Escape speed of stellar clusters from multiple-generation black-hole mergers in the upper mass gap

Understand

Pair instabilities in supernovae might prevent the formation of black holes with masses between $\sim 50 M_\odot$ and $\sim 130 M_\odot$.

• Multiple generations of black-hole mergers provide a possible way to populate this "mass gap" from below.
• However this requires an astrophysical environment with a sufficiently large escape speed to retain merger remnants, and prevent them from being ejected by gravitational-wave recoils.
• We show that, if the mass gap is indeed populated by multiple mergers, the observation of a single black-hole binary component in the mass gap implies that its progenitors grew in an environment with escape speed $v_{\rm esc} \gtrsim 50$ km/s.