Impact of Spin Priors on the Population Inference of Merging Binary Black Holes

TL;DR

The paper analyzes how the choice of spin priors affects gravitational-wave inferences for merging binary black holes, showing that conventional isotropic priors can bias population results, especially for subpopulations with large aligned spins. It introduces a prior uniform in the effective spin parameters $(\chi_\mathrm{eff}, \chi_\mathrm{p})$ conditioned on mass ratio and demonstrates, via simulated populations and hierarchical Bayesian inference, that this prior more faithfully recovers the true spin and, due to mass-spin correlations, improves mass distribution recovery as well. Event-level analyses reveal biases under the isotropic prior when the true population concentrates near $\chi_\mathrm{p}\approx 0$ or large $\chi_\mathrm{eff}$, while the new prior maintains better coverage and parameter recovery; population-level results show markedly improved effective sample sizes and reduced bias with the proposed prior. The work highlights the practical importance of prior choice in BBH population studies and motivates applying the $(\chi_\mathrm{eff}, \chi_\mathrm{p})$-uniform prior to real LVK data to avoid systematic biases in spin-based formation-channel inferences.

Abstract

The spins of merging binary black holes (BBHs) inferred from gravitational-wave (GW) observations provide key insights into their formation channels. However, spin parameters are typically weakly constrained from data, and their inferred values are often strongly influenced by the assumed prior in Bayesian analyses. A commonly used prior, uniform in spin magnitudes and isotropic in spin directions, assigns vanishing probability density to spin-orbit-aligned configurations, potentially biasing inferences for BBH parameters. The prior choice can also affect population-level analyses by degrading the convergence of Monte Carlo integrations used to evaluate the likelihood in hierarchical Bayesian inference. In this work, we propose a novel spin prior that is uniform in the effective spin parameters Xeff and Xp, two spin combinations that can be relatively well measured from GW data, conditioned on the mass ratio. Using simulated BBH populations, we show that the inferred spin population can depend on the choice of prior, and that the proposed prior more accurately recovers the underlying spin population, particularly when the true distribution favors aligned-spin configurations. Because mass and spin measurements are correlated, our prior also enables a more accurate recovery of the underlying mass distribution.

Figures (13)

• Figure 1: Corner plot of $\chi_\mathrm{eff}$ and $\chi_\mathrm{p}$ under the isotropic prior that is used in parameter estimation by the LVK collaboration. The plot is generated from samples drawn according to that prior distribution. Here, the prior on $q$ is chosen so that $m_1$ and $m_2$ are uniformly distributed, which gives a prior on $q$ proportional to $(1+q)^{2/5} / q^{6/5}$Thesaurus_prior. In addition, due to the constraint of dimensionless spin magnitude $a\leq 1$, the allowed region in the $\chi_\mathrm{eff}$–$\chi_\mathrm{p}$ plane takes an approximately elliptical shape. The explicit form of the boundary is given by Eq. \ref{['X_p_max']}. The dashed line shows 90% confidence line.
• Figure 2: Corner plot of $\chi_\mathrm{eff}$ and $\chi_\mathrm{p}$ under the $\chi_\mathrm{eff}$-$\chi_\mathrm{p}$ uniform prior. The plot is generated from samples drawn according to the prior distribution of Eq. \ref{['Xe_Xp_uni_prior']}. The plotting procedure is the same as in Fig. \ref{['prior_amp_theta']}. Although this prior is uniform over the allowed region in the $\chi_\mathrm{eff}$–$\chi_\mathrm{p}$ plane, it does not appear uniform near the boundary in the $\chi_\mathrm{eff}$–$\chi_\mathrm{p}$ plane because the allowed region itself depends on $q$, which is not fixed here.
• Figure 3: Corner plot of $\chi_\mathrm{eff}$ and $\chi_\mathrm{p}$ under the only $\chi_\mathrm{eff}$ uniform prior. The plot is generated from samples drawn according to the prior distribution (see Eq. (2) of Ref. pop_IAS). The plotting procedure is the same as in Fig. \ref{['prior_amp_theta']}.
• Figure 4: Prior and posterior distributions of the effective spins, chirp mass, mass ratio and redshift. The leftmost distribution corresponds to the prior distribution, while each of the distributions to the right corresponds to the results obtained from analyses of the corresponding injections, where the injection parameters were drawn from the GWTC-3–like population. The red stars represent injection values. The blue distribution on the left represents the parameter estimation results using an isotropic prior, which is used in the LVK analysis. The orange distribution on the right represents the results using $\chi_\mathrm{eff}$-$\chi_\mathrm{p}$ uniform prior.
• Figure 5: Prior and posterior distributions of the effective spins, chirp mass, mass ratio and redshift for each injection from large-$\chi_\mathrm{eff}$ population. The figure settings and color scheme follow those used in Fig. \ref{['XeXp_GWTC3like_violin']}.