2-dimensional models of rapidly rotating stars. II. Hydrostatic and acoustic models with Omega=Omega(r,theta)

International audienceAims.We show how to construct 2-dimensional models of rapidly rotating stars in hydrostatic equilibrium for any Omega(r,theta), given the density rho_m(r) along any one angle theta_m. If the hydrogen abundance X_m(r) is given on thetam then the adiabatic exponent Gamma_1(r,theta) can by determined, yielding a self consistent acoustic model that can be used to investigate the oscillation properties of rapidly rotating stars. Methods: .The system of equations governing the hydrostatic structure is solved by iteration using the method of characteristics and spectral expansion, subject to the condition that rho(r,theta)=rho_m(r) on theta=theta_m. Gamma_1(r,theta) is calculated from the equation of state under the assumption that X(r,theta_m)=X_m(r) and is constant on surfaces of constant entropy. Alternatively Gamma1 can be approximated by taking X constant in the equation of state and equal to the surface value. Results: .Results are presented for an evolved main sequence star of 2~M_&sun; with the angular velocity a function only of radius Omega=Omega(r), evolved to a central hydrogen abundance of X_c=0.35. The model is first calculated using a spherically averaged stellar evolution code, where the averaged centrifugal force 2Omega2 r/3 is added to gravity. The resulting rho_m(r), X_m(r) are then used as input to determine the 2-dimensional model. Conclusions: .The procedure described here gives self consistent hydrostatic and acoustic models of rapidly rotating stars for any Omega(r,theta)