Probing Binary Black Hole Formation Channels through Cosmic Large-Scale Structure

TL;DR

This work introduces a clustering-based method to distinguish binary black hole formation channels by treating mergers as cosmological tracers of large-scale structure. Using the Illustris hydrodynamic simulation and the Illustris-sBBH dataset, the authors compute two-point correlation functions and relative biases $b(r)$ for stellar, AGN-disk, and PBH scenarios, then project to mock catalogs for next-generation detectors like Cosmic Explorer. They find channel-dependent clustering signatures that evolve with redshift and separation scale, with separability achievable on timescales of $\lesssim$ a decade at $1.2$ Mpc and shorter at $z\sim 1$ for CE-like sensitivities; PBH scenarios could yield quicker constraints via DM-biased signatures. This framework links gravitational-wave populations to the cosmic matter field, offering a complementary probe to population inferences and enabling future extensions to LISA-era observations and lunar detectors.

Abstract

The growing number of binary black hole mergers detected through gravitational waves offers unprecedented insight into their underlying population, yet their astrophysical formation channels remain unresolved. We present a new method to distinguish binary black hole formation channels using their spatial clustering at cosmological scales. Employing the cosmological hydrodynamic simulation Illustris, we trace the distribution of mergers across cosmic time and compare them with the underlying matter distribution associated with three candidate origins: isolated binary stellar evolution, binaries embedded in AGN disks, and primordial black holes within dark matter halos. For mergers at redshift $z \lesssim 0.5$, these channels show distinct clustering signatures that could be accessible with proposed upgrades to current ground-based gravitational-wave detectors. Using mock catalogs for next- generation facilities such as Cosmic Explorer, we find that their sensitivities would enable differentiation of these formation pathways out to redshift $z \sim 5$ within the first decade of observations. This approach provides a new framework to link gravitational-wave populations with the large-scale structure of the Universe. By treating black hole mergers as cosmological tracers, our results demonstrate how cross- correlations between gravitational-wave catalogs and the cosmic matter field can constrain the relative contribution of stellar, AGN, and primordial channels, offering a complementary probe to population- inference studies. These findings underscore the emerging potential of gravitational-wave cosmology to reveal where and how black holes form and merge across cosmic history.

Figures (2)

• Figure 1: Visualization slices (top row), two-point correlation functions (middle row) and relative clustering biases (bottom row) for $z = 0.5$ (far left column), $z = 1$ (middle left column), $z = 3$ (middle right column), and $z = 5$ (far right column) data. Visualization slices include dark matter particles (green dots, representing a 10% downsample of the total data), stellar particles (orange dots), SMBHs (black dots), all simulated sBBH mergers (blue dots), and sBBH mergers observed by CE in a five year observing run (red dots) for a slice thickness of $1.2$ Mpc. Two-point correlation functions include stellar particles (solid orange), SMBHs (solid black), dark matter particles (solid green), gas particles (solid purple), and all sBBH mergers in the Illustris-sBBH dataset matched to that redshift slice (solid blue). The stellar particles, dark matter particles, and gas particles are downsampled to a random sample of $10^{6}$ particles for computational feasibility. The relative clustering biases with 90% confidence intervals include the mock-observed sBBH to SMBH bias (shaded purple), the mock-observed sBBH to stellar bias (shaded orange), and the mock-observed sBBH to dark matter bias (shaded gray). The dashed lines represent the true underlying bias of the simulated data, the dotted black horizontal line represents where no underlying bias is present, and the dotted red line represents the $1.2$ Mpc bin, used in creating Figure \ref{['fig:bias_time']}. The stellar clustering bias statistically significantly differs from the SMBH and DM bias at $z = 0.5$ and $z = 1$. The DM bias differs from SMBH and stellar at $z = 3$ and $z = 5$. Given CE sensitivity, the merger rate plays a larger part in constraining the relative clustering bias than redshift.
• Figure 2: Evolution of 90% confidence intervals of relative clustering biases of SMBH to observed sBBHs, stellar particles to observed BBHs, and dark matter particles to observed sBBHs, by years of observation on a CE-like detector at different redshifts ($z = 0.5$ far left column, $z = 1$ middle left column, $z = 3$ middle right column, and $z = 5$ far right column). The top row shows a separation distance of 1.2 Mpc (represented by the vertical dotted red lines on the bottom row of \ref{['fig:5yr_big_multiplot']}, and the bottom row shows a separation distance of 17.2 Mpc. From the Figure, $z = 1$ at the closer separation distance shows by far the highest chance of non-overlap between the sBBH to stellar and sBBH to SMBH relative clustering biases, with marginal non-overlapping regions in $z = 3$ and $z = 5$ for 1.2 Mpc, and for $z =1$ at 17.2 Mpc.