GRAVITATIONAL-WAVES FROM BINARY-SYSTEMS IN CIRCULAR ORBITS - DOES THEPOST-NEWTONIAN EXPANSION CONVERGE

Gravitational radiation can be expressed in terms of an infinite serie s of radiative, symmetric trace-free (STF) multipole moments which can be connected to the behaviour of the source. We consider a truncated model for gravitational radiation from binary systems in which each ST F mass and current moment of order l is given by the lowest-order, New tonian-like l-pole moment of the orbiting masses; we neglect post-Newt onian corrections to each STF moment. Specializing to orbits which are circular (apart from the radiation-induced inspiral), we find an expl icit infinite series for the energy flux in powers of nu/c, where nu i s the orbital velocity. We show that the series converges for all valu es nu/c < 2/e when one mass is much smaller than the other, and nu/c < 4/e for equal masses, where e is the base of natural logarithms. Thes e values include all physically relevant values for a compact binary i nspiral. This convergence cannot indicate whether or not the full seri es (obtained from the exact moments) will converge. But if the full se ries does not converge, our analysis shows that this failure to conver ge does not originate from summing over the Newtonian part of the mult ipole moments.