SPIN EFFECTS IN GRAVITATIONAL-RADIATION BACK-REACTION - II - FINITE MASS EFFECTS

A convenient formalism for averaging the losses produced by gravitatio nal radiation back reaction over one orbital period was developed in a n earlier paper. In the present paper we generalize this formalism to include the case of a closed system composed from two bodies of compar able masses, one of them having the spin S. We employ the equations of motion given by Barker and O'Connell, where terms up to linear order in the spin (the spin-orbit interaction terms) are kept. To obtain the radiative losses up to terms linear in the spin, the equations of mot ion are taken to the same order. Then the magnitude L of the angular m omentum L, the angle kappa subtended by S and L and the energy E are c onserved. The analysis of the radial motion leads to a new parametriza tion of the orbit. From the instantaneous gravitational radiation loss es computed by Kidder the leading terms and the spin-orbit terms are t aken. Following Apostolatos, Cutler, Sussman, and Theme, the evolution of the vectors S and L in the momentary plane spanned by these vector s is separated from the evolution of the plane in space. The radiation -induced change in the spin is smaller than the leading-order spin ter ms in the momentary angular momentum loss. This enables us to compute the averaged losses in the constants of motion E, L and L-S=L cos kapp a. In the latter, the radiative spin loss terms average to zero. An al ternative description using the orbital elements a, e, and kappa is gi ven. The finite mass effects contribute terms, comparable in magnitude , to the basic, test-particle spin terms in the averaged losses.