Double black hole mergers in nuclear star clusters: eccentricities, spins, masses, and the growth of massive seeds (2308.10884v2)

Abstract: We investigate the formation of intermediate mass black holes (IMBHs) through hierarchical mergers of stellar origin black holes (BHs), as well as BH mergers formed dynamically in nuclear star clusters. Using a semi-analytical approach which incorporates probabilistic mass-function-dependent double BH (DBH) pairing, binary-single encounters, and a mass-ratio-dependent prescription for energy dissipation in hardening binaries, we find that IMBHs with masses of $O(10^2)$-$O(10^4)\rm M_\odot$ can be formed solely through hierarchical mergers in timescales of a few $100$ Myrs to a few Gyrs. Clusters with escape velocities $\gtrsim400$ km s$^{-1}$ inevitably form high-mass IMBHs. The spin distribution of IMBHs with masses $\gtrsim 10^3$ M$\odot$ is strongly clustered at $\chi\sim 0.15$; while for lower masses, it peaks at $\chi\sim 0.7$. Eccentric mergers are more frequent for equal-mass binaries containing first-and/or second-generation BHs. Metal-rich, young, dense clusters can produce up to $20\%$ of their DBH mergers with eccentricity $\geq0.1$ at $10\,\rm Hz$, and $\sim2$-$9\%$ of all in-cluster mergers can form at $>10$ Hz. Nuclear star clusters are therefore promising environments for the formation of highly-eccentric DBH mergers, detectable with current gravitational-wave detectors. Clusters of extreme mass ($\sim10^8$ M$\odot$) and density ($\sim10^8$ M$\odot$pc$^{-3}$) can have about half of all of their DBH mergers with primary masses $\geq100$ M$\odot$. The fraction of in-cluster mergers increases rapidly with increasing cluster escape velocity, being nearly unity for $v_{\rm esc}\gtrsim 200$ km s$^{-1}$. Cosmological merger rate of DBHs from nuclear clusters varies $\lessapprox0.01-1$ Gpc$^{-3}$yr$^{-1}$.