Strong-field signatures of a regular black hole in an Einasto dark matter halo

Abstract: We investigate the strong-field phenomenology of a static and spherically symmetric regular black hole supported by an Einasto dark matter (DM) distribution. For the exponential Einasto profile, the geometry is controlled by a single dimensionless halo parameter $a$, and we restrict the analysis to the black hole branch $0<a\leq a_{\rm crit}\simeq0.388$. We study both timelike and null geodesics, including the effective potential, circular orbits, ISCO radius, orbital period, periapsis advance, photon sphere, shadow radius, effective photon force, and representative photon trajectories. We also construct image-plane intensity profiles and face-on thin-disk images in a static-emitter approximation. The analysis reveals a hierarchy of strong-field sensitivity. Timelike observables remain largely degenerate with the Schwarzschild limit along most of the black hole branch, while the photon sphere scale, shadow diameter, and residual optical structures provide the most sensitive response to the Einasto halo near the critical black hole regime. A comparison with the EHT shadow-scale measurements shows that the full branch is consistent with Sgr A* at the $1σ$ level, whereas M87* mildly disfavors values very close to criticality. These results indicate that the most promising signatures of the Einasto halo are not expected from ordinary timelike orbital quantities, but from near-critical photon propagation and its imprint on the optical appearance.