Observational properties of relativistic fluid spheres with thin accretion disks

In this work we analyze the observational properties of incompressible relativistic fluid spheres with and without thin-shells, when surrounded by thin accretion disks. We consider a set of six configurations with different combinations of the star radius $R$ and the thin-shell radius $r_\Sigma$ to produce solutions with neither thin-shells nor light-rings, with either of those features, and with both. Furthermore, we consider three different models for the intensity profile of the accretion disk, based on the Gralla-Lupsasca-Marrone (GLM) disk model, for which the peaks of intensity occur at the Innermost Stable Circular Orbit (ISCO), the Light-Ring (LR), and the center of the star. The observed images and intensity profiles for an asymptotic observer are produced using a Mathematica-based ray-tracing code. Our results indicate that, in the absence of a light-ring, the presence of a thin-shell produces a negligible effect in the observational properties of the stars. However, when the spacetime features a light-ring, the portion of the mass of the star that is stored in the thin-shell has a strong effect on its observational properties, particularly in the magnitude of the central gravitational redshift effect responsible for causing a central shadow-like dimming in the observed images. A comparison with the Schwarzschild spacetime is also provided and the most compact configurations are shown to produce observational imprints similar to those of black-hole solutions, with subtle qualitative differences, most notably extra secondary image components that decrease the radius of the shadow and are potentially observable.