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Using ground-based gravitational-wave detectors, we probe the mass functionof intermediate-mass black holes (IMBHs) wherein we also include BHs in theupper mass gap $\sim 60-130~M_\odot$. Employing the projected sensitivity ofthe upcoming LIGO and Virgo fourth observing (O4) run, we perform Bayesiananalysis on quasi-circular non-precessing, spinning IMBH binaries (IMBHBs) withtotal masses $50\mbox{--} 500\, M_\odot$, mass ratios 1.25, 4, and 10, anddimensionless spins up to 0.95, and estimate the precision with which thesource-frame parameters can be measured. We find that, at $2\sigma$, the massof the heavier component of IMBHBs can be constrained with an uncertainty of$\sim 10-40\%$ at a signal-to-noise ratio of $20$. Focusing on the stellar-massgap with new tabulations of the $^{12}\text{C}(\alpha, \gamma)^{16} \text{O}$reaction rate and its uncertanties, we evolve massive helium core stars using\MESA\, to establish the lower and upper edge of the mass gap as$\simeq$\,59$^{+34}_{-13}$\,$M_{\odot}$ and$\simeq$\,139$^{+30}_{-14}$\,$M_{\odot}$ respectively, where the error barsgive the mass range that follows from the $\pm 3\sigma$ uncertainty in the$^{12}\text{C}(\alpha, \gamma) ^{16} \text{O}$ nuclear reaction rate. We findthat high resolution of the tabulated reaction rate and fine temporalresolution are necessary to resolve the peak of the BH mass spectrum. We thenstudy IMBHBs with components lying in the mass gap and show that the O4 runwill be able to robustly identify most such systems. Finally, we re-analyseGW190521 with a state-of-the-art aligned-spin waveform model, finding that theprimary mass lies in the mass gap with 90\% credibility.

Observing intermediate-mass black holes and the upper--stellar-mass gap with LIGO and Virgo