Zhen Li
Context. It is widely believed that Sgr A* , located at the center of the Milky Way, is a supermassive black hole. Recent observations of its shadow by the Event Horizon Telescope and long-term monitoring of the S2 star orbit have provided strong evidence supporting this interpretation. These observational developments also open new possibilities for probing the physical properties of the central black hole and its surrounding environment. Since a dark matter halo is expected to exist in the Galactic center region, studying the black hole embedded within it offers a promising way to simultaneously investigate both black hole physics and the dark matter distribution. Aims. We aim to investigate how a surrounding dark matter halo affects the space-time structure around the Galactic center black hole and explore the resulting observational signatures in the black hole shadow and stellar orbital motion. Methods. We constructed a black hole metric incorporating a generalized double power-law dark matter halo profile. Based on this space-time, we analyzed the corresponding null- and time-like geodesics to study the influence of halo parameters on the shadow of the black hole and on the orbital dynamics of the S2 star. We further constrain the halo parameters by comparing the theoretical predictions with available observational data of the shadow and S2 orbit. Results. We find that the dark matter halo modifies both the size and shape of the black hole shadow and produces measurable effects on the orbital motion of the S2 star. By confronting our model with observational constraints, we derive bounds on the parameters of the generalized double power-law halo profile. Conclusions. Our results provide theoretical and phenomenological insights into the interplay between the Galactic center black hole and the surrounding dark matter halo and offer potential constraints on the dark matter distribution in the central region of the Milky Way.