Using full information when computing modes of post-Newtonian waveforms from inspiralling compact binaries in circular orbit

The increasing sophistication and accuracy of numerical simulations of compact binaries (especially binary black holes) presents the opportunity to test the regime in which post-Newtonian (PN) predictions for the emitted gravitational waves are accurate. In order to confront numerical results with those of post-Newtonian theory, it is convenient to compare multipolar decompositions of the two waveforms. It is pointed out here that the individual modes can be computed to higher post-Newtonian order by examining the radiative multipole moments of the system, rather than by decomposing the 2.5PN polarization waveforms. In particular, the dominant (l=2, m=+/- 2) mode can be computed to 3PN order. Individual modes are computed to as high a post-Newtonian order as possible given previous post-Newtonian results.