2-dimensional models of rapidly rotating stars II.: Hydrostatic and acoustic models with Ω=Ω(r,θ)

Aims. 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 theta(m) 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 Gamma(1) 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-circle dot with the angular velocity a function only of radius. =.( 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 2 Omega(2)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).