Strong gravitational lensing by SMBHs in Hernquist dark matter halos: Implications from EHT observations

We examine strong gravitational lensing signatures of supermassive black holes (SMBHs) embedded in Hernquist-type dark matter halos, comparing theoretical predictions with Event Horizon Telescope (EHT) observations of M87^⁎ and Sgr A^⁎. Our analysis demonstrates that a Hernquist halo with ${\rho }_s=1.4M^{-2}$ and $r_s=0.5M$ increases the photon sphere radius by 20.3% (from 3M to 3.61M) and critical impact parameter from 5.196M to 10.471M, while modifying strong deflection coefficients to $\overline{a}=1.02629$ and $\overline{b}=-1.32863$ (vs. Schwarzschild values 1 and −1.34983). EHT data constrain the central density to ${\rho }_s=2.37\pm 0.30M^{-2}$ ($5.2\pm 0.7\times {10}^{-3}{M}_{\odot }/{\text{pc}}^3$) and scale radius to $r_s={0.53}_{-0.09}^{+0.12}M$ (3.25–4.25 pc) for M87^⁎, and ${\rho }_s=2.08\pm 0.18M^{-2}$ ($0.18\pm 0.02M_{\odot }/{\text{pc}}^3$) with $r_s={0.48}_{-0.11}^{+0.15}M$ (0.019–0.025 pc) for Sgr A^⁎, excluding ${\rho }_s>2.97M^{-2}$ (M87^⁎) and $>2.44M^{-2}$ (Sgr A^⁎) at 95% CL. Characteristic signatures include 12.8–18.3% larger Einstein rings, 9.6–13.0% reduced time delays, and shifted magnification ratios ($r_{mag}=6.64$–6.65 vs. 6.82). These results establish strong lensing as a powerful probe of galactic dark matter, with future EHT observations capable of detecting halos down to ${\rho }_s\approx 1.2M^{-2}$.