Can Big Black Holes Merge with the Smallest Black Holes?

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.

💡 Research Summary

This paper investigates whether the minimum mass of the secondary black hole (m ₂, min) in binary black‑hole (BBH) mergers depends on the mass of the primary black hole (m ₁). Traditional population‑modeling efforts have assumed a constant m ₂, min, but the authors introduce three flexible functional forms that allow m ₂, min to vary with m ₁: (i) a power‑law model with an exponent γ, (ii) an “increasing parabola” with positive linear (ξ) and quadratic (ζ) coefficients, and (iii) a “relaxed parabola” that permits a negative ξ, thereby allowing m ₂, min to decrease as m ₁ grows.

Using hierarchical Bayesian inference, the authors fit these models to the GWTC‑3 catalog (69 BBH events with false‑alarm rate < 1 yr⁻¹). They treat the primary‑mass distribution with the standard PowerLaw+Peak mixture, spin magnitudes with a beta distribution, spin tilts with an isotropic‑plus‑Gaussian mixture, and redshift with a power law. The mass‑ratio distribution incorporates the new minimum‑mass prescriptions, while all other hyper‑parameters retain the priors used in Abbott et al. (2023a). Selection effects are accounted for with a combined set of semi‑analytic and real injection campaigns.

A key methodological twist is the treatment of GW190814, an event with an extreme mass ratio (q ≈ 0.11) and a secondary mass of ≈ 2.6 M⊙, which sits near the putative neutron‑star/black‑hole mass gap. The authors perform the analysis twice: once excluding GW190814 (the “standard” BBH sample) and once including it (testing whether the event can be accommodated as a BBH outlier).

Results without GW190814
Log Bayes factors for the variable‑minimum models relative to the constant‑minimum baseline range from –2.49 to –0.98, indicating a clear preference for a fixed m ₂, min. In this scenario the data suggest that the most massive black holes can indeed merge with the lightest black holes; there is no statistical evidence that the minimum secondary mass rises with primary mass.

Results with GW190814
When GW190814 is added, the relaxed‑parabola model (which allows m ₂, min to drop for large m ₁) is favored with a log Bayes factor of +4.44 over the constant‑minimum model. The power‑law model yields posterior γ > 2.8 (90 % credible), while the increasing‑parabola model remains disfavored. The favored relaxed parabola implies that, for the most massive primaries (≈ 80–100 M⊙), the smallest permissible secondary mass can be substantially below the canonical ≈ 5 M⊙ floor, effectively accommodating GW190814 as a BBH merger rather than a neutron‑star–black‑hole system.

Population‑wide implications
Despite the differing treatment of m ₂, min, the inferred primary‑mass, mass‑ratio, spin, and redshift distributions remain remarkably stable between the two analyses. This robustness indicates that the added flexibility primarily serves to absorb outlier events without reshaping the bulk population. The posterior on γ in the power‑law model peaks at values > 4, reflecting a near‑flat m ₂, min up to high m ₁, with a sharp rise only near the maximum stellar‑mass black hole.

Interpretation and future directions
The findings have several astrophysical ramifications. First, they demonstrate that current GW data do not require a rising minimum secondary mass with primary mass, a scenario that would be expected if common‑envelope evolution strongly suppressed highly unequal‑mass mergers. Second, the ability of a decreasing‑m ₂, min model to reconcile GW190814 suggests that the “mass gap” between neutron stars and black holes may be partially populated by BBH mergers, or that formation channels (e.g., dynamical assembly in dense clusters or hierarchical mergers) can produce extreme mass‑ratio systems. Third, the analysis underscores the importance of model flexibility: a rigid assumption about m ₂, min can label genuine BBH events as outliers, whereas a modestly more complex prescription can integrate them naturally.

Future work should (i) expand the sample with forthcoming O4/O5 detections, (ii) explore non‑parametric or mixture‑model approaches to the m ₂, min–m ₁ relation, and (iii) couple the mass‑ratio–mass correlation to spin and redshift evolution to test specific formation‑channel predictions (e.g., hierarchical mergers producing high‑mass primaries with low‑mass companions). Ultimately, a statistically significant detection of a decreasing minimum secondary mass with primary mass would provide a powerful diagnostic of the relative contributions of isolated binary evolution, dynamical assembly, and exotic pathways to the observed BBH population.