Capture-driven growth model predicts M ≈ 10^5 M_⊙ × (σ/50 km s^{-1})^{2.5}, requiring the M-σ relation to flatten to 2.26 < β < 2.5 below 10^5 M_⊙.
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N-body simulations demonstrate runaway GW BBH mergers in dense BH clusters (≥5×10^9 M⊙/pc³) produce ~10³ M⊙ IMBHs within 10 Myr.
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The $M$-$\sigma$ Relation Has to Break
Capture-driven growth model predicts M ≈ 10^5 M_⊙ × (σ/50 km s^{-1})^{2.5}, requiring the M-σ relation to flatten to 2.26 < β < 2.5 below 10^5 M_⊙.
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Rapid intermediate-mass black hole formation via runaway mergers of black holes
N-body simulations demonstrate runaway GW BBH mergers in dense BH clusters (≥5×10^9 M⊙/pc³) produce ~10³ M⊙ IMBHs within 10 Myr.