Identifying when Precession can be Measured in Gravitational Waveforms

Abstract

In binary-black-hole systems where the black-hole spins are misaligned with the orbital angular momentum, precession effects leave characteristic modulations in the emitted gravitational waveform. Here, we investigate where in the parameter space we will be able to accurately identify precession, for likely observations over coming LIGO-Virgo-KAGRA observing runs. Despite the large number of parameters that characterise a precessing binary, we perform a large scale systematic study to identify the impact of each source parameter on the measurement of precession. We simulate a fiducial binary at moderate mass-ratio, signal-to-noise ratio (SNR), and spins, such that precession will be clearly identifiable, then successively vary each parameter while holding the remaining parameters fixed. As expected, evidence for precession increases with signal-to noise-ratio (SNR), higher in-plane spins, more unequal component masses, and higher inclination, but our study provides a quantitative illustration of each of these effects, and informs our intuition on parameter dependencies that have not yet been studied in detail, for example, the effect of varying the relative strength of the two polarisations, the total mass, and the aligned-spin components. We also measure the "precession SNR" $ρ_p$, which was introduced in Refs[1,2] to quantify the signal power associated with precession. By comparing $ρ_p$ with both Bayes factors and the recovered posterior distributions, we find it is a reliable metric for measurability that accurately predicts when the detected signal contains evidence for precession.