Calibration of Moving Puncture Simulations

TL;DR

This work calibrates moving-puncture binary black-hole simulations using a moving-box AMR framework (BAM), validating fourth-order convergence for single and binary black holes and exploring the influence of conformal-factor choices, gauge conditions, and finite-radius wave extraction. By comparing φ- and χ-based moving-puncture evolutions and cross-validating with the LEAN code, the authors establish robust, efficient workflows suitable for large-scale parameter studies. They demonstrate that PN-based initial data approaches yield accurate quasi-circular configurations and quantify how gauge parameters (notably the damping η) affect coordinate behavior and horizon properties. The study provides practical guidance for achieving high-accuracy gravitational-wave predictions with moderate computational resources, enabling broader explorations of BBH parameter space.

Abstract

We present single and binary black hole simulations that follow the moving puncture paradigm of simulating black-hole spacetimes without excision, and use moving boxes mesh refinement. Focussing on binary black hole configurations where the simulations cover roughly two orbits, we address five major issues determining the quality of our results: numerical discretization error, finite extraction radius of the radiation signal, physical appropriateness of initial data, gauge choice and computational performance. We also compare results we have obtained with the BAM code described here with the independent LEAN code.

Figures (21)

• Figure 1: The BSSN variables $\tilde{g}_{xx}$, $\chi$, $\alpha$, and $\beta^y$ after $50M$ of evolution of a Schwarzschild puncture using the $\chi$ method. A small pulse due to the initial adjustment of the gauge can be seen at about $y = 60M$ in $\tilde{g}_{xx}$. The main features of the other variables are confined to $y < 10M$.
• Figure 2: Fourth-order convergence of a Schwarzschild puncture after $50M$ of evolution, using the $\phi$ method. Results were taken from runs with $N = 64^3, 96^3$ and $128^3$ points with octant symmetry. The plots show the differences between the three runs, scaled to be consistent with fourth-order accuracy. For the Hamiltonian constraint and $y$-component of the momentum constraint, which should converge to zero, we show the logarithm of the scaled values.
• Figure 3: Fourth-order convergence of a Schwarzschild puncture after $50M$ of evolution, using the $\chi$ method. The parameters match those used for the runs discussed in Figure \ref{['fig:cvg_phi_t50']}.
• Figure 4: Left: coordinate location of $R = 2M$ after 50$M$ of evolution, as a function of the damping parameter, $\eta$, with initial lapse $\alpha =1$ and $\alpha = \psi^{-2}$. Right: coordinate location $R=2M$ as a function of time, for $M \eta = 0, 2.0, 3.5$, using initial $\alpha = 1$.
• Figure 5: Real part of the $l=2, m=0$ mode of $r\Psi_4$, extracted at $r = 30m_1$.