Kavli Affiliate: Scott A. Hughes

| First 5 Authors: Anuj Apte, Scott A. Hughes, , ,

| Summary:

The last gravitational waves emitted in the coalescence of two black holes

are quasi-normal ringing modes of the merged remnant. In general relativity,

the mass and the spin of the remnant black hole uniquely determine the

frequency and damping time of each radiated mode. The amplitudes of these modes

are determined by the mass ratio of the system and the geometry of the

coalescence. This paper is part I of an analysis that aims to compute the

"excitation factors" associated with misaligned binary black hole coalescence.

To simplify the analysis, we consider a large mass ratio system consisting of a

non-spinning body of mass $mu$ that inspirals on a quasi-circular trajectory

into a Kerr black hole of mass $M$ and spin parameter $a$, with $mu/M ll 1$.

Our goal is to understand how different modes are excited as a function of the

black hole spin $a$ and an angle $I$ which characterizes the misalignment of

the orbit with the black hole’s spin axis. Though the large mass ratio limit

does not describe the binaries that are being observed by gravitational-wave

detectors today, this limit makes it possible to quickly and easily explore the

binary parameter space, and to develop insight into how the system’s late

ringing waves depend on the binary’s geometry. In this first analysis, we

develop the worldline which the small body follows as it inspirals and then

plunges into the large black hole. Our analysis generalizes earlier work by Ori

and Thorne to describe how a non-equatorial circular inspiral transitions into

a plunging trajectory that falls into the black hole. The worldlines which we

develop here are used in part II as input to a time-domain black hole

perturbation solver. This solver computes the gravitational waves generated by

such inspirals and plunges, making it possible to characterize the modes which

the coalescence excites.

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