The curious case of parabolic encounters: gravitational waves with linear & non-linear memory

TL;DR

This paper investigates gravitational wave signals from parabolic encounters, focusing on both linear and non-linear memory effects, and highlights unique features and challenges in modeling these events using an effective field theory approach.

Contribution

It introduces a specialized parameterization for parabolic encounters and calculates their gravitational wave signals and energy spectrum, revealing new features in the zero frequency limit.

Findings

Parabolic encounters exhibit unique features in the zero frequency limit.

A specialized parameterization is necessary for accurate memory effect calculations.

The study advances understanding of gravitational wave memory in special encounter cases.

Abstract

The memory effect is known to introduce a permanent displacement in the gravitational wave (GW) detectors after the passage of a GW signal. While the linear memory adheres to the source properties, the non-linear memory is a secondary effect sourced by the GW itself. In the present work, we discuss GW signals with both these kinds of memory effects, while focusing on the parabolic limit of an encounter. This special case is theoretically intriguing and emerges as a limiting situation for both eccentric and hyperbolic events. However, in this paper, we argue that a simple extrapolation of memory calculations for eccentric or hyperbolic cases to the parabolic case may lead to incorrect estimations. Therefore, we treat the parabola as a special case and use an intrinsic parameterization, with which we calculate gravitational wave signals and their energy spectrum via an effective field theory formalism. Unlike the hyperbolic case, which is known to have linear memory, we notice that parabolic encounters bring out new features in the zero frequency limit (ZFL). Our work highlights some of the key challenges and salient aspects of these encounters, and paves the way to study such binary evolution with nonzero memory.