  In a previous paper we studied the effect of latitudinal rotation on solar
equatorial Rossby modes in the beta-plane approximation. Since then, a rich
spectrum of inertial modes has been observed on the Sun, which is not limited
to the equatorial Rossby modes and includes high-latitude modes.
  Here we extend the computation of toroidal modes in 2D to spherical geometry,
using realistic solar differential rotation and including viscous damping. The
aim is to compare the computed mode spectra with the observations and to study
mode stability.
  At fixed radius, we solve the eigenvalue problem numerically using a
spherical harmonics decomposition of the velocity stream function. Due to the
presence of viscous critical layers, the spectrum consists of four different
families: Rossby modes, high-latitude modes, critical-latitude modes, and
strongly damped modes. For each longitudinal wavenumber m<4, up to three
Rossby-like modes are present on the sphere, in contrast to the equatorial beta
plane where only the equatorial Rossby mode is present. The least damped modes
in the model have eigenfrequencies and eigenfunctions that resemble the
observed modes; the comparison improves when the radius is taken in the lower
half of the convection zone. For radii above 0.75R and Ekman numbers E<10^{-4},
at least one mode is unstable. For either m=1 or m=2, up to two Rossby modes
are unstable when the radial dependence of the Ekman number follows a quenched
diffusivity model (E=2. 10^{-5} at the base of the convection zone). For m=3,
up to two Rossby modes can be unstable, including the equatorial Rossby mode.
  Although the 2D model discussed here is highly simplified, the spectrum of
toroidal modes appears to include many of the observed solar inertial modes.
The self-excited modes in the model have frequencies close to those of the
observed modes with the largest amplitudes.
