Null geodesics and shadows of slowly rotating wormholes immersed in dark matter halos

We study slowly rotating traversable wormholes embedded in realistic galactic dark matter halos, including Navarro-Frenk-White (NFW), Bose-Einstein Condensate (Thomas-Fermi, TF), and pseudo-isothermal (PI) profiles. Using the Teo-type rotating wormhole metric, we construct shape functions from halo density distributions and analyze the resulting geometrical properties, such as throat structure, flaring-out conditions, and violations of the null energy condition. We examine null geodesics, effective potentials, photon spheres, and Lense-Thirring (LT) precession, highlighting differences between cuspy and cored halo models. Finally, we calculate wormhole shadows, observing that cuspy NFW halos tend to produce smaller, asymmetric shadows, while cored TF and PI halos yield smoother, nearly circular silhouettes. The findings provide a theoretical characterization of photon dynamics and shadow morphology in wormholes embedded within different dark matter environments.