Fig. 1: Visualizations of eigenfunctions of the six dominant oscillation modes using the data of three equilibrium models (T1K1, T1K3 and T1K7).

The fundamental quasi-radial (\({{{{{\mathcal{l}}}}}}\) = 0) mode F and its first overtone H₁ are predominantly excited under \({{{{{\mathcal{l}}}}}}\) = 0 perturbation; the fundamental quadrupole (\({{{{{\mathcal{l}}}}}}\) = 2) mode ²f and its first overtone ²p₁ are predominantly excited under \({{{{{\mathcal{l}}}}}}\) = 2 perturbation; the fundamental hexadecapole (\({{{{{\mathcal{l}}}}}}\) = 4) mode ⁴f and its first overtone ⁴p₁ are predominantly excited under \({{{{{\mathcal{l}}}}}}\) = 4 perturbation. Each polar colour plot shows the spatial map of FFT amplitude at the eigenfrequency of the mode, where the radial axis is normalized to the equatorial radius r_e of each model. On top of each colour plot, there is a polar line plot visualizing the θ-part of the spherical harmonic in the corresponding perturbation function, where the distance from the origin to the line measures the magnitude of the spherical harmonic in that θ-direction, while the solid and dotted portions represent the positive and negative parts of the spherical harmonic, respectively. Each line plot is scaled arbitrarily for clearer illustration. It can be seen that the eigenfunctions of the higher-order quadrupole (\({{{{{\mathcal{l}}}}}}\) = 2) and hexadecapole (\({{{{{\mathcal{l}}}}}}\) = 4) modes have more nodes in the θ-direction compared to the quasi-radial (\({{{{{\mathcal{l}}}}}}\) = 0) modes, while the eigenfunction of each first overtone has more nodes in the r-direction compared to its fundamental mode. Furthermore, each eigenfunction qualitatively agrees with the spherical harmonic in the corresponding perturbation function.