Gravitational waves (GWs) have enabled direct detections of compact binary coalescences (CBCs). However, their poor sky localisation and the typical lack of observable electromagnetic (EM) counterparts make it difficult to confidently identify their hosts and study the environments that nurture their evolution. In this work, we show that detailed information of the host environment (e.g., the mass and steepness of the host potential) can be directly inferred by measuring the kinematic parameters (acceleration and its time derivatives) of the binary’s center of mass using GWs alone, without requiring an EM counterpart. We consider CBCs in various realistic environments such as globular clusters, nuclear star clusters, and active galactic nuclei disks to demonstrate how orbit and environment parameters can be extracted for CBCs detectable by ground- and space-based observatories, including the LIGO detector at $\mathrm{A}+$ sensitivity, Einstein Telescope of the XG network, LISA, and DECIGO, on a single-event basis. These constraints on host stellar environments promise to shed light on our understanding of how CBCs form, evolve, and merge.

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• Gravitational waves