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Global-scale Rossby waves have recently been unambiguously identified on theSun. Here we study the latitude and depth dependence of the Rossby waveeigenfunctions. By applying helioseismic ring-diagram analysis and granulationtracking to SDO/HMI observations, we compute maps of the radial vorticity offlows in the upper solar convection zone (down to depths of more than $16$ Mm).We use a Fourier transform in longitude to separate the different azimuthalorders m in the range $3 \le m \le 15$. At each $m$ we obtain the phase andamplitude of the Rossby waves as a function of depth using the helioseismicdata. At each $m$ we also measure the latitude dependence of the eigenfunctionsby calculating the covariance between the equator and other latitudes. We thenstudy the horizontal and radial dependences of the radial vorticityeigenfunctions. The horizontal eigenfunctions are complex. As observedpreviously, the real part peaks at the equator and switches sign near $\pm30^\circ$, thus the eigenfunctions show significant non-sectoral contributions.The imaginary part is smaller than the real part. The phase of the radialeigenfunctions varies by only roughly $\pm 5^\circ$ over the top $15$ Mm. Theamplitude of the radial eigenfunctions decreases by about $10\%$ from thesurface down to $8$ Mm (the region where ring-diagram analysis is mostreliable, as seen by comparing with the rotation rate measured by global-modeseismology). The radial dependence of the radial vorticity eigenfunctionsdeduced from ring-diagram analysis is consistent with a power-law down to $8$Mm and is unreliable at larger depths. However, the observations provide onlyweak constraints on the power-law exponents. For the real part, the latitudedependence of the eigenfunctions is consistent with previous work (usinggranulation tracking). The imaginary part is smaller than the real part butsignificantly nonzero.

Exploring the latitude and depth dependence of solar Rossby waves using ring-diagram analysis