EXISTENCE OF NON-AXISYMMETRICAL POLYTROPES SUSTAINED BY INTERNAL MOTIONS

We have succeeded in developing a numerical code to obtain structures of nonaxisymmetric polytropes the shapes of which are sustained by int ernal flows. In order to compute stationary non-axisymmetric polytrope s, two important points must be properly treated: (i) how to specify t he boundary condition for the flow velocity, and (ii) how to handle th e boundary condition on the stellar surface which is not known beforeh and. As for the boundary condition for the flow velocity, we specify t he form of the distribution of the difference between the phi componen t of the flow velocity and its mean value at one meridional cross-sect ion. Concerning the surface condition, we introduce a 'surface-fitted' coordinate system in numerical computations. By applying our new nume rical code we have obtained many stationary non-axisymmetric equilibri um models the shapes of which are nonrotating in the inertial frame. T wo main results of our computations are as follows: (i) the cp compone nt of the flow velocity must depend on the height from the equator for polytropes to be deformed to some extent and (ii) the flow is compres sible. Unless we include this z-dependence for the flow, it seems that stationary states can exist only for nearly incompressible polytropes and only for very slightly deformed non-axisymmetric configurations a s far as 'bar'-type non-axisymmetric configurations are concerned.