Observational properties of hot-spots orbiting relativistic fluid spheres

TL;DR

This paper investigates the observational signatures of hot spots orbiting relativistic fluid stars across different compactness regimes, revealing similarities to black holes and other exotic objects, and highlighting potential observational distinctions.

Contribution

It provides a comprehensive analysis of how relativistic fluid stars' observational properties vary with compactness, including the effects of light-rings and stability, offering alternatives to black hole models.

Findings

Fluid stars at the Buchdahl limit mimic Schwarzschild black hole observations.

Dilute configurations show properties similar to bosonic stars.

Presence of light-rings leads to secondary images and distinguishable signatures.

Abstract

In this work we analyze the observational properties of relativistic fluid spheres when orbited by isotropically emitting sources, known as hot spots. We consider fluid star configurations in four different regimes of compacticity, from the Buchdahl limit to non-ultra compact solutions, thus obtaining fluid stars with qualitatively different geodesic structures and observational properties. We show that the observational properties for fluid stars at the Buchdahl limit are qualitatively similar to the ones for the Schwarzschild black hole, whereas for more dilute configurations one can find observational properties similar to other fundamentally different models e.g. bosonic star configurations with and without self interactions. For solutions with a radius in the range $2.25M<R<3M$, where $M$ is the total mass of the fluid star, the presence of a light-ring (LR) pair, which becomes degenerate at $R=3M$, leads to the appearance of additional observational signatures e.g. secondary images and LR contributions, which allow one to distinguish these models from their black-hole counterparts. Fluid star configurations supported by thin shells are also analyzed and it is proven that the stability of the inner LR is increased for these solutions, resulting in a non-differentiable extremum in the effective potential of the photons. Our results suggest that compact fluid star configurations provide a suitable and physically relevant alternative to the black-hole scenario in accordance with the current generation of observational experiments.