Is J enough? Comparison of gravitational waves emitted along the total angular momentum direction with other preferred orientations

TL;DR

This study challenges the idea that gravitational wave emissions along certain angular momentum directions are representative, showing that such directions do not capture the full complexity of the emission pattern in precessing black hole binaries.

Contribution

The paper provides a concrete counterexample demonstrating that common preferred emission directions do not reliably represent the full gravitational wave emission complexity.

Findings

Preferred directions are not representative of the emission pattern.

Only a small fraction of directions produce signals similar to the fiducial ones.

Orientation-dependent emission complexity requires comprehensive modeling.

Abstract

The gravitational wave signature emitted from a merging binary depends on the orientation of an observer relative to the binary. Previous studies suggest that emission along the total initial or total final angular momenta leads to both the strongest and simplest signal from a precessing compact binary. In this paper we describe a concrete counterexample: a binary with $m_1/m_2=4$, $a_1=0.6 \hat{x} = -a_2$, placed in orbit in the x,y plane. We extract the gravitational wave emission along several proposed emission directions, including the initial (Newtonian) orbital angular momentum; the final (~ initial) total angular momentum; and the dominant principal axis of $<L_a L_b>_M$. Using several diagnostics, we show that the suggested preferred directions are not representative. For example, only for a handful of other directions (< 15%) will the gravitational wave signal have comparable shape to the one extracted along each of these fiducial directions, as measured by a generalized overlap (>0.95). We conclude that the information available in just one direction (or mode) does not adequately encode the complexity of orientation-dependent emission for even short signals from merging black hole binaries. Future investigations of precessing, unequal-mass binaries should carefully explore and model their orientation-dependent emission.