Paper detail

Distinguishing Black Holes and Neutron Stars through Optical Images

This paper employs the backward ray tracing method to study the optical images of neutron stars under the conditions of a spherical light source and a thin accretion disk, considering a polynomial equation of state given by $p = K ρ^{1 + 1/n_c}$. By numerically solving the TOV equations, we obtain the interior solutions of neutron stars for different densities. The results indicate that as the polynomial index $n_c$ increases, the mass, radius, and compactness of the neutron star all increase, which has a significant impact on its optical properties. Under the assumption that the light is truncated at the surface of the neutron star, we find that for a spherical light source, an increase in $n_c$ leads to an enlargement of the Einstein ring radius. For a thin accretion disk, the light intensity always reaches its maximum at the surface of the neutron star. The increase in $n_c$ also causes the outline of the neutron star to grow. When the observer inclination angle $θ_o$ changes, the neutron star's outline deforms from a circular shape to a D shape, with the left side being significantly brighter than the right side. In addition, this paper also investigates the distribution characteristics of the redshift factor. At lower observer inclination angles, gravitational redshift dominates, while at higher inclination angles, the Doppler effect induces noticeable blueshift. Compared to the Schwarzschild black hole, the optical appearance of the neutron star shows significant differences. The study provides a theoretical basis for distinguishing neutron stars from black holes using high-resolution imaging and for constraining the equation of state.