Boson Stars as Gravitational Lenses

We discuss boson stars as possible gravitational lenses and study the lensingeffect by these objects made of scalar particles. The mass and the size of aboson star may vary from an individual Newtonian object similar to the Sun tothe general relativistic size and mass of a galaxy close to its Schwarzschildradius. We assume boson stars to be transparent which allows the light to passthrough them though the light is gravitationally deflected. We assume bosonstars of the mass $M = 10^{10}M_\odot$ to be on non-cosmological distance fromthe observer. We discuss the lens equation for these stars as well as thedetails of magnification. We find that there are typically three images of astar but the deflection angles may vary from arcseconds to even degrees. Thereis one tangential critical curve (Einstein ring) and one radial critical curvefor tangential and radial magnification, respectively. Moreover, the deflectionangles for the light passing in the gravitational field of boson stars can bevery large (even of the order of degrees) which reflects the fact they are verystrong relativistic objects. We also propose a suitable formula for the lensequation for such large deflection angles, and with the reservation that largedeflection angle images are highly demagnified but in the area of thetangential critical curve, their existence may help in observational detectionof suitable lenses possessing characteristic features of boson stars whichcould also serve as a direct evidence for scalar fields in the universe.Comment: accepted by Astrophys. J., 31 pages, AASTeX, 6 figure