A single-spin precessing gravitational wave in closed form
In coming years, gravitational wave detectors should find black hole-neutron star binaries, potentially coincident with astronomical phenomena like short GRBs. These binaries are expected to precess. Gravitational wave science requires a tractable model for precessing binaries, to disentangle precession physics from other phenomena like modified strong field gravity, tidal deformability, or Hubble flow; and to measure compact object masses, spins, and alignments. Moreover, current searches for gravitational waves from compact binaries use templates where the binary does not precess and are ill-suited for detection of generic precessing sources. In this paper we provide a closed-form representation of the single-spin precessing waveform in the frequency domain by reorganizing the signal as a sum over harmonics, each of which resembles a nonprecessing waveform. This form enables simple analytic calculations (e.g., a Fisher matrix) with easily-interpreted results. We have verified that for generic BH-NS binaries, our model agress with the time-domain waveform to 2\%. Straightforward extensions of the derivations outlined here [and provided in full online] allow higher accuracy and error estimates.