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Inspired by the observations of supermassive black hole M87* in \emph{EventHorizon Telescope }(EHT) experiment, a remarkable surge in black hole physicsis to use the black hole shadow's observables to distinguish general relativity(GR) and modified theories of gravity (MoG), which could also help to disclosethe astrophysical nature of the center black hole in EHT observation. In thispaper, we shall extensively carry out the study of a charged rotating blackhole in conformal gravity, in which the term related with the charge hasdifferent falloffs from the usual Kerr-Newman (KN) black hole. We investigatethe spacetime properties including the horizons, ergospheres and the photonregions; afterward, we show the boundary of black hole shadow and investigateits characterized observables. The features closely depend on the spin andcharge parameters, which are compared with those in Kerr and KN black holes.Then presupposing the M87* a charged rotating black hole in conformal gravity,we also constrain the black hole parameters via the observation constraintsfrom EHT experiment. We find that the constraints on the inferred circularitydeviation, $\Delta C \lesssim 0.1$, and on the shadow axial ratio, $1< D_x\lesssim 4/3$, for the M87* black hole are satisfied for the entire parameterspace of the charged rotating black hole in conformal gravity. However, theshadow angular diameter $\theta_d = 42 \pm 3 \mu as$ will give upper bound onthe parameter space. Our findings indicate that the current charged rotatingblack hole in conformal gravity could be a candidate for astrophysical blackholes. Moreover, the EHT observation on the axial ratio $D_x$ may help us todistinguish Kerr black hole and the current charged rotating black hole inconformal gravity in some parameter space.

Photon regions, shadow observables and constraints from M87* of a charged rotating black hole