[Paper Review] New insights on binary black hole formation channels after GWTC-2: young star clusters versus isolated binaries

Y. Bouffanais, Michela Mapelli+6 more|arXiv (Cornell University)|Feb 24, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy146 references72 citations

TL;DR

This study uses Bayesian hierarchical modeling and N-body/population synthesis simulations to compare isolated binary evolution and dynamical formation in young star clusters as formation channels for binary black holes (BBHs) using GWTC-2 data. It finds that a mixture of both channels best explains the observations, with dynamical formation favored (median f = 0.26) when spin magnitudes are moderate, and strongly favored (f ≤ 0.1) for high spin magnitudes, while metallicity spread significantly affects inferred mixing fractions.

ABSTRACT

With the recent release of the second gravitational-wave transient catalogue (GWTC-2), which introduced dozens of new detections, we are at a turning point of gravitational wave astronomy, as we are now able to directly infer constraints on the astrophysical population of compact objects. Here, we tackle the burning issue of understanding the origin of binary black hole (BBH) mergers. To this effect, we make use of state-of-the-art population synthesis and N-body simulations, to represent two distinct formation channels: BBHs formed in the field (isolated channel) and in young star clusters (dynamical channel). We then use a Bayesian hierarchical approach to infer the distribution of the mixing fraction $f$, with $f=0$ ($f=1$) in the pure dynamical (isolated) channel. %that controls the proportion of isolated and dynamical BBHs. We explore the effects of additional hyper-parameters of the model, such as the spread in metallicity $\sigma_{ ext{Z}}$ and the parameter $\sigma_{ ext{sp}}$, describing the distribution of spin magnitudes. We find that the dynamical model is slightly favoured with a median value of $f=0.26$, when $\sigma_{ ext{sp}}=0.1$ and $\sigma_{ ext{Z}}=0.4$. Models with higher spin magnitudes tend to strongly favour dynamically formed BBHs ($f\le{}0.1$ if $\sigma_{ ext{sp}}=0.3$). Furthermore, we show that hyper-parameters controlling the rates of the model, such as $\sigma_{ m Z}$, have a large impact on the inference of the mixing fraction, which rises from $0.18$ to $0.43$ when we increase $\sigma_{ ext{Z}}$ from 0.2 to 0.6, for a fixed value of $\sigma_{ ext{sp}}=0.1$. Finally, our current set of observations is better described by a combination of both formation channels, as a pure dynamical scenario is excluded at the $99\%$ credible interval, except when the spin magnitude is high.

Motivation & Objective

• To determine the relative contribution of isolated binary evolution and dynamical formation in young star clusters to the observed binary black hole mergers in GWTC-2.
• To assess how uncertainties in spin magnitude distribution and metallicity spread affect the inferred mixing fraction between formation channels.
• To test whether the observed BBH population in GWTC-2 can be explained by a pure isolated binary scenario or requires a dynamical component.
• To quantify the impact of astrophysical model hyper-parameters on the inference of formation channel mixing fractions.
• To evaluate whether current data support a single formation channel or require a combination of isolated and dynamical pathways.

Proposed method

• Employs state-of-the-art population synthesis (mobse) and N-body simulations to model BBH formation in isolated binaries and young star clusters.
• Uses a Bayesian hierarchical framework to infer the mixing fraction f, where f = 0 represents pure dynamical formation and f = 1 pure isolated evolution.
• Incorporates hyper-parameters σsp (standard deviation of spin magnitude distribution) and σZ (metallicity spread) to explore model sensitivity.
• Applies detection probability weighting (pdet) based on O3a sensitivity to correct for selection effects in the observed GWTC-2 sample.
• Compares simulated BBH populations (mass, spin, chirp mass) to observed GWTC-2 events using likelihood-based inference.
• Performs model comparison via Bayesian evidence to assess support for dynamical vs. isolated formation under varying assumptions.

Experimental results

Research questions

• RQ1 What is the inferred mixing fraction f between dynamical and isolated BBH formation channels based on GWTC-2 data?
• RQ2 How do variations in spin magnitude distribution (σsp) and metallicity spread (σZ) affect the inferred formation channel preference?
• RQ3 Is a pure isolated binary formation scenario consistent with the observed GWTC-2 BBH population?
• RQ4 To what extent do model hyper-parameters such as σZ and σsp influence the inferred value of f?
• RQ5 Can the observed distribution of effective spin χeff, including negative values, be explained by isolated formation alone?

Key findings

• The dynamical formation channel is slightly favored, with a median mixing fraction f = 0.26 when σsp = 0.1 and σZ = 0.4.
• Models with high spin magnitudes (σsp = 0.3) strongly favor dynamical formation, with f ≤ 0.1, due to support for negative χeff values in GWTC-2 events.
• The metallicity spread σZ has a strong impact: increasing σZ from 0.2 to 0.6 raises the inferred f from 0.18 to 0.43 when σsp = 0.1.
• A pure isolated binary scenario is excluded at the 99% credible interval, except when spin magnitudes are high (σsp = 0.3).
• The observed BBH population in GWTC-2 is best described by a combination of both formation channels, with dynamical processes essential for explaining high chirp masses and negative effective spins.
• Massive BBHs (primary mass > 60 M⊙) contribute significantly to the data, and their presence is best explained by dynamical formation in young star clusters.