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While many intermediate- and high-mass main sequence stars are rapidly anddifferentially rotating, the effects of rotation on oscillation modes arepoorly known. In this communication we present a first study of axisymmetricgravito-inertial modes in the radiative zone of a differentially rotating star.We consider a simplified model where the radiative zone of the star is alinearly stratified rotating fluid within a spherical shell, with differentialrotation due to baroclinic effects. We solve the eigenvalue problem withhigh-resolution spectral computations and determine the propagation domain ofthe waves through the theory of characteristics. We explore the propagationproperties of two kinds of modes: those that can propagate in the entire shelland those that are restricted to a subdomain. Some of the modes that we findconcentrate kinetic energy around short-period shear layers known asattractors. We describe various geometries for the propagation domains,conditioning the surface visibility of the corresponding modes.

Gravito-inertial modes in a differentially rotating spherical shell