Researchers have explored how the presence of a Hernquist-type dark matter halo affects the optical properties of a rotating Kerr black hole. The study focused on the spacetime geometry generated by this configuration, deriving the null geodesic equations and effective potentials. This approach allowed for the analysis of three-dimensional photon trajectories around the event horizon and ergoregion, as well as the calculation of critical impact parameters for unstable spherical photon orbits.

The team constructed the black hole shadow contours for a distant observer, finding that the rotation parameter primarily shifts and distorts the shadow. However, the presence of the Hernquist dark matter halo significantly increases the photon capture region and, consequently, the apparent size of the shadow. By comparing the area-equivalent shadow diameter with Event Horizon Telescope (EHT) measurements for Sgr A* and M87*, they were able to establish constraints on the dimensionless halo parameter, $\hat{\rho}=M^2\rho$. The strongest restrictions come from Sgr A*, with values of $\hat{\rho}\sim(2.7-3.8)\times10^{-3}$ at $1\sigma$ and $\hat{\rho}\sim(4.1-5.2)\times10^{-3}$ at $2\sigma$.

In addition to the shadow analysis, the study examined gravitational lensing in both the strong-field and weak-field regimes. In the strong-field regime, the halo shifts the unstable photon orbit and critical impact parameter, influencing the logarithmic deflection angle and the position of relativistic images. In the weak-field regime, the halo contributes to the leading bending angle and amplifies deviations from the Kerr metric as $\rho$ increases. Using the Einstein ring of ESO325-G004, further constraints were obtained for the parameter $\hat{\rho}$: $0\leq\hat{\rho}\lesssim0.00939$ at $1\sigma$ and $0\leq\hat{\rho}\lesssim0.01963$ at $2\sigma$.