# Precessional Effects on Gravitational Wave Data Analysis

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## Abstract

Black holes (BHs) that closely orbit each other can form a binary black hole (BBH) system. We can divide the lifetime of these BBH systems into three distinct phases: the adiabatic inspiral, the merger and the ringdown. BBHs can emit gravitational waves (GW) during every phase of their lifetimes. The spins of the individual BHs are expected to have non-zero values and to be misaligned with the orbital angular momentum. This misalignment can induce precession and nutation of the orbital angular momentum around the total angular momentum. These phenomena modify the GW phase and amplitude. Efforts are underway to quantify these effects via two spin parameters, χeff, χp, inside post-Newtonian (PN) templates used in parameter-estimation methods. There are claims that precession has been detected both statistically in the third observing run(O3) catalog, and in individual systems like GW200129 but the consensus is not yet clear. We quantify precession and nutation by introducing five new parameters. We believe these parameters may provide a more complete characterization of the amplitude and frequency of precession and nutation as binaries inspiral through the sensitivity band of GW detectors. We introduce the parameters inside a PN template and study the modulation of the GWs. We then calculate the mismatch between templates to determine the minimum signal-to-noise needed to identify precession and in both the next LIGO collaboration runs as well as proposed future detectors. Then we move on to the strong gravitational lensing of GWs which occurs when the GWs from a compact binary system travel near a massive object. The lensed waveform is given by the product of the lensing amplification factor F and the unlensed waveform. In the geometrical-optics approximation, lensing produces at most two discrete images which can be parameterized by two image parameters, the flux ratio I and time delay ∆td between images. In the macrolensing regime for which ∆td is large compared to the time T they spend within the sensitivity band of GW detectors, it is natural to parameterize lensing searches in terms of these image parameters. The functional dependence of the lensed signal on these image parameters is far simpler, facilitating data analysis for events with modest signal-to-noise ratios, and constraints on I and ∆td can be found. We then propose that this use of image parameters can be extended to the microlensing regime (∆td < T) in which the two interfering images are observed as a single GW event. Finally, we use image parameters to determine the detectability of gravitational lensing in GW the microlensing regime.