MULTI-LAYERED CONFIGURATIONS IN DIFFERENTIALLY ROTATIONAL EQUILIBRIUM

We present a new formula to numerically construct configurations in rotational equilibrium, which consists of multiple layers. Each layer rotates uniformly or differentially according to cylindrical rotation laws that are different from layer to layer. Assuming a different barotropic equation of state (EOS) for each layer, we solve the Bernoulli equation in each layer separately and combine the solutions by imposing continuity of the pressure at each boundary of the layers. It is confirmed that a single continuous barotropic EOS is incompatible with the junction condition. Identifying appropriate variables to be solved, we construct a convergent iteration scheme. For demonstration, we obtain two-layered configurations, each layer of which rotates rapidly with either an "Omega-constant law" or a "j-constant law" or a "v-constant law." Other rotation laws and/or a larger number of layers can be treated similarly. We hope that this formula will be useful in studying the stellar evolution in multi-dimension with the non-spherical configuration induced by rotation being fully taken into account.