Adapted gauge to small mass ratio binary black hole evolutions

TL;DR

This paper introduces adapted gauge conditions for small mass ratio binary black hole simulations, reducing noise and improving stability, enabling more accurate and efficient numerical evolutions across a range of mass ratios.

Contribution

The authors develop and test new gauge conditions, including approximate late-time lapse and shift behaviors and a position-dependent damping term, enhancing simulation stability and accuracy for small mass ratio binaries.

Findings

Reduced initial noise in simulations

Enhanced grid stability around black holes

Successful application to binaries with high mass ratios

Abstract

We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $(\alpha_0,\beta_0)$, and use them as initial values for their evolutions. We also use a position and black hole mass dependent damping term, $\eta[\vec{x}_1(t),\vec{x}_2(t),m_1,m_2]$, in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a 7:1 mass ratio, and then use 15:1 and 32:1 binaries for a convergence study. Finally, we apply our new gauge to a 64:1 binary and a 128:1 binary to well cover the comparable and small mass ratio regimes.