Ultra-compact objects describe horizonless solutions of the Einstein field equations which, like black-hole spacetimes, possess null circular geodesics (closed light rings). We study { \it analytically} the physical properties of spherically symmetric ultra-compact isotropic fluid spheres with a polytropic equation of state. It is shown that these spatially regular horizonless spacetimes are generally characterized by two light rings $\{ r^{ \text{ inner}}_{ \gamma},r^{ \text{ outer}}_{ \gamma}\}$ with the property ${ \cal C}(r^{ \text{ inner}}_{ \gamma})\leq{ \cal C}(r^{ \text{ outer}}_{ \gamma})$, where ${ \cal C}\equiv m(r)/r$ is the dimensionless compactness parameter of the self-gravitating matter configurations. In particular, we prove that, while black-hole spacetimes are characterized by the lower bound ${ \cal C}(r^{ \text{ inner}}_{ \gamma})\geq1/3$, horizonless ultra-compact objects may be characterized by the opposite dimensionless relation ${ \cal C}(r^{ \text{ inner}}_{ \gamma})\leq1/4$. Our results provide a simple analytical explanation for the interesting numerical results that have recently presented by Novotn\'y, Hlad\'ik, and Stuchl\'ik [Phys. Rev. D 95, 043009 (2017)].
Categories: gr-qc astro-ph.HE hep-th