlier studies. We found that spatial leakage and even pure noise in the measurements of non-sectoral components can also explain the above-mentioned characteristics of the latitudinal eigenfunctions. This realization underscores the necessity for careful interpretation when considering the latitudinal eigenfunctions of Rossby modes. Exploring the depth-dependent characteristics of these modes will enable us to capture interior dynamics distinctly, separate from p-mode seismology.