Detecting regular precession using a new gravitational waveform model directly parameterized by both precession amplitude and frequency

Nearly 210 binary black hole (BBH) mergers have been observed by the LIGO-Virgo-KAGRA network during its four observing runs. Generic BBHs are spinning, and their spins are misaligned with the orbital angular momentum $\vec{L}$. These misaligned spins cause $\vec{L}$ to precess in a cone with dimensionless precession amplitude $\tilde{\theta}$ and frequency $\tilde{\Omega}$ about the nearly constant direction of the total angular momentum. This precession modulates the observed GWs. We propose a model of regularly precessing (RP) waveforms that incorporates $\tilde{\theta}$ and $\tilde{\Omega}$ directly as parameters. We investigate how these waveforms vary as functions of these precessional parameters, as well as binary orientation and sky location. We use the Lindblom criterion to estimate that precession can be detected in a RP source with signal-to-noise ratio $\rho$ when the mismatch $\epsilon$ with a non-precessing (NP) source with otherwise identical parameters exceeds $1/2\rho^2$. Precession is most detectable when $\vec{L}$ precesses through configurations we call +~nulls during the inspiral. At +~nulls, a NP source only emits +-polarization to which the GW detector is insensitive. The large mismatch between a RP source and this vanishing NP signal enhances the detectability of precession. We also explore the detectability of precession as a function of redshift $z$ for different BBH populations. We find that for BBHs with isotropically oriented maximal spins, precession is detectable in a majority of systems out to $z \approx 0.3$ for chirp masses $10 \lesssim M_c/M_\odot \lesssim 40$ and mass ratios $q \gtrsim 0.5$. Reduced spin magnitudes or greater alignment between the spins and $\vec{L}$ make it difficult to observe beyond $z \approx 0.1$. (abridged)