We investigate the gravitational constraints imposed on dark matter halos in the context of finite temperature scalar field dark matter. We find constraints to produce multiple images by dark matter, and we show that there are differences with respect to the full Bose-Einstein condensate halo when the temperature of the scalar field in dark matter halos is taken into account. The nonzero temperature allows the scalar field to be in excited states, and, recently, their existence has proven to be necessary to fit rotation curves of dark matter dominated galaxies of all sizes, and it also explained the nonuniversality of the halo density profiles. Therefore, we expect that combining observations of rotation curves and strong lensing systems can give us a clue to the nature of dark matter. Finally, we propose a method to identify the excited state of a halo in a strong lens system, knowing that various halo excited states can provide information of the scalar field dark matter halo evolution which can be tested by using numerical simulations.

• Received 28 February 2013

DOI:https://doi.org/10.1103/PhysRevD.88.083008