Yang and X.-X

This paper investigates the optical images of neutron stars within the framework of the radiatively inefficient accretion flow model, taking into account a polytropic equation of state. After obtaining the numerical solutions of the neutron star, we solved numerically the geodesic equations together with the radiative transfer equation. We mainly examine the effects of the polytropic index $N$ and the observer inclination angle $\theta_o$ on the image morphology. The obtained images are also compared with the shadow of a Schwarzschild black hole. It is shown that, under the assumption that photon trajectories are terminated at the neutron star surface, the image exhibits a bright higher order structure surrounding an inner dark region. As $N$ increases, the size of the higher-order image gradually expands. As $\theta_o$ increases, the obscuration of the neutron star silhouette by radiation originating outside the equatorial plane becomes more pronounced. Compared with the black hole shadow obtained under the same parameter configuration, the neutron star exhibits a larger higher order image and a more extended obscured inner dark region, whereas the higher order image of the black hole is more readily distinguishable. These results indicate significant differences in the optical appearance of neutron stars and black holes, and thus provide a theoretical basis for distinguishing between them through high resolution imaging.