Are black hole spins truly near-zero?

TL;DR

The paper demonstrates that the widely reported near-zero BH spins in GWTC-4 can be driven by prior geometry rather than data likelihood alone. By contrasting the conventional uniform-in-magnitude prior with a geometrically agnostic, uniform-in-volume prior in the 3D spin configuration space, it shows that $χ_{ m eff}$ constraints are relatively robust while spin magnitudes and $χ_p$ distributions can shift substantially, especially in high-spin regions. These prior-driven effects propagate to tests of general relativity, Kerr remnant constraints, and formation-channel diagnostics, underscoring the need for priors that truly reflect agnosticism in spin geometry. The work also provides practical diagnostics for sampling adequacy in spin-space (e.g., $N_{CR}$ and $E_R$) and cautions against over-reliance on reweighting between priors when high-spin regions are under-sampled. Overall, the authors advocate adopting priors uniform in spin-configuration space (e.g., $oldsymbol{oldsymbol{ heta}} ightsquigarrow V=B^3$) to ensure unbiased GR tests and population inferences as GW catalogs grow.

Abstract

The fourth gravitational-wave transient catalog, GWTC-4.0, reports 153 binary black hole mergers with false-alarm rates $<1,\mathrm{yr}^{-1}$. Chirp masses are typically measured well, with the smallest fractional uncertainty being $2%$ at the $90%$ credible level. Spins, on the other hand, are poorly constrained: the median of the best-measured spin component of the population, the effective spin, is $χ_{\rm eff}=0.04$, with a typical $90%$ credible uncertainty of $Δχ_{\rm eff}=0.44$. The large majority -- $90%$ of the observed black holes -- are consistent with spin magnitudes $χ<0.57$ and are weakly aligned with the orbits. At $90%$ credibility, the peaks of the inferred posteriors for spin magnitude are found to lie in the range $0.01$--$0.23$. We show that this ``near-zero spins'' conclusion may be prior-driven, and that uniform-in-magnitude spin priors lead to under-exploration of the moderate-to-high spin region of parameter space. Adopting a physically agnostic prior that is uniform in spin-vector configuration space (i.e., spin states uniform within a unit sphere) yields similar constraints on $χ_{\rm eff}$, but substantially different spin-magnitude inferences than GWTC-4.0. The resulting shift in spins directly impacts tests of general relativity, constraints on near-extremal Kerr remnants, and astrophysical conclusions, including diagnostics of formation channels and hierarchical growth. In short, the data do not require vanishing spins -- the prior does, and accounting for this is essential for robust GR tests and population inferences.

Figures (9)

• Figure 1: Distribution of the endpoints of the spin vectors. The left half contains points drawn from a uniform distribution in magnitude (blue) and an isotropic-in-direction distribution. The points in the right hemisphere (orange) are drawn uniformly in the volume, and as a consequence, are also isotropic in directions. Each plot contains about $10^5$ points.
• Figure 2: Marginal distribution $p'(\chi')$ of the spin magnitude $\chi'$ (blue, left panel) in the space $V'$, and that ($p(\chi)$) of spin magnitude $\chi$ in the space $V'$ (orange, left panel). Although $\chi'$ is seemingly uninformative in $V'$, it is heavily biased towards lower spins in 3D (see Fig. \ref{['fig:priors3D']}). Similarly, the seemingly biased power-law marginal distribution $p(\chi)$ is actually uniform in volume, as can be seen in \ref{['fig:priors3D']}. The solid orange line denotes the analytic distribution in \ref{['eq:magnitudeV']}. The marginal distributions in $V$ of any of the Cartesian components $\chi_k$ are shown on the right panel. The uniform in spin-magnitude distribution is shown in blue, and the uniform in spin configuration volume is shown in orange. The solid line denotes the logarithmic distribution derived in \ref{['eq:pdfMcomponents']}. In both plots, the histograms are sampled from the prior distributions for spin magnitude $\chi$ under the assumption of isotropic spin directions, from which the samples for the Cartesian components are deduced.
• Figure 3: The most probable value of the spin magnitude vs the maximum likelihood value of the spin magnitude, from 50 draws of the spin vectors from a uniform in magnitude and isotropic in directions prior distribution This clearly portrays the effect of preferential sampling near the origin (as shown in Fig. \ref{['fig:priors3D']}) when the existing priors are used to infer the posterior.
• Figure 4: Marginal distributions for the spins magnitudes of GW150914 (left), GW230814 (centre) and GW250114 (right). In the case of GW150914, there is insufficient information in the likelihood, and in both cases, the prior is recovered for the posterior. One can see that the posterior distribution has better support around the region of maxL when there is sufficient information in the likelihood (GW230814 and GW250114). In the case of GW250114, the new priors also end up accumulating posteriors in an entirely different, high-spin region of the spin configuration space, where they find a marginally higher log-likelihood value.
• Figure 5: Performance of reweighting of posterior samples with uniform-in-magnitude priors to obtain the marginal posterior distribution for the spin magnitudes with uniform-in-volume priors, in the GW250114 analysis. The reweighted samples are in blue, while the samples run with uniform-in-volume priors are in orange.