Shadows from thin accretion disks of parametrized black hole solutions

We discuss the optical appearance from thin accretion disks in parametrized black holes, namely, solutions characterized by an arbitrarily large number of parameters without any regards to the theory of the gravitational and matter fields they come from. More precisely, we consider the leading-order terms of the spherically symmetric Johanssen-Psaltis (JP) and Konoplya-Rezzolla-Zhidenko (KRZ) parametrizations after imposing constraints from asymptotic flatness and solar system observations. Furthermore, we use the inferred correlation, by the Event Horizon Telescope Collaboration, between the size of the bright ring (which is directly observable) and the size of the central brightness depression (which is not) of M87 and Sgr ${\mathrm{A}}^{*}$ central supermassive objects, to constrain the parameters of the leading-order JP and KRZ solutions. Using ten samples of the Standard Unbound distribution previously employed in the literature to reproduce certain scenarios of General Relativistic HydroDynamical simulations, we produce images of four samples of JP and KRZ geometries enhancing and diminishing the shadow's size, respectively. Via a qualitative and quantitative analysis of the features of the corresponding photon rings and, in particular, of their relative brightness, we argue that it should be possible to distinguish between such parametrized solutions and the Schwarzschild geometry via future upgrades of very long baseline interferometry. We furthermore consider images of some naked objects within these parametrizations, and also discuss the role of inclination in comparing images of different black holes.