Gravitational Lensing of Fermion Stars

We discuss the fermion stars, the self-gravitating systems of Fermi gases, as possible gravitational lenses. It is supposed that the fermions interact with themselves and other particles only by gravity, so they are the candidates of dark matter. We calculate Einstein deflection angles, study the image configurations, and calculate the magnification factors for a number of fermion stars that range from strong relativistic configurations to nonrelativistic ones. We find that typically there are three images, one Einstein ring and one radial critical curve for both cases. Two of the images are within the Einstein ring, and the other is outside, which may be very far. All these lensing characteristics can help to identify fermion stars as potential lensing objects, thus might give direct evidence that dark fermion stars exist in the universe.