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GW241011 and GW241110: Hints of Hierarchical Mergers from the Merger Entropy Index

Guo-Peng Li, Xi-Long Fan

TL;DR

The paper investigates whether GW241011 and GW241110 originate from hierarchical (2G+) black hole mergers by applying the merger entropy index $\mathcal{I}_{\rm BBH}$, which compresses mass-spin information into a single diagnostic via $\mathcal{I}_{\rm BBH} = \frac{\pi}{9}\frac{\Delta S_{\rm BBH}}{S_1+S_2}$ with $S_i = \frac{2\pi G}{c\hbar} m_i^2 (1+\sqrt{1-\chi_i^2})$ and $\Delta S_{\rm BBH}=S_f-(S_1+S_2)$. The index is computed for the events using GW posterior data and compared to two population models, the CMC dense-star-cluster catalog and the PP parametric model, via likelihood matching and KS tests. The results indicate GW241011 is strongly consistent with hierarchical mergers in dense clusters, while GW241110 remains ambiguous due to large uncertainties, highlighting method-dependent inferences. Overall, the study demonstrates that $\mathcal{I}_{\rm BBH}$ provides an efficient, one-dimensional diagnostic to screen hierarchical-merger scenarios and emphasizes the importance of accounting for observational uncertainties in interpretation.

Abstract

GW241011 and GW241110 both exhibit extremely asymmetric masses, high primary spins, and significant spin-orbit misalignment, which challenge the formation of first-generation binary black hole mergers formed from stellar collapse. This implies that these two gravitational wave events might originate from the hierarchical merger mechanism, with at least one of the black holes being the remnant of a previous merger. Here we investigate the origin of hierarchical mergers for GW241011 and GW241110 using the merger entropy index which measures the efficiency of entropy transfer for binary black hole mergers in general relativity. We find that GW241011 is consistent with hierarchical mergers in dense star clusters. The origin of GW241110 remains under debate due to its large distribution uncertainty, which leads to method-dependent inference and should be taken into account when interpreting this event in terms of hierarchical mergers.

GW241011 and GW241110: Hints of Hierarchical Mergers from the Merger Entropy Index

TL;DR

The paper investigates whether GW241011 and GW241110 originate from hierarchical (2G+) black hole mergers by applying the merger entropy index , which compresses mass-spin information into a single diagnostic via with and . The index is computed for the events using GW posterior data and compared to two population models, the CMC dense-star-cluster catalog and the PP parametric model, via likelihood matching and KS tests. The results indicate GW241011 is strongly consistent with hierarchical mergers in dense clusters, while GW241110 remains ambiguous due to large uncertainties, highlighting method-dependent inferences. Overall, the study demonstrates that provides an efficient, one-dimensional diagnostic to screen hierarchical-merger scenarios and emphasizes the importance of accounting for observational uncertainties in interpretation.

Abstract

GW241011 and GW241110 both exhibit extremely asymmetric masses, high primary spins, and significant spin-orbit misalignment, which challenge the formation of first-generation binary black hole mergers formed from stellar collapse. This implies that these two gravitational wave events might originate from the hierarchical merger mechanism, with at least one of the black holes being the remnant of a previous merger. Here we investigate the origin of hierarchical mergers for GW241011 and GW241110 using the merger entropy index which measures the efficiency of entropy transfer for binary black hole mergers in general relativity. We find that GW241011 is consistent with hierarchical mergers in dense star clusters. The origin of GW241110 remains under debate due to its large distribution uncertainty, which leads to method-dependent inference and should be taken into account when interpreting this event in terms of hierarchical mergers.
Paper Structure (5 sections, 2 equations, 2 figures, 1 table)

This paper contains 5 sections, 2 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Merger entropy index
  3. Hints to hierarchical mergers
  4. Conclusions
  5. Acknowledgments

Figures (2)

  • Figure 1: $90\%$ credible bounds on the merger entropy indices, mass ratios (left), and primary spins (right) of GW241011 (red) and GW241110 (blue), compared to expected properties of merging BBHs in dense star clusters from the CMC catalog 2020ApJS..247...48K2022ApJS..258...22R (green) and the PP model 2023PhRvD.107f3007L2025ApJ...981..177L (purple). Dashed contours correspond to first-generation mergers, while solid contours correspond to hierarchical mergers. Dotted contours represent the properties of GW231123 2025ApJ...993L..25A for comparison. The CMC catalog assumes black holes to be born non-rotating, while the PP model assumes 1G BHs are born with low spins following a beta distribution.
  • Figure 2: Probability density distributions (left) and cumulative distributions (right) of the merger entropy indices of GW241011 and GW241110, compared to those of merging BBHs in dense star clusters from the CMC catalog 2020ApJS..247...48K2022ApJS..258...22R and the PP model 2023PhRvD.107f3007L2025ApJ...981..177L. The legend is the same as Figure \ref{['fig1']}.