Hierarchical Black Hole Mergers in Nuclear Star Clusters: A Combined Dynamical-Secular Channel for GW231123-like Events

Abstract

The recent binary black hole (BH) merger GW231123, with both components likely in the high-mass gap and with high spins, challenges standard BH binary formation models. It is usually thought that the BHs are of second (or higher) generation (2G), resulting from the mergers of smaller BHs. But the physical processes that produce the merging 2G BH binaries are unclear and highly unconstrained. We show that such 2G mergers can be naturally produced in the nuclear star cluster of Milky Way-like galaxy. The dominant channel combines a sequence of binary-single interactions with secular evolution driven by the central supermassive BH. Our model produces a merger rate consistent with GW231123 and further predicts an abundant population of 2G BH-star (or low-mass BH) binaries; these binaries may observationally manifest as micro tidal disruption events or low-frequency gravitational-wave (GW) sources. Detecting these binaries would provide crucial insights into the dynamical pathways of hierarchical BH assembly.

Figures (4)

• Figure 1: Dynamical pathways for 2G/2G mergers in NSCs. The evolution begins with a 2G BH (left), which may form a 2G/2G binary through GW capture (Channel 1). Alternatively, it can first form a 2G/star (S) binary via tidal capture (Channel 2) or binary–single (S/S binary-2G) interaction (Channel 3), followed by an exchange interaction with another 2G BH that yields a 2G/2G binary. This binary then merges into a 3G BH driven by secular forcing from the SMBH (ZLK effect), potentially initiating further hierarchical growth.
• Figure 2: Key timescales for forming 2G/2G mergers via different channels, evaluated at distance $R$ from an SMBH of mass $M_\bullet=4\times10^6M_\odot$, assuming a density profile index $\gamma$ constant for all populations. The merger time of various binaries due to GW emission (without the influence of the SMBH) are denoted by $T_\mathrm{m}$.
• Figure 3: Top panel: 2G/2G BHB merger rates versus the galactic distance $R$. The rates are derived per galaxy from Eq. (\ref{['eq:Bateman equations']}). Different slopes of the density profile for star ($\gamma_s$) and BH ($\gamma_\mathrm{BH}$) are taken into account (as labeled; see Eq. \ref{['eq:density profile']}). We adopt $f_1=10\%$ and $T_\mathrm{m}= T_\mathrm{evap}$ in Eq. (\ref{['eq:Bateman equations']}); $f_2$ denotes the fraction of systems that reach eccentricities high enough to merge within $T_\mathrm{evap}$ (ZLK window), calculated assuming isotropic orbital orientations Liu-HierarchicalMerger. Middle/Bottom panels: 2G/1G and 1G/1G merger rates for $\gamma=1.75$. Thick solid lines correspond to $M_\bullet=4\times10^6M_\odot$ and thin solid lines represent $M_\bullet=10^7M_\odot$.
• Figure 4: Distribution of merger kick velocity versus final spin magnitude for equal-mass spinning BH mergers, assuming isotropic spin orientations (see the analytical fits in Lousto 2010). Color indicates the value of effective spin parameter $\chi_\mathrm{eff}$, defined as $\chi_{\rm eff}=(m_1 \chi_1 \theta_1+m_2 \chi_2 \theta_2)/(m_1+m_2)$, where $\theta_{1,2}$ are the spin-orbit misalignment angles. The black dashed contour shows the boundary of distribution for the case of $\chi_{1,2}=0.7$. For reference, the black solid contour corresponds to low spin case ($\chi_{1,2}=0.3$), and the red dot-dashed contours represent high unequal spins ($\chi_1=0.9$, $\chi_2=0.8$).