Observational Signatures of Accretion Disks around a Schwarzschild Black Hole in a Hernquist Dark Matter Halo

Abstract: We investigate how a Hernquist type dark matter (DM) halo, parametrized by its core radius $r_{s}$ and central density $ρ{s}$, influences both the gravitational wave (GW) emission from timelike periodic orbits and the electromagnetic appearance of a thin accretion disk around a Schwarzschild black hole (BH). By analyzing the effective potential for timelike geodesics, we show that the DM halo shifts the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO) outward, reflecting its modification of the spacetime geometry and the energy-angular momentum structure of particle motion. Employing a semi-analytical method, we compute orbital trajectories and the associated GW waveforms, revealing that the DM halo alters the characteristic zoom-whirl dynamics and induces measurable changes in waveform morphology. Furthermore, we generate direct and secondary images of the accretion disk across various observer inclinations and find that increasing $r{s}$ or $ρ_{s}$ results in cooler, dimmer disks with modified flux distributions. Our results demonstrate that the presence of a DM halo imprints distinct signatures in both gravitational and electromagnetic observables, offering a multimessenger pathway to probe DM environments near BHs.