Optical properties of black holes immersed in Galactic Dark Matter Halo

Abstract

We present a comprehensive investigation into the optical and topological properties of black holes (BHs) immersed in a Galactic Dark Matter Halo (GDMH). Our analysis focuses on shadow morphology, photon ring luminosity, and thermodynamic classification, using spherically symmetric accretion models in both static and infalling frameworks. In both scenarios, we observe that the shadow radius decreases monotonically with increasing halo parameter ($a$), reflecting the influence of dark matter on photon trajectories. Within the static accretion model, the brightness of the photon ring intensifies significantly with increasing $a$, more prominently than with variations in the asymptotic circular velocity ($V_c$). BHs surrounded by radially infalling accretion flows exhibit darker shadows compared to those with static flows, a consequence of relativistic Doppler dimming; however, the shadow size remains invariant, reaffirming its geometric origin. We further analyze the visual manifestation and observational significance of these luminous features, including shadow contours and intensity profiles. Finally, using the generalized off-shell Helmholtz free energy framework, we classify the BH in GDMH as belonging to the $W^{1-}$ topological class, indicating a thermodynamically unstable configuration with a single negative winding number.