# Compact Binary Waveform Center-of-Mass Corrections

## TL;DR

This paper analyzes the center-of-mass motion in binary black hole simulations, identifying it as largely a gauge effect that causes mode mixing in gravitational waveforms, and proposes methods to improve c.m. correction techniques.

## Contribution

It investigates the physical versus gauge origins of c.m. motion and introduces a new waveform-based method for optimal c.m. correction.

## Key findings

- Large c.m. motion is mainly a gauge effect, not physical.
- Mode mixing persists even at large distances from the source.
- Waveform-based c.m. correction methods can improve waveform accuracy.

## Abstract

We present a detailed study of the center-of-mass (c.m.) motion seen in simulations produced by the Simulating eXtreme Spacetimes (SXS) collaboration. We investigate potential physical sources for the large c.m. motion in binary black hole simulations and find that a significant fraction of the c.m. motion cannot be explained physically, thus concluding that it is largely a gauge effect. These large c.m. displacements cause mode mixing in the gravitational waveform, most easily recognized as amplitude oscillations caused by the dominant (2,$\pm$2) modes mixing into subdominant modes. This mixing does not diminish with increasing distance from the source; it is present even in asymptotic waveforms, regardless of the method of data extraction. We describe the current c.m.-correction method used by the SXS collaboration, which is based on counteracting the motion of the c.m. as measured by the trajectories of the apparent horizons in the simulations, and investigate potential methods to improve that correction to the waveform. We also present a complementary method for computing an optimal c.m. correction or evaluating any other c.m. transformation based solely on the asymptotic waveform data.