Higher-order inner photon rings of a horizonless ultracompact object with an antiphoton sphere and their interferometric pattern

Abstract: A horizonless ultracompact object can have a stable antiphoton sphere, which causes the strong deflection of photons inside the unstable photon sphere, leading to the formation of distinctive inner photon rings. In this work, we present analytical descriptions for the shape, thickness and interference pattern of higher-order inner photon rings. By taking the static spherically symmetric Schwarzschild star with a photon sphere as an example, we find that its inner photon rings can be more non-circular and thicker than the outer ones, and show that the inclusion of the inner photon rings can give rise to new features in the interferometric pattern. Our formulae can also be applied to other ultracompact objects, providing a convenient way to study the observational properties of their higher-order photon rings.