THE ACCURACY OF THE QUADRUPOLE APPROXIMATION FOR THE GRAVITATIONAL-RADIATION FROM PULSATING STARS

Two methods for computing the damping of the non-radial oscillations of stars due to gravitational radiation emission are compared: (i) solving the complete linearized equations of general relativity and (ii) using an approximate method based on the quadrupole formula. It is shown that the results of the fully relativistic calculation approach the results based on the quadrupole formula for sufficiently non-relativistic stars (i.e. GM/c2R sufficiently small). The accuracy of the approximation method is investigated by considering polytropic stars with a range of polytropic indices. The approximation is worse for larger polytropic indices, i.e. for greater central condensation. We conclude that when Newtonian models are used to approximate relativistic ones, models with the same value of GM/c2R (rather than, say, central density) should be compared. © 1985 Royal Astronomical Society. Provided by the NASA Astrophysics Data System.