Chaotic shadow of a non-Kerr rotating compact object with quadrupole mass moment

We have studied numerically the shadows of a non-Kerr rotating compact object with a quadrupole mass moment, which belongs to the Manko-Novikov family. The nonintegrable photon motion caused by a quadrupole mass moment sharply affects the shadow of the compact object. As the deviation parameter related to the quadrupole mass moment is negative, the shadow of the compact object is prolate, and there are two disconnected main shadows with eyebrows located symmetrically on both sides of the equatorial plane. As the deviation parameter is positive, the shadow becomes oblate, and the main shadow is joined together in the equatorial plane. Moreover, in these positive cases, there is a disorder region in the left of the shadow that increases with the quadrupole-deviation parameter. Interestingly, we also find that the Einstein ring is broken as the deviation from the Kerr metric is larger than a certain critical value. This critical value decreases with the rotation parameter of the black hole. Especially, the observer on the direction of the rotation axis will find some concentric bright rings in the black disk. Finally, supposing that the gravitational field of the supermassive central object of the galaxy is described by this metric, we estimate the numerical values of the observables for the black hole shadow.