$\texttt{GR-Athena++}$ Simulations of Spinning Binary Black Hole Mergers

Abstract

We present the second release of the $\texttt{GR-Athena++}$ waveform catalog, comprising four new quasi-circular, non-precessing, spinning binary black hole simulations. These simulations are performed at high resolutions and represent a step toward generating high-fidelity gravitational waveforms that can eventually meet the accuracy requirements of upcoming next-generation detectors, including LISA, Cosmic Explorer, and Einstein Telescope. Gravitational waves are extracted at future null infinity ( $\mathscr{I}^{+}$) using both Cauchy characteristic extraction and finite-radius extraction. For each simulation, we provide strain data across multiple resolutions and analyze waveform accuracy via convergence studies and self-mismatch analyses. The absolute phase and relative amplitude differences reach their largest values near the merger, while the smallest errors are of order $\mathscr{O}(10^{-2})$ and $\mathscr{O}(10^{-3})$, respectively. A self-mismatch analysis of the dominant $(2,2)$ mode yields mismatches between $\mathscr{O}(10^{-5})$ and $\mathscr{O}(10^{-7})$ for a total binary mass of $10^{6}$ $M_{\odot}$ over the frequency range $[0.002, 0.1]$ Hz using LISA noise curve. All waveforms are publicly available via $\texttt{ScholarSphere}$.

Figures (5)

• Figure 1: gw strains for the dominant $(\ell, m) = (2,2)$ mode from the highest-resolution simulations of four binary black hole systems. Each panel displays the real part (blue), imaginary part (orange), and amplitude (green) of the complex strain $h = h_+ - i h_\times$ as a function of retarded time $u/M$. The simulations differ in their spin configurations: ID 0005 ($\chi_1 = -0.1$, $\chi_2 = 0.1$), ID 0006 ($\chi_1 = 0.1$, $\chi_2 = 0.1$), ID 0007 ($\chi_1 = -0.4$, $\chi_2 = 0.4$), and ID 0008 ($\chi_1 = 0.4$, $\chi_2 = 0.4$). All these waveforms are calculated using fre.
• Figure 2: Highest-resolution gw strains for the spin configuration ID 0008 ($\chi_1 = 0.4$, $\chi_2 = 0.4$), showing various $(\ell, m)$ modes—(2,2), (2,1), (3,2), (3,3), (4,4), and (5,5)—as a function of retarded time $u/M$. Each panel displays the real part (blue), imaginary part (orange), and amplitude (green) of the complex strain. The vertical black lines mark the merger time, defined as the time of maximum amplitude of the dominant (2,2) mode. The side panel displays the zoom-in around the merger time.
• Figure 3: Convergence study of strains using fre waveforms. We show the absolute phase differences $|\Delta\phi|$ between different numerical resolutions and the highest-resolution simulation for $(\ell,m)=(2,2)$ mode as a function of retarded time $u/M$. The vertical black lines mark the merger time.
• Figure 4: Convergence study of strains using fre waveform. We show the relative amplitude differences $|\Delta A|/A$ between different numerical resolutions and the highest-resolution simulation for $(\ell,m)=(2,2)$ mode. The vertical black lines mark the merger time. The amplitude differences have been smoothed with a 50$M$ window to reduce numerical noise.
• Figure 5: Self-mismatch study using $(\ell,m)= (2,2)$ mode of fre waveforms. We compute the self-mismatch (Eq. \ref{['eq:mismatch']}) between the highest-resolution run and its lower-resolution counterparts for each simulation using lisa noise curve. We set the total mass of the binary as $10^{6} M_{\odot}$ and calculate mismatch within the frequency band $f \in [0.002, 0.1]~\mathrm{Hz}$.