Extending superposed harmonic initial data to higher spin

TL;DR

This paper introduces a new class of initial data, called superposed modified harmonic (SMH), that extends superposed harmonic data to higher black hole spins, reducing junk radiation in numerical simulations.

Contribution

The authors develop a novel spatial coordinate transformation enabling superposed harmonic initial data for higher spins, improving simulation accuracy.

Findings

SMH initial data reduces junk radiation compared to previous methods.

The new data maintains small changes in black hole parameters.

Constraint violations decrease with resolution during the junk radiation stage.

Abstract

Numerical simulations of binary black holes are accompanied by an initial spurious burst of gravitational radiation (called `junk radiation') caused by a failure of the initial data to describe a snapshot of an inspiral that started at an infinite time in the past. A previous study showed that the superposed harmonic (SH) initial data gives rise to significantly smaller junk radiation. However, it is difficult to construct SH initial data for black holes with dimensionless spin $\chi\gtrsim0.7$. We here provide a class of spatial coordinate transformations that extend SH to higher spin. The new spatial coordinate system, which we refer to as superposed modified harmonic (SMH), is characterized by a continuous parameter -- Kerr-Schild and harmonic spatial coordinates are only two special cases of this new gauge. We compare SMH with the superposed Kerr-Schild (SKS) initial data by evolving several binary black hole systems with $\chi=0.8$ and $0.9$. We find that the new initial data still leads to less junk radiation and only small changes of black hole parameters (e.g. mass and spin). We also find that the volume-weighted constraint violations for the new initial data converge with resolution during the junk stage $(t\lesssim700M)$, which means there are fewer high-frequency components in waveforms at outer regions.