Can Big Black Holes Merge with the Smallest Black Holes?

TL;DR

The paper tests whether the minimum secondary black hole mass $m_2^{\min}$ evolves with the primary mass $m_1$ by introducing variable-$m_2^{\min}(m_1)$ forms (Power Law, Increasing Parabola, Relaxed Parabola) into a hierarchical Bayesian framework applied to GWTC-3 binary black hole events, with and without GW190814. Using a joint distribution over $m_1$, $q=m_2/m_1$, spins, and redshift, the study finds no strong evidence for an increasing $m_2^{\min}(m_1)$ when GW190814 is excluded, while including GW190814 strongly favors a Relaxed Parabola form that allows $m_2^{\min}$ to dip at certain $m_1$ and accommodate the low-mass companion of GW190814 (\(\log_{10}\mathcal{B}=4.44\)). This increased model flexibility helps reconcile GW190814 with the bulk BBH population and highlights the role of outliers in shaping population inferences. The work underscores the need to model correlations between mass, mass ratio, and spin to reveal the astrophysical processes behind BBH formation and to guide future analyses with larger GW catalogs.

Abstract

Gravitational-wave measurements of the binary black hole population provide insights into the evolution of merging binaries. We explore potential correlation between mass and mass ratio with phenomenological population models where the minimum mass of the smaller (secondary) black hole can change with the mass of the bigger (primary) black hole. We use binary black hole signals from the third Gravitational-Wave Transient Catalog with and without the relatively extreme mass-ratio GW190814. When excluding GW190814, models with a variable minimum mass are disfavoured compared to one with a constant minimum mass, with log Bayes factors of -2.49 to -0.98, indicating that the biggest black holes can merge with the smallest. When including GW190814, a parabola model that allows the minimum mass to decrease with increasing primary mass is favoured over a constant minimum-mass model with a log Bayes factor of 4.44. When allowing the minimum mass to decrease, the overall population distributions remain similar whether or not GW190814 is included. This shows that with added model flexibility, we can reconcile potential outlier observations within our population. These investigations motivate further explorations of correlations between mass ratio and component masses in order to understand how evolutionary processes may leave an imprint on these distributions.

Figures (7)

• Figure 1: Example evolution of $m_2^{\mathrm{min}}$ with $m_1$ for the Power Law, Increasing Parabola, and Relaxed Parabola model variations we consider, for some fiducial hyperparameters within our prior range. The shaded region indicates where $m_1>m_2^{\mathrm{min}}>0$.
• Figure 2: Inferred evolution of the minimum secondary mass with primary mass for the Power Law (left), Increasing Parabola (middle), and Relaxed Parabola (right) models. Each panel shows the resulting median and $90\%$ credible interval on the minimum secondary mass, including and excluding GW190814. The grey shows the $99\%$ credible interval for the prior for each model, with the lower edge in black. The interval is evaluated over $m_1\in[2,100]~M_{\odot}$, where the plotted range extends to $m_1>m_{\mathrm{max}}$ for some individual hyperposterior samples. With GW190814, the entire distribution of $m_2^{\mathrm{min}}$ is lower, apart from the Relaxed Parabola model, which decreases to allow for the lower secondary mass at $m_1\sim20\,M_{\odot}$. Due to the driving of the prior, $m_2^{\mathrm{min}}$ then increases at higher $m_1$ for this model. Otherwise, there is no strong evidence for an increasing $m_2^{\mathrm{min}}$ with $m_1$ when accounting for model limitations.
• Figure 3: Hyperposteriors on the key mass and mass-ratio hyperparameters with Power Law model, with and without GW190814. The $m_2^{\mathrm{min}}$ hyperparameter $\gamma$ prefers high values, supporting a non-increasing or shallowly increasing $m_2^{\mathrm{min}}$ with $m_1$. The other hyperparameters show disagreement between the choice to include or exclude GW190814.
• Figure 4: Hyperposteriors on the key mass and mass-ratio hyperparameters with the Increasing Parabola model, with and without GW190814. The $m_2^{\mathrm{min}}$ hyperparameters, $\xi$ and $\zeta$ are railing at $0$, showing a preference for a non-increasing $m_2^{\mathrm{min}}$ with $m_1$. The other hyperparameters show disagreement between the choice to include or exclude GW190814.
• Figure 5: Hyperposteriors on the key mass and mass-ratio hyperparameters with the Relaxed Parabola model, with and without GW190814. The $m_2^{\mathrm{min}}$ hyperparameters, $\xi$ and $\zeta$ are consistent with zero without GW190814, but negative $\xi$ is preferred when including GW190814. The other hyperparameters are in agreement between the two choices of observations.