[Paper Review] Gravitational background from dynamical binaries and detectability with 2G detectors

C. Périgois, Filippo Santoliquido+6 more|arXiv (Cornell University)|Dec 2, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy113 references18 citations

TL;DR

This study investigates the gravitational wave (GW) background from dynamical binary black holes (BBHs) formed in young star clusters, using N-body and population synthesis simulations. It finds that dynamical BBHs dominate the GW background at 25 Hz, yielding Ωgw(25Hz) = 1.2⁺¹.³⁸₋₀.⁶⁵ × 10⁻⁹, consistent with current LIGO-Virgo upper limits, and predicts a detectable bump in the spectrum due to a mass peak in dynamical mergers, potentially measurable with 8 years of 2G detector data.

ABSTRACT

We study the impact of young clusters on the gravitational wave background from compact binary coalescence. We simulate a catalog of sources from population I/II isolated binary stars and stars born in young clusters, corresponding to one year of observations with second-generation (2G) detectors. Taking into account uncertainties on the fraction of dynamical binaries and star formation parameters, we find that the background is dominated by the population of binary black holes, and we obtain a value of $\Omega_{gw}(25 m{Hz}) = 1.2^{+1.38}_{-0.65} imes 10^{-9}$ for the energy density, in agreement with the actual upper limits derived from the latest observation run of LIGO--Virgo. We demonstrate that a large number of sources in a specific corrected mass range yields to a bump in the background. This background could be detected with 8 years of coincident data by a network of 2G detectors.

Motivation & Objective

• To assess the contribution of dynamical binary black holes formed in young star clusters to the stochastic gravitational wave background.
• To compare the GW background from dynamical binaries with that from isolated binaries in population I/II stars.
• To evaluate the detectability of the resulting GW background with second-generation (2G) gravitational wave detectors.
• To identify spectral features—particularly bumps—arising from mass-dependent merger redshifts in dynamical populations.

Proposed method

• Simulated 1.2 × 10⁸ isolated binary systems using the MOBSE population-synthesis code with updated stellar wind, supernova, and black hole formation models.
• Generated 106,000 N-body simulations of young star clusters (300–30,000 M⊙) using NBODY6++GPU, interfaced with MOBSE to model binary evolution consistently.
• Evolved source populations across cosmic time using CosmoRate, incorporating redshift-dependent star formation rates, metallicity evolution, and delay-time distributions.
• Calculated the energy density of the GW background, Ωgw(f), using the merger rate density R(z) and redshift-dependent chirp mass distributions.
• Identified sub-populations in the background spectrum by analyzing chirp mass and merger redshift distributions, particularly for exchanged and original binaries.
• Assessed detectability using signal-to-noise ratio estimates for a network of 2G detectors over 8 years of coincident observation.

Experimental results

Research questions

• RQ1 What is the contribution of dynamical binary black holes formed in young star clusters to the stochastic gravitational wave background?
• RQ2 How does the spectral shape of the GW background from dynamical binaries differ from that of isolated binaries, and what causes these differences?
• RQ3 Can a detectable spectral feature (bump) in the GW background arise from a concentration of dynamical BBHs in a specific mass range?
• RQ4 What is the expected detectability of the dynamical BBH background with 8 years of data from a network of second-generation (2G) gravitational wave detectors?
• RQ5 How do the merger redshifts and chirp masses of dynamical binaries (especially exchanged systems) shape the overall GW background?

Key findings

• The gravitational wave background at 25 Hz is dominated by binary black holes formed through dynamical processes in young star clusters, yielding Ωgw(25Hz) = 1.2⁺¹.³⁸₋₀.⁶⁵ × 10⁻⁹.
• A distinct bump in the GW background spectrum arises from a concentration of dynamical BBHs with chirp masses around 6–12 M⊙ merging at high redshift (z ~ 2–3), driven by metal-poor progenitors.
• Exchanged binaries (dynamically assembled) contribute significantly to the high-mass end of the background, with ~1% of mergers involving black holes in the pair-instability mass gap.
• The background from dynamical binaries is consistent with current LIGO-Virgo upper limits, validating the model's realism.
• With 8 years of coincident data from a network of 2G detectors, the combined GW background from dynamical binaries—especially the spectral bump—could be detectable.
• The sub-populations in the background spectrum are primarily shaped by the interplay between merger redshift and chirp mass, with sharp features arising from preferential delay times and metallicities in the CosmoRate model.