Implementation of a generalized precession parameter in the RIFT parameter estimation algorithm

Since the discovery of gravitational waves in 2015, major developments have been made towards waveform interpretation and estimation of compact binary source parameters. We discuss the implementation of the generalized precession parameter $\langle \chi_p \rangle$ within the Rapid Iterative FiTting (RIFT) parameter estimation framework. While the original precession parameter $\chi_p$ characterizes the single largest dynamical spin in a binary, $\langle \chi_p \rangle$ preserves misalignment information from both objects in the binary by averaging over all angular variations on the precession timescale. Additionally, $\langle \chi_p \rangle$ has a unique domain $1 < \langle \chi_p \rangle < 2$, which is exclusive to binaries with two precessing spins. We review the physical differences between these two parameters, and apply this new statistic to the 36 events from the second half of LIGO's third operating run (O3b). Of these, ten events show significant precession, with $\langle \chi_p \rangle > 0.5$. Of particular interest is GW191109\_010717, with a $\sim28\%$ probability that the originating system necessarily contains two misaligned spins.