The Non Parametric Reconstruction of Binary Black Hole Mass Evolution from GWTC-4.0 Gravitational Wave Catalog

TL;DR

This paper addresses whether the binary black hole (BBH) mass distribution evolves with redshift, a question tied to stellar evolution and metallicity, while correcting for strong gravitational-wave selection effects. It introduces a fully non-parametric Bayesian method that models $p(m,z)$ via a Taylor expansion around $z_{\rm ref}$ up to second order, and fits it to GWTC-3 and GWTC-4.0 with selection calibrated from LVK injections, showing that the linear term $p_1(m)$ is near zero for $m \lesssim 30\,M_\odot$ but positive for higher masses while the quadratic term $p_2(m)$ remains consistent with zero up to $z \sim 1$. The results support metallicity-driven formation channels and demonstrate the utility of non-parametric, selection-corrected population inference for interpreting current and future gravitational-wave catalogs.

Abstract

The distribution of binary black hole (BBH) masses and its evolution with redshift provide key insights into the different formation channels of the compact objects and their evolution with cosmic time and stellar properties such stellar metallicity and star formation rate history. We present a non parametric, model-independent joint reconstruction of the redshift evolution of BBH mass distribution from gravitational wave (GW) catalog GWTC-4.0 from the fourth observation of LIGO-Virgo-KAGRA (LVK). This method simultaneously searches for the signature of any linear and quadratic redshift evolution with respect to the low redshift in a Bayesian framework taking into accounting the detector selection effects. We find tentative evidence for a linear redshift-dependent evolution of the mass distribution, consistent over a mass range ($m \gtrsim 50\,M_\odot$). While lower mass systems shows no signature of evolution. The quadratic term remains consistent with zero, indicating that a simple linear dependence adequately describes the population up to redshift $z \sim 1$. In future with more GW sources, this technique can shed light into the true nature of the redshift dependence and possibility to uncover subtle evolutionary features in BBH populations and to probe the cosmic history of black hole formation.

Figures (3)

• Figure 1: Schematic illustration of the impact of selection effects and intrinsic mass evolution on the observable black hole mass distribution. The red regions denote parameter space inaccessible to detectors due to selection bias. The green area represents the detectable mass range under scenarios with no intrinsic evolution, while the yellow region highlights where signatures of positive mass evolution would appear. For negative evolution, part of the green region below the blue line and above the lower red boundary remains observable. Arrows and shaded bands indicate the characteristic observational trends: constant distribution for no evolution, downward shifts for negative evolution, and upward shifts for positive evolution, emphasizing how evolutionary effects manifest relative to the standard detection boundaries.
• Figure 2: Exploratory visualization of observed BBH component mass and distance distributions from the GWTC-3 and GWTC-4.0 catalogs. The top left panel shows a scatter plot of median posterior component masses versus median luminosity distance for GWTC-3, categorized as low (20-40 M$_\odot$, blue), medium (40-60 M$_\odot$, purple), and high ($>$60 M$_\odot$, orange) mass ranges, highlighting the distribution of detected systems. The top right panel presents violin plots for GWTC-3, with the left violins showing the distributions of primary component masses and the right violins showing distributions for secondary masses, grouped in three luminosity distance bins (0-2, 2-4.5, and 4.5-8 Gpc), illustrating how both mass components vary with distance. The bottom left panel repeats the mass versus luminosity distance scatter plot for GWTC-4.0, revealing analogous mass-dependent distance patterns. The bottom right panel displays violin plots for GWTC-4.0, again distinguishing primary (left) and secondary (right) mass distributions within each distance bin, revealing the changing spread and range of observed masses at increasing distances. Collectively, these panels illustrate the evolving mass-distance relationship across observing runs and motivate the application of hierarchical population analyses that rigorously account for uncertainties and selection biases. Importantly, low-mass BBHs are not detectable at higher redshifts primarily due to selection effects, while the absence of high-mass BBHs at lower distances cannot be explained by selection biases alone, suggesting intrinsic astrophysical factors influence their local detectability.
• Figure 3: Posterior constraints on the redshift evolution of the BBH mass distribution, shown as a function of component mass. Left: Linear coefficient $p_1(m)$, measuring the first-order rate of change of the mass distribution with redshift. Right: Quadratic coefficient $p_2(m)$, capturing any curvature in the redshift dependence. Error bars denote $1\sigma$ credible intervals from the hierarchical Bayesian analysis. Two binning schemes are presented: a coarse $5 \times 5$ grid with $\Delta m = 10\,M_{\odot}$ and $\Delta z = 0.2$, and a finer $10 \times 10$ grid with $\Delta m = 5\,M_{\odot}$ and $\Delta z = 0.1$. The latter exhibits larger uncertainties consistent with reduced event counts per bin. The linear term is consistent with zero for low mass systems ($m \lesssim 30\,M_{\odot}$) but increases toward higher masses, indicating massive black holes are relatively more abundant at earlier cosmic times. The quadratic term remains consistent with zero across all mass bins, implying a simple linear dependence on redshift adequately describes the current observational range $z \lesssim 1$ accessible to LVK.