Probing the peak of star formation with the stochastic background of binary black hole mergers

TL;DR

This work demonstrates that a Bayesian Templated Background Search can detect a stochastic background from binary black hole mergers and simultaneously infer high-redshift population properties without relying on individually resolved events. By analyzing one day of simulated O4-sensitivity data, the authors show that the dominant information for SGWB detection comes from mergers with signal-to-noise ratios just below the individual-event threshold, while the weakest mergers still inform the redshift distribution beyond the peak of star formation. Through hierarchical Bayesian inference and careful handling of selection effects and Monte Carlo biases, they recover the Madau-Dickinson–like redshift distribution out to $z$ beyond what current detectors resolve. The results imply that unresolved BBH mergers contribute meaningfully to constraining the redshift evolution of BBH populations, offering a path to study earlier cosmic epochs with future data and improved methods.

Abstract

Although the LIGO-Virgo-KAGRA collaboration detects many individually resolvable gravitational-wave events from binary black hole mergers, those that are too weak to be identified individually contribute to a stochastic gravitational-wave background. Unlike the standard cross-correlation search for excess correlated power, a Bayesian search method that models the background as a superposition of an unknown number of mergers enables simultaneous inference of the properties of high-redshift binary black hole populations and accelerated detection of the background. In this work, we apply this templated background search method to one day of simulated data at current LIGO Hanford-Livingston detector network sensitivity to determine whether the weakest mergers contribute information to the detection of the background and to the constraint on the merger redshift distribution at high redshifts. We find that the dominant source of information for the detection of the stochastic background comes from mergers with signal-to-noise ratios just below the individual detection threshold. However, we demonstrate that the weakest mergers do contribute to the constraint on the shape of the redshift distribution not only beyond the peak of star formation, but also beyond the redshifts accessible with individually detectable sources.

Figures (8)

• Figure 1: Histogram of the median of the posterior on the network matched filter SNR for the full dataset with $N=21600$ segments. The dotted vertical orange line at $\mathrm{SNR}=3$ is labeled with the number of segments with SNR below this threshold, 20751, which is $\sim96\%$ of the total dataset. The dotted vertical black line at $\mathrm{SNR}=8$ is labeled with the number of segments with SNR above this threshold, 48, which is $\sim 0.2\%$ of the total dataset.
• Figure 3: Left: Posterior on the duty cycle for a population beginning with only noise segments, and replacing them with signal segments with $\mathrm{SNR} < \mathrm{SNR}^\mathrm{S}_{\max}$, for $\mathrm{SNR_{\max}^S} = \{0,~6,~6.5,~7,~8,~10,~12,~40\}$ until $\xi=0.05$ (shown in orange). Note that all signal segments have $\mathrm{SNR} \leq 40$. Right: Posterior on the duty cycle beginning with a population with $\xi=0.05$ and replacing signal segments with $\mathrm{SNR} < \mathrm{SNR}^\mathrm{S}_{\max}$ with noise segments until $\xi=0.0$.
• Figure 4: Posterior on the duty cycle with selection effects taken into account calculated on the population while only including segments with SNR below the maximum SNR threshold in the top two rows of the grid, and only including segments with SNR above the minimum SNR threshold in the bottom two rows of the grid. The colored lines show the posterior on the duty cycle for 200 bootstrapped realization of the dataset while holding the duty cycle of the segments that pass that threshold fixed. The white lines show the posterior calculated with the full population, and the true value of the duty cycle is shown in orange, $\xi = 0.05$. The $\alpha, \beta$ values shown above each plot are the fractions of signal and noise segments, respectively, that pass the selection criteria (see Eq. \ref{['eq:norm_constant']}).
• Figure 5: Median 90% credible interval of 200 bootstrapped posterior calculations on $\xi$ in orange, with the shaded blue showing the 50% credible interval of the median $\mathrm{CI}_{90}$s as a function of the minimum SNR threshold imposed. Each bootstrapped posterior is calculated by randomly down-sampling with replacement a set of the segments whose SNR are greater than the thresholds such that all posterior calculations include the same number of total segments.
• Figure 6: Inferred redshift distribution obtained using hierarchical inference. In blue thin lines are posteriors on the redshift distribution calculated using the Madau-Dickinson parameterization for individual hyper-parameter posterior samples. The solid blue lines bound the $\mathrm{CI}_{90}$ for the full population analysis, the orange solid line is the true population prior Madau-Dickinson distribution, and the dashed black lines are the $\mathrm{CI}_{90}$ prior bound. The shaded red region is the $\mathrm{CI}_{90}$ for the analysis including only resolved segments and taking into account selection effects, and the solid black vertical line at $z=1.97$ marks the redshift of the farthest signal in the population with $\mathrm{SNR}> 8$.