  Context. The Event Horizon Telescope (EHT) collaboration recently obtained
first images of the surroundings of the supermassive compact object M87* at the
center of the galaxy M87. Aims. We want to develop a simple analytic disk model
for the accretion flow of M87*. Compared to general-relativistic
magnetohydrodynamic (GRMHD) models, it has the advantage of being independent
of the turbulent character of the flow, and controlled by only few
easy-to-interpret, physically meaningful parameters. We want to use this model
to predict the image of M87* assuming that it is either a Kerr black hole, or
an alternative compact object. Methods. We compute the synchrotron emission
from the disk model and propagate the resulting light rays to the far-away
observer by means of relativistic ray tracing. Such computations are performed
assuming different spacetimes (Kerr, Minkowski, non-rotating ultracompact star,
rotating boson star or Lamy spinning wormhole). We perform numerical fits of
these models to the EHT data. Results. We discuss the highly-lensed features of
Kerr images and show that they are intrinsically linked to the accretion-flow
properties, and not only to gravitation. This fact is illustrated by the notion
of secondary ring that we introduce. Our model of spinning Kerr black hole
predicts mass and orientation consistent with the EHT interpretation. The
non-Kerr images result in similar quality of the numerical fits and may appear
very similar to Kerr images, once blurred to the EHT resolution. This implies
that a strong test of the Kerr spacetime may be out of reach with the current
data. We notice that future developments of the EHT could alter this situation.
Conclusions. Our results show the importance of studying alternatives to the
Kerr spacetime in order to be able to test the Kerr paradigm unambiguously.
