Seeking Spinning Subpopulations of Black Hole Binaries via Iterative Density Estimation

TL;DR

This paper tackles the challenge of inferring the joint distribution of BBH component masses and the effective spin $\chi_\mathrm{eff}$ from gravitational-wave data by employing a fully non-parametric iterative kernel density estimation (KDE) framework with elliptical kernels. The method accounts for selection effects via the sensitive volume-time $\text{VT}$, measurement uncertainties through reweighting of posterior samples, and finite-event statistics via bootstrap resampling, enabling a 3D reconstruction of $f(m_1,m_2,\chi_\mathrm{eff})$. Applied to GWTC-3, the analysis reproduces known features such as a small positive $\langle\chi_\mathrm{eff}\rangle$ at low masses and reveals a high-spin subpopulation for $m_1\gtrsim 40\,M_\odot$, with $|\chi_\mathrm{eff}|$ reaching up to ~0.75, plus a new trend where the derivative of $\chi_\mathrm{eff}$ with respect to $m_1$ is positive in the $10$–$15\,M_\odot$ range. These findings, consistent with broader spin distributions at high mass and potential mass-ratio–spin correlations, demonstrate the utility of a non-parametric, data-driven approach to uncover subpopulations and guide formation-channel modelling as the GW catalog grows.

Abstract

Attempts to understand the formation of binary black hole (BBH) systems detected via gravitational wave (GW) emission are affected by many unknowns and uncertainties, from both the observational and theoretical (astrophysical modelling) sides. Binary component spins have been proposed as a means to investigate formation channels, however obtaining clear inferences is challenging, given the apparently low magnitude of almost all merging BH spins and their high measurement uncertainties. Even for the effective aligned spin $χ_{\mathrm{eff}}$ which is more precisely measured than component spins, specific model assumptions have been required to identify any clear trends. Here, we reconstruct the joint component mass and $χ_{\mathrm{eff}}$ distribution of BBH mergers with minimal assumptions using the GWTC-3 catalog, using an iterative kernel density estimation (KDE)-based method. We reproduce some features seen in previous analyses, for instance a small but preferentially positive $χ_{\mathrm{eff}}$ for low-mass mergers; we also identify a possible subpopulation of higher-spin BBH with $|χ_{\mathrm{eff}}|$ up to $\sim\! 0.75$ for primary masses $m_1 \gtrsim 40\,M_\odot$, in addition to the bulk of the distribution with $|χ_{\mathrm{eff}}| \lesssim 0.2$. This finding is consistent with previous studies indicating a broader spin distribution at high mass, suggesting a distinct origin for the high-spin systems. We also identify a new potential trend of low-mass BBHs: the \emph{derivative} of $χ_{\mathrm{eff}}$ with respect to $m_1$ ($m_2$) is positive (negative) over the $10$--$15\,M_\odot$ range. This apparent structure may be related to} a previously reported anticorrelation between mass ratio and $χ_{\mathrm{eff}}$.

Figures (8)

• Figure 1: Chirp mass $\mathcal{M}$ and $\chi_\mathrm{eff}$ of PE samples for 69 BBH events from GWTC-3, with color showing the sensitive volume-time (VT).
• Figure 2: Merger rate density over binary component masses, marginalized over $\chi_\mathrm{eff} \xspace$. Median estimate over bootstrap iterations.
• Figure 3: Rate density over BBH component masses obtained by marginalizing 3d rate estimates over $\chi_\mathrm{eff}$ and one component mass. Color bands show 90% confidence regions obtained from bootstrap iterations.
• Figure 4: Population mean $\chi_\mathrm{eff}$ as a function of BH component masses (median estimate over bootstrap iterations). Contours show rate density as in Fig. \ref{['fig:2Dmass-rate']}.
• Figure 5: Population standard deviation of $\chi_\mathrm{eff}$ as a function of BH component masses (median estimate over bootstrap iterations). Contours show rate density as in Fig. \ref{['fig:2Dmass-rate']}.