Intermediate-Mass Black Hole Formation from Hierarchical Mergers in Galactic Nuclei

TL;DR

The study investigates IMBH formation and GW-source production in nuclear star clusters (NSCs) surrounding a $4\times10^6\,M_\odot$ SMBH by evolving 1000 BHs over $10$ Gyr with a semianalytic model that includes GW capture, BH–star collisions, relaxation, dynamical friction, and recoil. It compares four initial BH distributions (lower/upper limits, with/without primordial binaries) to assess how initial conditions shape mass/spin growth and the generation of GW events. Key findings show that IMBHs ($>100\,M_\odot$) form mainly for upper-limit mass distributions (up to $\sim 526\,M_\odot$), often via either hierarchical mergers or star-collision channels; mass growth is dominated by GW capture rather than stellar accretion, and stellar collisions drive a broad, often lower, spin distribution. The results imply observable GW-source populations and EMRI signatures in galactic nuclei, with merger-generation and spin patterns strongly dependent on the initial BH mass function and binary content.

Abstract

Dense stellar environments like nuclear star clusters (NSCs) can dynamically assemble gravitational wave (GW) sources. We consider a population of single stellar mass black holes (BHs) in the inner $0.1$~pc of a NSC surrounding a $4 \times 10^6$~M$_\odot$ supermassive black hole (SMBH). Using a semianalytic model, we account for direct collisions between BHs and stars and GW capture between BHs. We explore the effect of the initial BH mass and spin distributions on their final properties and the production of GW sources. Specifically, we consider upper and lower limits for the BH initial mass distribution, and we account for the possibility that a subset of our initial population are the merger products of primordial BH binaries. We find that $\sim 500$ M$_{\odot}$ intermediate mass black holes (IMBHs) can form for our upper limit mass distribution, while our lower limit mass distribution forms none. Most IMBHs $\gtrsim 200$~M$_\odot$ eventually sink towards the center of the cluster and merge with the SMBH. We also find that BH-star collisions create a more uniform spin distribution. Our results have implications for LIGO-Virgo-KAGRA sources. We find that the overall merger rate depends primarily on the upper limits of the initial BH mass distribution, ranging from $\sim10^{-10}$ to $\sim10^{-9}$~yr$^{-1}$ per galaxy. However, primordial binaries increase the number of second and higher generation mergers by an order of magnitude.

Figures (10)

• Figure 1: We show the distributions for the four initial BH mass distributions described in Section 2.1. Left: The lower limit refers to the conservative case of all initially low mass stellar BHs from Kremer+20Belczynski+16, as well as the lower limit where 30% of the binary BHs have primordial mergers. Right: The upper limit describes a case that includes primordial binaries and single BHs. The right top panel describes a case where BHs are evaporated describes a mass distribution of all initially single BHs from Hoang+18.
• Figure 2: We show the resulting spins and the change in mass of 1000 BHs after 1 billion years with the Hoang+18 Single BHs (gold) initial conditions, as described in Section \ref{['sec:BHstar_coll_spin_effects']}. All BHs underwent at least two collisions with stars, with a maximum number of collisions per BH of 194. As shown in Table \ref{['tab:bh_summary']}, after 1 billion years, 2.3% of the population are IMBHs with mass above $\sim$ 100 $M_{\odot}$.
• Figure 3: Left: We plot the distributions of initial mass in gray and final mass in color for the four initial conditions described in Section \ref{['sec:initialconditions']}, as well as IC gold (Hoang+18 Single BHs) with only stellar collisions with density $\alpha=1.25$. Right: We plot the distributions of initial spin in gray and final spin in color for the four initial conditions described in Section \ref{['sec:initialconditions']}.
• Figure 4: Contribution of each dynamical channel to that mass growth for each BH with $M_{f}>M_{i}$. The x-axis shows the amount of mass accreted over the entirety of the simulation from direct collisions with stars, which is limited by both feedback during the accretion process and environmental conditions like stellar density and velocity dispersion. The y-axis shows the growth through BH-BH gravitational wave capture. For all four sets of simulations, most mass growth for the BHs came from GW capture. To guide the eye, we plot a line in black showing where the change in mass from BH-BH mergers and BH-star collisions are equal.
• Figure 5: For four simulations described in Table \ref{['tab:bh_summary']}, number of mergers from GW capture per highest generation of BH in the event. In calculating the generation of the BH, we account for both previous GW captures in the simulation and primordial mergers from the initial conditions. We find that primordial binaries increases the merger rate with 2G BHs. The initial masses of the BHs seem to have the strongest effect on the number of higher generation mergers. We only show merger generations up to 7G, but the shape can be extrapolated to 7G+ mergers. The highest generation merger was 16G (12G) for blue (gold).