Characterization of precessional and nutational effects on gravitational waveforms via the introduction of five new parameters.*

Binary black holes can emit gravitational waves (GW) during their lifetime. BHs are expected to have non-zero spins and the spins can become 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 phase and the amplitude of GW. Efforts are underway to quantify these effects via two spin parameters, χ_{eff ,} χ_p inside Post-Newtonian (PN) templates. However, neither precession nor nutation have been detected. We will try to 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 sensitive band of GW detectors. We introduce the parameters inside a PN template and study the modulation of the GW. Then, we use the Fisher matrix analysis on the precessing templates to assess the detectability of our five parameters and to try and break parameter degeneracies. Finally, we calculate the mismatch between templates, to acquire the minimum signal-to-noise needed to distinguish precession and nutation.