Breaking the Degeneracy: Spectral Hardening of Accretion Disks around Rotating Hayward Black Holes in Dark Matter Halos

Abstract

We investigate the thermodynamic and observable signatures of thin accretion disks surrounding rotating, regular Hayward black holes embedded within a macroscopic dark matter (DM) envelope. The spacetime is rigorously modelled as a three-region composite: an inner Hayward core regularised by a de~Sitter limit, an intermediate DM shell modelled as a pressureless dust envelope governed by an exponential sphere density profile, and an asymptotically flat outer vacuum. By matching these regions via the mass profile, we compute the explicit modifications to the Innermost Stable Circular Orbit (ISCO), radiative efficiency, local thermal flux, and multi-colour blackbody spectral luminosity. A systematic comparison across four distinct configurations (Kerr vacuum, Hayward vacuum, Kerr\,+\,DM, and Hayward\,+\,DM) reveals a strict hierarchical compression of the ISCO. We demonstrate that the quantum-inspired core regularity and the macroscopic DM halo exert an additive enhancement on the radiative efficiency, reaching $\sim 14.4\%$ for highly spinning black holes ($j=0.8$). However, this additive behaviour introduces a profound macroscopic degeneracy between purely geometric (Hayward vacuum) and purely astrophysical (Kerr\,+\,DM) configurations at low-to-intermediate frequencies. We establish that this degeneracy is structurally broken only in the extreme Wien tail of the multi-wavelength spectrum, providing a critical diagnostic footprint for future high-frequency spectropolarimetry to distinguish non-singular black holes from classical dark matter environments.