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Various types of inertial modes have been observed and identified on the Sun,including the equatorial Rossby modes, critical-latitude modes, andhigh-latitude modes. Recent observations further report a detection ofequatorially-antisymmetric radial vorticity modes which propagate in aretrograde direction about three times faster than those of the equatorialRossby modes when seen in the corotating frame with the Sun. Here, we study theproperties of these equatorially-antisymmetric vorticity modes using arealistic linear model of the Sun's convection zone. We find that they areessentially non-toroidal, involving a substantial radial flow at the equator.Thus, the background density stratification plays a critical role indetermining their dispersion relation. The solar differential rotation is alsofound to have a significant impact by introducing the viscous critical layersand confining the modes near the base of the convection zone. Furthermore, wefind that their propagation frequencies are strikingly sensitive to thebackground superadiabaticity $\delta$ because the buoyancy force acts as anadditional restoring force for these non-toroidal modes. The observedfrequencies are compatible with the linear model only when the bulk of theconvection zone is weakly subadiabatic ($-5\times 10^{-7} \lesssim \delta\lesssim -2.5\times 10^{-7}$). Our result is consistent with but tighter thanthe constraint independently derived in a previous study ($\delta<2 \times10^{-7}$) employing the high-latitude inertial mode. It is implied that, belowthe strongly superadiabatic near-surface layer, the bulk of the Sun'sconvection zone might be much closer to adiabatic than typically assumed andmay even be weakly subadiabatic.

Numerical study of non-toroidal inertial modes with l=m+1 radial vorticity in the Sun's convection zone