Spin it as you like: The (lack of a) measurement of the spin tilt distribution with LIGO-Virgo-KAGRA binary black holes

Abstract

Context. The growing set of gravitational-wave sources is being used to measure the properties of the underlying astrophysical populations of compact objects, black holes, and neutron stars. Most of the detected systems are black hole binaries. While much has been learned about black holes by analyzing the latest LIGO-Virgo-KAGRA (LVK) catalog, GWTC-3, a measurement of the astrophysical distribution of the black hole spin orientations remains elusive. This is usually probed by measuring the cosine of the tilt angle (cosτ) between each black hole spin and the orbital angular momentum, with cosτ = +1 being perfect alignment. Aims. The LVK Collaboration has modeled the cosτ distribution as a mixture of an isotropic component and a Gaussian component with mean fixed at +1 and width measured from the data. We want to verify if the data require the existence of such a peak at cosτ = +1. Methods. We used various alternative models for the astrophysical tilt distribution and measured their parameters using the LVK GWTC-3 catalog. Results. We find that (a) augmenting the LVK model, such that the mean μ of the Gaussian is not fixed at +1, returns results that strongly depend on priors. If we allow μ > +1, then the resulting astrophysical cosτ distribution peaks at +1 and looks linear, rather than Gaussian. If we constrain −1 ≤ μ ≤ +1, the Gaussian component peaks at μ = 0.48−0.99+0.46 (median and 90% symmetric credible interval). Two other two-component mixture models yield cosτ distributions that either have a broad peak centered at 0.19−0.18+0.22 or a plateau that spans the range [ − 0.5, +1], without a clear peak at +1. (b) All of the models we considered agree as to there being no excess of black hole tilts at around −1. (c) While yielding quite different posteriors, the models considered in this work have Bayesian evidences that are the same within error bars. Conclusions. We conclude that the current dataset is not sufficiently informative to draw any model-independent conclusions on the astrophysical distribution of spin tilts, except that there is no excess of spins with negatively aligned tilts.

Potential Subpopulations and Assembling Tendency of the Merging Black Holes

“…Dynamical assembly in dense stellar environments like globular clusters predicts isotropic spins, while the features for the mergers in the AGN disks can change in a variety of ranges depending on the properties of the disk (Vajpeyi et al 2022) and the dynamics in play (Tagawa et al 2020). Though at this stage, we might not be able to clearly resolve the tilted angle distribution from the available data (Vitale et al 2022;Tong et al 2022), our analysis disfavors both the perfect alignment case (σ ct,dyn = 1) and the isotropically tilted case (σ ct,dyn ? 1) of the spin, implying that not all of the dynamical mergers happen in old, dense AGNs, or, young, dilute AGNs/globular clusters (Benacquista & Downing 2013;Vajpeyi et al 2022).…”

“…Very recently, both Callister et al (2022) and Tong et al (2022) suggested that there is no evidence for the existence of a nonspinning subpopulation, and they found support for the presence of mergers with extreme spin tilt angles. Nevertheless, Vitale et al (2022) found that the exact shape for the inferred distribution of tilt angle of component BHs strongly depends on the assumed population model and the priors for the model parameters.…”

What You Don’t Know Can Hurt You: Use and Abuse of Astrophysical Models in Gravitational-wave Population Analyses

“…the spin orientation (Vitale et al 2022a). On the positive side, if a parameter can be reliably measured, it often has a clear connection with a meaningful astrophysical quantity (e.g., the slope of a mass power law).…”

“…On the positive side, if a parameter can be reliably measured, it often has a clear connection with a meaningful astrophysical quantity (e.g., the slope of a mass power law). Heuristic models also allow correlations between parameters to be probed in a straightforward manner (Callister et al 2021;Adamcewicz & Thrane 2022;Biscoveanu et al 2022;Vitale et al 2022a;Baibhav et al 2023). 2.…”

Searching for Candidates of Coalescing Binary Black Holes Formed through Chemically Homogeneous Evolution in GWTC-3

“…Therefore, these two features can be used as a probe to investigate whether or not there is quantitative high-confidence evidence of any merging BBHs formed through the CHE channel. Recent studies (Galaudage et al 2021;Roulet et al 2021;Vitale et al 2022) have pointed out that the inferred spin and mass parameters are dependent on the choice of priors. 13 This is because the measurements of spin and mass are poorly constrained, and so the resulting broad posteriors can be heavily swayed by one's choice of prior.…”