Investigating the mixing between two black hole populations in LIGO-Virgo-KAGRA GWTC-3

We introduce a population model to analyze the mixing between hypothesised power-law and $\ensuremath{\sim}35{M}_{\ensuremath{\bigodot}}$ Gaussian-bump black hole populations in the latest gravitational wave catalog, GWTC-3, estimating their colocation and separation. We find a relatively low level of mixing, ${3.1}_{\ensuremath{-}3.1}^{+5.0}%$, between the power-law and Gaussian populations, compared to the percentage of mergers containing two Gaussian-bump black holes, ${5.0}_{\ensuremath{-}1.7}^{+3.2}%$. Our analysis indicates that black holes within the Gaussian bump are generally separate from the power-law population, with only a minor fraction engaging in mixing and contributing to the $\mathcal{M}\ensuremath{\sim}14{M}_{\ensuremath{\bigodot}}$ peak in the chirp mass. This leads us to identify a distinct population of binary Gaussian black holes (BGBHs) that arise from mergers within the Gaussian bump. We suggest that current theories for the formation of the massive $35{M}_{\ensuremath{\bigodot}}$ Gaussian-bump population may need to reevaluate the underlying mechanisms that drive the preference for BGBHs.