Frequency space derivation of linear and nonlinear memory gravitational wave signals from eccentric binaries

Abstract

The memory effect in gravitational wave (GW) signals is the phenomenon, wherein the relative position of two inertial GW detectors undergoes a permanent displacement owing to the passage of GWs through them. Measurement of the memory signal is an important target for future observations as it establishes a connection between observations with field-theoretic results like the soft-graviton theorems. Theoretically, the memory signal is predicted at the leading order quadrupole formula for sources like binaries in hyperbolic orbits. This can be in the realm of observations by Advanced LIGO, Einstein-Telescope, or LISA for black holes with masses ∼O(10^3M⊙) scattered by the supermassive black hole at the galactic center. Apart from the direct memory component, there is a nonlinear memory signal in the secondary GW emitted from the primary GW chirp signals emitted by coalescing binaries.

In this talk, I will discuss the computation of the gravitational wave signals and their energy spectrum using the field-theoretic method for eccentric elliptical and hyperbolic binary orbits. The field-theoretic calculation gives us the gravitational waveforms of linear and nonlinear memory signals directly in frequency space. The frequency domain templates are useful for extracting signals from the data.