Exploration of features in the black hole mass spectrum inspired by non-parametric analyses of gravitational wave observations

TL;DR

This paper interrogates features in the black hole mass spectrum suggested by non-parametric population analyses by testing two parametric extensions of the PowerLaw+Peak model against GWTC-3 data within a hierarchical Bayesian framework that accounts for selection effects. It uses a mixture-model population approach to jointly infer primary mass, mass ratio, and redshift, comparing models such as PowerLawMR and Beta for the mass-ratio distribution and an evolving two-component redshift model. The results show marginal evidence for two redshift-evolving subpopulations and indicate that the mass-ratio distribution for symmetric binaries ($q>0.7$) is not well constrained with current data, while the two-channel redshift evolution aligns with prior hints from non-parametric analyses. These findings have implications for population synthesis and the interpretation of BBH formation channels, emphasizing the need for more sensitive future GW observations to decisively distinguish between competing scenarios.

Abstract

Current gravitational-wave data reveal structures in the mass function of binary compact objects. Properly modelling and deciphering such structures is the ultimate goal of gravitational-wave population analysis: in this context, non-parametric models are a powerful tool to infer the distribution of black holes from gravitational waves without committing to any specific functional form. Here, we aim to quantitatively corroborate the findings of non-parametric methods with parametrised models incorporating the features found in such analyses. We propose two modifications of the currently favoured PowerLaw+Peak model, inspired by non-parametric studies, and use them to analyse the third Gravitational Wave Transient Catalogue. Our analysis marginally supports the existence of two distinct, differently redshift-evolving subpopulations in the black hole primary mass function, and suggests that, to date, we are still unable to robustly assess the shape of the mass ratio distribution for symmetric ($q>0.7$) binaries.

Figures (5)

• Figure 1: Left: Posterior distribution for the $\alpha_q$ and $\beta_q$ parameters of the Beta model (blue) compared with the corresponding $\beta + 1$ parameter of the PowerLawMR model. Right: Marginal posterior probability density for the mass ratio $q$ using the two different models described in Sec. \ref{['sec:plmassratio']}. The shaded areas correspond to the 68% and 90% credible regions.
• Figure 2: Differential information entropy between prior and marginal posterior as a function of mass ratio (left) and primary mass (right). Each thin blue solid line represents one individual GW event, whereas the thick dashed red line marks the average differential information entropy. Note that the top and bottom part of both panels have different limits.
• Figure 3: Joint posterior distribution for $\kappa_\mathrm{PL}$, $\kappa_\mathrm{Peak}$ and $\lambda$ for the Evolving model.
• Figure 4: Left: Marginal posterior distribution for $\lambda$ for the Evolving model conditioned on $\kappa_\mathrm{PL} = \kappa_\mathrm{Peak}$ and for the PowerLaw+Peak model. Right: Marginal posterior distribution for the redshift spectral index $\kappa$ for the PowerLaw, Peak and PowerLaw+Peak population model.
• Figure 5: Left: probability density for the source redshift. Right: Merger rate density as a function of redshift. In both panels, the coloured regions refer to the two components of the Evolving model, whereas the areas delimited by the dashed black line refers to the common evolution of the PowerLaw+Peak model. The hatched areas mark the extrapolation beyond detector horizon for the corresponding mass range.