Star clusters as factories of gravitational wave sources

Over the past few years, the groundbreaking detections of gravitational wave signals from merging binary black holes and neutron stars by LIGO/Virgo have opened a new window to the cosmos. A key question regarding these gravitational wave sources is the nature of their origin. Dynamical formation in dense environments like globular clusters has emerged as an important formation channel, corroborated by recent numerical simulations and observational indications suggesting that globular clusters contain dynamically significant populations of BHs throughout their lifetimes. In the coming years, the field of gravitational wave astronomy will blossom further with the growing catalog of new detections by LIGO/Virgo and the dawn of multiband gravitational wave astronomy coinciding with upcoming detectors such as LISA. A primary component of my work is studying the role of dense stellar clusters in the formation of gravitational wave sources.

A key consequence of the presence of black holes in globular clusters is the dynamical formation, and ultimate merger, of binary black holes. In connection with the latest catalog of GW detections (Abbott et al. 2021), recent from by myself and collaborators (e.g., Rodriguez et al. 2021) suggests that dense star clusters may in principle constitute a significant fraction of the overall binary black hole merger rate in the local universe (see top panel of Figure 1). Furthermore, binary black holes formed in dense star clusters, may have fundamentally different properties than those formed through isolated stellar evolution. In particular, dynamical interactions may uniquely facilitate the formation of massive binary black hole (e.g., Kremer et al. 2020b), plausibly explaining peculiarly massive binary black hole merger detections like GW190521 (see bottom panel of Figure 1; Abbott et al. 2020).

Dense star clusters provide several avenues through which massive black holes may form. If the gravitational wave recoil velocities of binary black hole mergers in a cluster are less than their host cluster's escape speed, the newly-formed black holes will be retained by the cluster, creating a new generation of black holes that may merge a second time (Rodriguez et al. 2019). Additionally, heavy black holes in, or beyond, the upper mass gap may also arise from the collapse of anomalously massive progenitor stars (e.g., Kremer et al. 2020b) . These can form via massive stellar collisions, which occur frequently at early times in dense clusters (e.g., Portegies Zwart et al. 2004). If stellar mergers occur in a runaway scenario, even more massive black holes may form, potentially connecting to the elusive intermediate-mass black holes with masses more than 100 Msun (e.g., Greene et al. 2020). 

Figure 1: Top panel: Adapted from Rodriguez et al. 2021. Volumetric merger rate for binary black holes formed in stellar clusters for a range of cluster virial radii (black curves). Blue bands show the phenomenological merger rate fit (median, 50%, and 90%) from the LIGO/Virgo GWTC-2 catalog (Abbott et al. 2020). 
Bottom panel: Primary mass distribution for black hole mergers from Kremer et al. 2020a (here combining all virial radii; black) compared to analogous distribution from LIGO/Virgo using their ``Power Law + Peak'' model (green). The gray background shows the (uncertain) theoretical boundary of the pair-instability mass gap. Critically, dynamics within globular clusters enable formation of black holes within the mass gap (as discussed in text), consistent with gravitational wave detections.

Additionally, my recent work has shown that the upcoming GW observatory LISA will observe dozens to hundreds of gravitational wave sources formed dynamically in clusters at mHz frequencies. In Kremer et al. 2018c , we showed that dynamically-formed compact binaries of various types (including white dwarf and neutron star binaries) may be resolved by LISA in the Milky Way globular clusters. In Kremer et al. 2019b, we went on to show that additional globular cluster binary black hole will be resolved by LISA as extragalactic sources (see Figure 2). Furthermore, I showed that roughly 30% of these resolvable binary black holes will have measurable eccentricities in the LISA band. This is in contrast to gravitational wave sources formed through isolated binary evolution, which are expected to be indistinguishable from circular (e.g., Postnov et al. 2014) . Thus, LISA may be able to use eccentricity to distinguish between sources that form in clusters from those that form through isolated binary evolution.

Figure 2: Adapted from Kremer et al. 2019b. Evolutionary tracks for a representative population of binary black hole mergers formed in clusters in strain--frequency space from formation to merger (assuming distance of 250 Mpc). Shown for reference are the sensitivity curves for the LISA, DECIGO, and LIGO detectors.