Binary Black Hole Mergers: Spin and mass ratio effects on gravitational waveforms

TL;DR

The paper addresses how binary black hole (BBH) merger remnants depend on mass ratio and aligned spins. It uses a large-scale parameter-space study based on the SEOBNRv4_opt waveform model across $q \in [1,2.0]$ and aligned spins, augmented by a GW150914 case study to illustrate practical workflow. The main findings show that the remnant final spin $χ_f$ and fractional mass loss $M_{\mathrm{FL}}$ generally decrease with increasing $q$ but exhibit non-monotonic behavior in certain spin configurations (notably a turning point near $q \sim 1.7$ for PP), with maxima around $χ_f \sim 0.91$ and $M_{\mathrm{FL}} \sim 9.2\%$ in BP. Comparisons to NR-based fitting formulas indicate ~2–3% agreement, supporting robustness while highlighting the value of cross-model validation and a framework applicable to population studies. The work also demonstrates how waveform models can be integrated with observational data (e.g., GW150914) to inform remnant-based astrophysical inference and future model development.

Abstract

We present a comprehensive parameter-space study of binary black hole (BBH) mergers using the SEOBNRv4\_opt waveform model. Our analysis spans $\sim 10^6$ simulated waveforms across a broad range of mass ratios \( q = \frac{m_1}{m_2} \in [1.0, 2.0] \) and aligned spin configurations. We investigate the influence of these parameters on remnant properties, including final spin ($χ_f$), fractional mass loss ($M_{\mathrm{FL}}$), and peak gravitational-wave strain ($h_{\max}$). By systematically analyzing the trends across four distinct spin alignments (PP, PN, BP, BN), we identify non-monotonic behaviors and turning points in $M_{\mathrm{FL}}$ and $χ_f$ as functions of $q$, highlighting subtle dynamical effects that are not explicitly emphasized in commonly used remnant fitting formulae. While confirming known correlations from numerical relativity, our results offer new insights into parameter interactions and waveform morphology, with implications for BBH population studies and remnant characterization. Across all configurations studied, the fractional mass loss due to gravitational-wave emission ranges between 2\% and 9.5\%, depending on the mass ratio and spin alignment. This work may also aid in understanding the spin and mass distributions of the more massive black holes formed post-merger, thereby contributing to future remnant-based astrophysical inference.

Figures (5)

• Figure 1: Final spin parameter $\chi_{\rm f}$ as a function of initial mass ratio $q$ for the BP (both positive spin) configuration. Modeled data points are color-coded by fractional mass loss $M_{\rm FL}$. Panels (a)–(d) display selected subsets of systems with representative initial spin values. Panel (e) combines all modeled points for this spin configuration. Observed BBH systems from Table \ref{['table:Obs_Catalog']} are overplotted and indicated with arrows.
• Figure 2: Variation of final spin $\chi_{\rm f}$ as a function of mass ratio for the BN configuration. Color coding indicates fractional mass loss ($M_{\rm FL}$). Panels (a)-(d) correspond to selected initial spins; panel (e) shows combined data.
• Figure 3: Variation of final spin $\chi_{\rm f}$ as a function of mass ratio $q$ for the PN configuration. Each panel (a–d) represents selected initial spin values. The color scale indicates the fractional mass loss $M_{\rm FL}$. Panel (e) combines all initial spin values for this spin orientation. Observational data points are marked with arrows for reference (see Table \ref{['table:Obs_Catalog']}).
• Figure 4: Final spin $\chi_{\rm f}$ versus mass ratio $q$ for the PP configuration. Modeled data points are color-coded by their corresponding fractional mass loss $M_{\rm FL}$. Panels (a–d) show representative initial spin values; panel (e) displays combined results. Benchmark observational systems are indicated for comparison.
• Figure 5: With $PN$ and $PP$ models, changes of the parameter M$_{\rm{FL}}$ with respect to $q$, are plotted according to each value $\chi_{1i}$. Particularly in the $\chi_{1i} > 0.50$ region, it is seen that the parameter M$_{\rm{FL}}$, follows a trend in the increasing direction with the mass ratio to certain $q$ values, while it becomes a decreasing trend with $q$ in the continuation of the plot.