## Binary Black-Hole Spin Precession: Dynamical Evolution and Gravitational-Wave Parameter Estimation

##### Abstract

##### Abstract

Einstein’s general relativity predicts the existence of black holes. A binary black hole is a
system of two black holes orbiting each other. During the inspiral of a binary black hole, the
separation between the two black holes shrinks slowly and gravitational waves are emitted
until the merger, at which time the gravitational waves peak. We use analytic solutions for
generic spin precession at second post-Newtonian(2PN) order to derive Fourier series for the
total and orbital angular momenta. On the precession timescale, the angle between the total
and orbital angular momenta oscillates with nutation period ⌧ , during which the orbital
angular momentum L precesses about the total angular momentum J by an angle ↵. As
black holes inspiral, they can pass through nutational resonances (⌦ = n!), at which the
total angular momentum tilts by an angle ✓tilt, where ⌦ ⌘ ↵/⌧ is the precession frequency
and ! ⌘ 2⇡/⌧ is the nutation frequency. We are the first to identify and study the nutational
resonances. We derive an approximate expression for this tilt angle and show the angle is
usually less than 103 radians at PN regime.
We also show that both precession and nutation can modulate the frequency and amplitude of the gravitational waveforms. In the absence of radiation reaction, the amplitudes
and frequencies of precession and nutation can be treated as constant parameters. Using
two different approximations to calculate the gravitational-waveform modulation (frequency
modulation and amplitude modulation), we calculate the Fisher matrix for waveform models
that include these parameters and use this to determine how accurately these parameters
can be measured.