Null geodesics and shadows of Dekel-Zhao-type dark matter black holes with a quintessential field: Constraints from EHT observations of M87* and Sgr A*

One compelling way to probe dark matter is by looking for its gravitational effects on black holes. Inspired by the study of Cardoso et al. (Phys. Rev. D 105, 6, L061501 (2022)) on black holes in galaxies, this work investigates static, spherically symmetric black holes surrounded by Dekel-Zhao-type dark matter halos and influenced by a quintessential field. By adopting a double power-law profile, we derive explicit expressions for the cumulative mass, tangential velocity, and the modified metric, providing a coherent description of the horizon structure and thermodynamic properties. Depending on the core density, the spacetime may feature multiple horizons or even a naked singularity. Our analysis of null geodesics reveals that both dark matter and quintessence significantly affect photon trajectories and the resulting black hole shadow. By combining theoretical modeling with EHT observations of Sgr A${}^{*}$ and M87${}^{*}$, we place constraints on the halo density and quintessence parameter, directly connecting them to observable features. However, a stability analysis of circular photon orbits confirms that the photon sphere is inherently unstable, with its location and sensitivity strongly influenced by the surrounding matter. Finally, we analyze how the impact parameter $\tilde{b}$ shapes photon trajectories around a black hole, determining the bending of null geodesics, the photon sphere location, and the event horizon structure, thereby illustrating the influence of spacetime geometry on light paths. This work highlights the intricate interplay between dark matter, quintessence, and black hole observables, bridging theoretical predictions with astrophysical measurements.