Regular black hole sourced by the Dehnen-type distribution of matter: The sound of the event horizon

Abstract: We compute the fundamental and overtone quasinormal modes of a regular, asymptotically flat black hole supported by a Dehnen-type matter halo. Gravitational perturbations in this background split into two distinct axial sectors, and our analysis confirms that the presence of the halo parameter $a$ breaks the isospectrality that holds in vacuum. The dependence of the quasinormal spectrum on $a$ is moderate for the fundamental modes and even weaker for the overtones, which approach one another in the complex-frequency plane as the halo parameter increases. No enhancement or rapid growth of overtone amplitudes is observed, indicating that the halo does not induce the type of strong near-horizon effects characteristic of quantum-corrected or exotic compact objects. Overall, our results show that the dark-matter halo introduces controlled and comparatively mild modifications to the ringdown spectrum while preserving its qualitative structure.