| Abstract: In dense astrophysical environments, the remnant of a compact binary merger can pair with another compact object and undergo a subsequent merger. Such hierarchical mergers are intriguing astrophysical phenomena that can be probed using gravitational-wave observations, providing insight into their merger histories. If the primary component of a binary population is produced as a consequence of a previous merger, then the source properties of such systems are correlated with those of the parent binaries. These correlations can be modelled using numerical relativity–based fitting formulae that map the properties of a compact binary to the parameters of the merger remnant. We consider the merger rates of two compact-binary populations, where the primary component of one population is the product of a previous merger. We develop a Bayesian framework that relates these two populations by explicitly modelling the redshift evolution of the parent binary merger rate, the time-delay distribution between successive mergers, and the probability that a merger remnant from a previous generation subsequently pairs with another compact object. Without the need to model complex astrophysical processes, this framework enables direct inference of population-level properties of compact binary mergers.We apply this method to potential hierarchical merger candidates GW190425 and GW230529. Using current observational constraints on the local merger rates of the relevant populations from LIGO, we show that meaningful constraints can be obtained on the redshift evolution and the time-delay distribution, while highlighting that existing degeneracies can be broken with improved merger-rate measurements. Finally, we demonstrate that the advent of next-generation detectors and future observing runs, which are expected to place much tighter constraints on the merger rates of different compact-binary populations, will significantly enhance our ability to probe hierarchical merger histories.
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