Existence of small-scale Rossby waves points to low convective velocity amplitudes in the Sun

Inertial waves occur naturally in rotating fluids such as the Sun and the Earth's atmosphere. Rossby waves in the Sun have the potential to shed fresh light on interior turbulence and convection that prior seismic methods, reliant on sound waves, have been unable to accomplish. Here, we utilize ∼13 years of observational products taken by the space-based helioseismic and magnetic imager, onboard the solar dynamics observatory, to characterize solar equatorial Rossby waves. By examining maps of motions at the surface using two different methods, we are able to identify Rossby modes up to azimuthal order m = 30, approximately up to twice the spatial wavenumber limit of previous studies. The dispersion relation of these modes departs significantly from the classical two-dimensional Rossby-Haurwitz description. A parameter study of the effect of superadiabaticity and viscous diffusion on these inertial modes indicates that each parameter plays a role in influencing both the frequencies and linewidths of high m modes. Using the Rhines-scale relation, we constrain the root mean square amplitude of turbulent convection more tightly to $∼2$ m/s, adding more evidence to the paradigm of weakly convective amplitudes at large scales.