Traveling convective modes in the sun's subsurface shear layer

Observations reveal that supergranular convective cells on the Sun rotate faster than the plasma on the solar surface. Recent time-distance helioseismology results from the Solar and Heliospheric Observatory Michelson Doppler Imager suggest that supergranulation has properties of traveling waves. We consider the idea that these properties are related to the steep increase of the angular rotation rate with depth, obtained by helioseismic inversions. The subsurface shear layer causes the convective modes to travel faster than the surface plasma. We calculate the phase speed of unstable modes of convection in the linear approximation for a standard solar model as a function of the velocity gradient in the shear layer. We find that for the helioseismically determined gradient, the calculated phase speed is significantly smaller than the observed speed of the supergranular pattern relative to the surface plasma. This suggests that, while the subsurface shear layer provides a plausible explanation for the wavelike behavior, it is necessary to study nonlinear effects in the dynamics of supergranulation.