On the Formation of GW231123 in Population III Star Clusters

TL;DR

GW231123 challenges conventional PI-gap interpretations; this work tests Pop III star clusters as the origin using $N$-body simulations of clusters embedded in mini dark matter halos and a top-heavy IMF. Candidate GW231123 progenitors arise via 1–3 mergers across stellar, BBH, and mixed channels, with $m_1\in[100,200]\,M_\odot$ and $q\in[0.1,1]$, matching GW231123's mass values. The implied merger-rate density is $\mathcal{R}\in[0.001,0.26]\,{\rm Gpc^{-3}yr^{-1}}$, consistent with the observationally inferred rate, and most events occur at $z>2$, with some late-time mergers depending on halo survival. Multi-band GW observations by next-generation detectors could test Pop III cluster scenarios and help distinguish them from isolated Pop III binaries, though the existence of Pop III clusters remains unconfirmed.

Abstract

GW231123 is a binary black hole merger whose primary component lies within or above the pair-instability mass gap, while the secondary component falls within this gap. The standard theory of stellar evolution is significantly challenged by this event. We investigate the formation of candidate progenitors of GW231123 in Population III (Pop III) star clusters. We find that they could form through stellar mergers, binary black hole mergers, and mixed mergers. The mass distribution of these candidate progenitors covers the component masses of GW231123. Under our model assumptions, their predicted merger rate density spans the range of $0.001-0.26{\rm Gpc^{-3}yr^{-1}}$, encompassing that of GW231123. These findings suggest that GW231123 may originate from Pop III star clusters. Furthermore, such candidate progenitors are expected to be detectable by future gravitational wave detectors LISA/Taiji/TianQin/DECIGO/Cosmic Explorer/Einstein Telescope, which would provide valuable insights into the formation scenarios of events like GW231123.

Figures (4)

• Figure 1: Distributions of the primary mass $m_{1}$ and mass ratio $q=m_{2}/m_{1}$ for candidate progenitors of GW231123. The upper and lower panels show results from models of Pop III clusters with PBF=0 and 1, respectively. Symbols indicate the formation channels of candidate progenitors. Circles and squares correspond to cases where both of $m_{1}$ and $m_{2}$ originate from stellar mergers (the massive components are PIBHs evolved from massive stars that underwent stellar mergers, thereby avoiding pair-instability supernovae) and BBH mergers, respectively. Triangles represent mixed mergers, i.e., $m_{1}$ and $m_{2}$ are from stellar mergers and BBH mergers, respectively. Symbols with a tan facecolor denote candidate progenitors whose components are ejected from their host clusters due to kick velocities exceeding the clusters’ escape velocities. Colors indicate the total number of mergers contributing to the formation of candidate progenitors, defined as the sum of the mergers producing $m_{1}$ and those producing $m_{2}$ ($n_{1}+n_{2}$), with red, blue and green denoting 1, 2 and 3, respectively. Note that almost $m_{2}$ originates from the evolution of ordinary single stars in stellar merger and mixed merger channels, i.e., $n_{2}=0$. The gray dot marks the median value of GW231123, with the error bar indicating the 90% probability intervals inferred from GW observations.
• Figure 2: The orbital element (eccentricity $e$ and semi-major axis $a$) distributions of candidate progenitors of GW231123 at their formation time, defined as the moment BBHs emerge during binary star evolution. The red and green dots represent the results from different models with PBF=0 and 1, respectively.
• Figure 3: Merger remnant masses $m_{\rm f}$ and merger time $t_{\rm merger}$ of candidate progenitors of GW231123. The merger time $t_{\rm merger}$ refers to the moment during the evolution of Pop III star clusters, at which the mergers occur. Red and green dots represent the results from different models with PBF=0 and 1, respectively.
• Figure 4: Peak frequency $f_{\rm peak}$ and the corresponding characteristic strain $h_{\rm cn_{peak}}$ of GWs emitted by candidate progenitors of GW231123 in all the models. The copper and winter color bars represent redshift $z$ and eccentricities at peak $f_{\rm peak}=0.01$ Hz, respectively. Sensitivity curves of GW detectors LISA, Taiji, TianQin, DECIGO, CE, ET, LIGO, and KAGRA are represented by different colors and line styles.