Second-Generation Mass Peak in the Gravitational-Wave Population as a Probe of Globular Clusters

Gravitational-wave observations have revealed an excess of binary black hole mergers with primary masses near $\sim 35M_{\odot }$. We show that if this feature originates from dynamical formation in dense stellar systems, and if the pair-instability supernova truncates the first-generation black hole mass spectrum, then second-generation mergers inevitably produce a second peak near $\sim 70M_{\odot }$. This structure reflects the suppression of first-generation black holes above a characteristic mass and the accumulation of merger remnants near twice that scale. Its location is robust, whereas its amplitude depends strongly on cluster initial conditions. Using a large suite of cluster population-synthesis models, we show that current gravitational-wave data already constrain the birth properties of globular clusters, irrespective of their overall contribution to the observed population. If clusters dominate mergers above the pair-instability scale, these constraints tighten further and imply a minimum first-generation merger rate of $\mathcal{R}(m_1\le 50M_{\odot })\ge 0.099{\mathrm{G}\mathrm{p}\mathrm{c}}^{-3}{\mathrm{y}\mathrm{r}}^{-1}$ ($99\mathrm{\%}$ confidence). We further show that a drop or gap in the secondary black hole mass spectrum is not a robust signature of a cluster origin for high-mass mergers within the pair-instability mass gap. A confirmed excess near $\sim 70M_{\odot }$ would support a dynamical origin of the $\sim 35M_{\odot }$ feature and provide independent evidence for a pair-instability mass gap with a lower edge at $\lesssim 50M_{\odot }$.