  This paper develops a novel numerical method for obtaining structures of
rapidly rotating stars based on a self-consistent field scheme. The solution is
obtained iteratively. Both rapidly rotating barotropic and baroclinic
equilibrium states are calculated self-consistently using this method. Two
types of rotating baroclinic stars are investigated by changing the isentropic
surfaces inside the star. Solution sequences of these are calculated
systematically and critical rotation models beyond which no rotating
equilibrium state exists are also obtained. All of these rotating baroclinic
stars satisfy necessarily the Bjerknes-Rosseland rules. Self-consistent
solutions of baro-clinic stars with shellular-type rotation are successfully
obtained where the isentropic surfaces are oblate and the surface temperature
is hotter at the poles than at the equator if it is assumed that the star is an
ideal gas star. These are the first self-consistent and systematic solutions of
rapidly rotating baroclinic stars with shellular-type rotations. Since they
satisfy the stability criterion due to their rapid rotation, these rotating
baroclinic stars would be dynamically stable. This novel numerical method and
the solutions of the rapidly rotating baroclinic stars will be useful for
investigating stellar evolution with rapid rotations.
