Stellar-mass black holes in young massive and open stellar clusters -- VII. Comparisons with gravitational-wave events until LVK-O4a and Gaia compact binaries

Abstract

Gravitational-wave (GW) detections by the LIGO-Virgo-KAGRA (LVK) observatories suggest multiple formation channels for GW compact binary mergers. Here I assess the role of young massive clusters (YMC) evolving into old open clusters (OC) -- the YMC/OC channel -- to the GW merger population. A homogeneous grid of 90 N-body evolutionary model star clusters, spanning initial masses of $10^4M_\odot\leq M_{cl}(0)\leq10^5M_\odot$, half-mass radii of 1-3 pc, and metallicities between 0.0002-0.02 is computed with the direct, post-Newtonian N-body code NBODY7. The N-body simulations include primordial binaries, delayed stellar-remnant model forming black holes (BH) and neutron stars (NS), BH spin prescriptions, and GW recoil kicks, and they are evolved until BH depletion. Most GW mergers from the cluster models are dynamically assembled binary black holes (BBH) that merge within their host clusters. Merger mass ratios reach down to 0.1-0.2 despite an overall bias toward nearly symmetric pairs. The GW merger efficiency varies non-monotonically with cluster mass, peaking around $M_{cl}(0)=7.5\times10^4M_\odot$ and also for $M_{cl}(0)\leq3.0\times10^4M_\odot$. The computed mergers reproduce some of the key features of the latest observed GW event catalogue, including asymmetric low-mass mergers, misaligned events among highly spinning, massive BHs, and an excess of $30M_\odot$ primaries, though they under-produce $10M_\odot$ primaries, hinting at contributions from other channels. The model merger rate density accounts for 25%-33% of the observed rate; it increases with redshift somewhat faster than the cosmic star formation, consistently with LVK's inferences. The model effective spin distribution is positively asymmetric at zero redshift and broadens with redshift. The models yield field BH- and NS-main sequence star binaries with parameters consistent with the Gaia-discovered candidates. [Abgd.]

Figures (20)

• Figure 1: Depiction of the computed grid of 90 evolutionary model star clusters spanning across ranges of cluster initial mass, $M_{\rm cl}(0)$, initial half-mass radius, $r_{\rm h}(0)$, and metallicity, $Z$. The panels in the upper, middle, and lower rows correspond to the computed grid points (filled circles) for the clusters with $r_{\rm h}(0)=1$, 2, and 3 pc, respectively. The greyscale color coding of the edge of a circle represents the end time in Myr, $T_{\rm end}$, of the corresponding N-body simulation. The circles' fill colour in the left column represents $f_{\rm end}$, which is the number of bound cluster members at the end of the simulation relative to the initial cluster membership. The circles' fill colour in the right column represents $f_{\rm BH,end}$, which is the number of BHs bound to the cluster at the end of the simulation relative to the peak BH membership of the cluster during its evolution. See Table. \ref{['tab:runlist']} (Appendix \ref{['runlist']}) for more details.
• Figure 2: Dependence of model cluster evolution with variation of cluster metallicity, $Z$ (upper panel), initial mass, $M_{\rm cl}(0)$ (middle panel), and initial size, $r_{\rm h}(0)$ (lower panel). For each variation (legend), the other two grid coordinates are kept constant, as indicated in each row's title. Shown are the time evolution of the half-mass radius, $r_{\rm h}$ (left column), and the number of BHs bound to the cluster, $N_{\rm BH}$ (right column).
• Figure 3: Time evolution of the luminous mass (total mass of luminous stars within the instantaneous tidal radius), $M_{{\rm cl},\ast}$, and size (corresponding projected half-mass radius, averaged over three orthogonal projections), $r^\prime_{\rm h,\ast}$, of the computed model star clusters as functions of the cluster-evolutionary age, $t$, at low ($Z=0.001$, 0.005; upper pair of panels) and high ($Z=0.01$, 0.02; lower pair of panels) metallicities (solid lines). The masses, sizes, and ages of the low-$Z$ (high-$Z$) models are compared with those of the observed star clusters across ages in the SMC Gatto_2021 (MW, M31, and LMC PortegiesZwart_2010) (filled symbols).
• Figure 4: Compilation of GW mergers of compact binaries produced by all the 90 evolutionary model clusters in this work. Left panel: the filled symbols represent the mergers' primary mass, ${m}_1$, along the X-axis versus the mergers' secondary mass, ${m}_2$, along the Y-axis (${m}_1\geq{m}_2$). The circles and the triangles mark the in-cluster and the ejected mergers, respectively. Those merging binaries that preserve their primordial pairing ( i.e., the primordially paired mergers) are indicated by an additional thick-lined edge around their respective symbols. The data points are colour-coded with respect to the initial half-mass density, $\rho_{\rm cl,0}$, of their respective parent cluster (colour bar). The canonical lower or NS-BH mass gap between $2.5{\rm M}_{\odot}-5.0{\rm M}_{\odot}$ and the upper or PSN mas gap between $40.5{\rm M}_{\odot}-120.0{\rm M}_{\odot}$ are marked along the axes with the horizontal and vertical lines. Right panel: the filled symbols represent the mergers' total mass, $m_{\rm tot}$, along the X-axis versus the mergers' mass ratio, $q\equiv{m}_2/{m}_1\leq1$, along the Y-axis. The meaning of the different symbols and the colour-coding is the same as in the left panel. See text for further details.
• Figure 5: Left panel: the filled symbols mark the delay times, $t_{\rm mrg}$ (X-axis), of all compact binary mergers from the model-cluster grid versus their corresponding total mass, $m_{\rm tot}$ (Y-axis). The data points are colour-coded according to the mergers' respective inspiral time until merger, $\tau_{\rm insp}$, since their decoupling from the parent cluster (colour bar). For convenient visibility, $\tau_{\rm insp}$ values below $\lesssim 1$ year share the same colour. The meaning of the different symbols is the same as in Fig. \ref{['fig:m1m2']}. Right panel: distribution (probability density function) of $t_{\rm mrg}$ shown for the in-cluster and ejected mergers separately (filled histograms), as well as for the combined merger population (empty histogram). The combined distribution is normalised to be integrated up to unity. The integrals of the in-cluster- and ejected-merger distributions are scaled according to the respective sub-population's count relative to the total merger count (so that the distributions add up to the normalised combined distribution).