Testing the validity of the single-spin approximation in inspiral-merger-ringdown waveforms

Gravitational-wave signals from black-hole binaries with nonprecessing spins are described by four parameters-each black hole's mass and spin. It has been shown that the dominant spin effects can be modeled by a single spin parameter, leading to the development of several three-parameter waveform models. Previous studies indicate that these models should be adequate for gravitational-wave detection. In this paper we focus on the systematic biases that would result from using them to estimate binary parameters, and consider a one-parameter family of configurations at mass ratio 4 and for one choice of effective single spin. We find that for low-mass binaries within that family of configurations, where the observable waveform is dominated by the inspiral, the systematic bias in all physical parameters is smaller than the parameter uncertainty due to degeneracies between the mass ratio and the spins, at least up to signal-to-noise ratios (SNRs) of 50. For higher-mass binaries, where the merger and ringdown make a greater contribution to the observed signal, the bias in the mass ratio is comparable to its uncertainty at SNRs of only similar to 30, and the bias in the measurement of the total spin is larger than the uncertainty defined by the 90% confidence region even at an SNR of only 10. Although this bias may be mitigated in future models by a better choice of single-effective-spin parameter, these results suggest that it may be possible to accurately measure both black-hole spins in intermediate-mass binaries.