The dependence of black hole formation in open clusters on the cluster formation process

TL;DR

The paper addresses how the formation history of star clusters—rapid monolithic formation versus coalescence of subclusters—affects their dynamical evolution and black hole production. It uses two simulation categories of N-body models (isolated clusters and coalesced cluster complexes) with varied gas expulsion modes parameterized by $\tau_g$ and $\tau_d$, implementing the gas removal as a time-dependent external potential. A key finding is a degeneracy among initial cluster mass, gas expulsion timescale, and formation channel, with slower expulsion enabling BH retention in lower-mass clusters and coalescence allowing BH survival even under fast expulsion. The results imply that initial conditions informed by star-formation physics are crucial for realistic dynamical simulations and Gaia BH searches, and highlight the need for integrating hydrodynamics with N-body dynamics to constrain early feedback and gas expulsion processes.

Abstract

We performed N-body simulations of both individual cluster evolution and subcluster coalescence, demonstrating that cluster evolution and its outcomes strongly depend on the cluster formation process through comparisons of different gas expulsion modes and formation channels. The evolution of star clusters is significantly shaped by the gas expulsion mode, with faster expulsion producing greater mass loss. A broader degeneracy exists among initial cluster mass, gas expulsion timescale, and formation channel (monolithic vs. coalescence), which manifests in both evolutionary pathways and black hole production. In individual cluster simulations, slower gas expulsion enables progressively lower-mass clusters to retain central black holes within the tidal radius. As the gas expulsion mode transitions from fast to moderate to slow, the fraction of high-velocity stars decreases. Variations in gas expulsion mode and formation channel ultimately influence the stellar velocity distribution (within the tidal radius), and thus the expansion speed, which governs both cluster mass loss and black hole retention. Slowly expanding clusters are more likely to retain black holes and multiple systems, making them prime candidates for black hole searches with {\it Gaia}. Our results highlight the crucial influence of early gas expulsion and cluster formation mechanisms on the dynamical evolution of star clusters and black hole production. These factors should be carefully incorporated into the initial conditions of N-body simulations, which necessarily rely on input from the star formation community.

Figures (6)

• Figure 1: The evolution of cluster mass over time under different gas expulsion modes. In panel (b), The total mass of the cluster complex "NGC6334" is 2207 M$_{\odot}$, close to the single cluster with mass 2371 M$_{\odot}$. Here we only consider the total cluster mass within the tidal radius.
• Figure 2: The evolution of cluster mass over time under different gas expulsion modes. The color of the line reflects the number of black holes contained in a cluster of a given mass at a certain age. Here, we only consider the total cluster mass and the number of black holes within the tidal radius. For each panel, from bottom to top, the cluster masses are [300, 562, 1000, 1333, 1778, 2371, 3000, 5623, 10000] M$_{\odot}$.
• Figure 3: Same as Fig.\ref{['num']}, but for the cluster complex "NGC6334" and the 2371 M$_{\odot}$ cluster.
• Figure 4: The evolution of the 3000 M$_{\odot}$ cluster under different gas expulsion modes. Snapshots projected on the $XY$ plane (20 pc $\times$ 20 pc around the cluster center) at ages 10 Myr, 50 Myr, and 100 Myr are shown here. The size of the black dots reflects the stellar mass (linear scale). Neutron stars and black holes are represented by orange plus signs and red dots, respectively, with the symbol sizes being purely illustrative. The central regions of the star clusters in Fig.\ref{['3000']}(a) and (b) contain 2 and 3 black holes, respectively. In panel (b), two of the three black holes are too close to be distinguished on the map.
• Figure 5: Velocity distribution of stars within the cluster complex "NGC6334" and the 2371 M$_{\odot}$ cluster under different gas expulsion modes at 20 Myr. (a) Probability density function (PDF) of stellar velocities, estimated using the kernel density estimation (KDE) method to provide a smooth representation of the distribution; (b) Cumulative fraction shows the proportion of stars with velocities below a given value. Here we do not distinguish between binaries and single stars; instead, we calculate the total velocity of each star ($v_{\rm tot}$) in the cluster and examine their distribution to roughly characterize the expansion state of the cluster. At 50 Myr, the velocity distributions remain unchanged, indicating that the binary fraction does not significantly affect the statistical results here.