The optical appearance of a nonsingular de Sitter core black hole geometry under several thin disk emissions

Abstract: We consider the optical appearance under a thin accretion disk of a regular black hole with a central de Sitter core implementing $\mathcal{O}(l^2/r^2)$ far-corrections to the Schwarzschild black hole. We use the choice $l=0.25M$, which satisfies recently found constraints from the motion of the S2 star around Sgr A$^*$ in this model, and which leads to thermodynamically stable black holes. As the emission model, we suitably adapt ten samples of the Standard Unbound emission profile for a monochromatic intensity in the disk's frame, which have been previously employed in the literature within the context of reproducing General Relativistic Magneto-Hydrodynamic simulations of the accretion flow. We find the usual central brightness depression surrounded by the bright ring cast by the disk's direct emission as well as two non-negligible photon ring contributions. As compared to the usual Schwarzschild solution, the relative luminosities of the latter are significantly boosted, while the size of the former is strongly decreased. We discuss the entanglement of the background geometry and the choice of emission model in generating these black hole images, as well as the capability of these modifications of Schwarzschild solution to pass present and future tests based on their optical appearance when illuminated by an accretion disk.