Identifying the source parameters from a gravitational-wave measurement aloneis limited by our ability to discriminate signals from different sources andthe accuracy of the waveform family employed in the search. Here we addressboth issues in the framework of an adapted coordinate system that allows forlinear Fisher-matrix type calculations of waveform differences that are bothaccurate and computationally very efficient. We investigate statistical errorsby using principal component analysis of the post-Newtonian (PN) expansioncoefficients, which is well conditioned despite the Fisher matrix becoming illconditioned for larger numbers of parameters. We identify which combinations ofphysical parameters are most effectively measured by gravitational-wavedetectors for systems of neutron stars and black holes with aligned spin. Weconfirm the expectation that the dominant parameter of the inspiral waveform isthe chirp mass. The next dominant parameter depends on a combination of thespin and the symmetric mass ratio. In addition, we can study the systematiceffect of various spin contributions to the PN phasing within the sameparametrization, showing that the inclusion of spin-orbit corrections up tonext-to-leading order, but not necessarily of spin-spin contributions, iscrucial for an accurate inspiral waveform model. This understanding of thewaveform structure throughout the parameter space is important to set up anefficient search strategy and correctly interpret future gravitational-waveobservations.
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