Gravitational Waves and Non-Linear Phenomena in Gravitational Astrophysics

In this talk I will describe some of my Ph.D. work. In particular, I will talk about modelling strong three-body interactions as random walks, and how binary-single encounters may lead to gravitational-wave source formation. Then, I will describe my study of the stochastic gravitational-wave, which is also modelled as a random walk. Chaotic three-body interactions are a dynamical pathway of gravitational-wave source production. Any such encounter terminates when one of the three stars is ejected to infinity, leaving behind a remnant binary; the problem of binary-single star-scattering consists of finding the probability distribution of the orbital parameters of the remnant binary, as a function of the total energy and the total angular momentum. In this talk I will model the encounter as a series of close, non-hierarchical, triple approaches, interspersed with hierarchical phases, in which the system consists of an inner binary and a star that orbits it – this turns the evolution of the entire encounter to a random walk between consecutive hierarchical phases. This is then generalised to account for dissipative processes, such as tides and gravitational-wave emission. Any coalescence of compact binary stars is expected to produce a stochastic background of gravitational waves (GW) observable with future GW detectors. In this part, I’ll present a method to calculate the full probability distribution of strain fluctuations as a random walk in the complex plane. I will describe applications both for time series data and a frequency-domain analysis. I will illustrate how this probability distribution can be evaluated numerically, and, additionally, derive accurate analytic asymptotic expressions for the large strain tail, demonstrating that it is dominated by the nearest source, and that it exhibits a universal power-law decline. I will also discuss to what extent the background may be treated as Gaussian, and how the accuracy of this approximation varies with frequency