Abstract

It has been shown that a self-gravitating system of massive keV fermions in thermodynamic equilibrium correctly describes the dark matter (DM) distribution in galactic halos (from dwarf to spiral and elliptical galaxies) and that, at the same time, it predicts a denser quantum core towards the center of the configuration. Such a quantum core, for a fermion mass in the range of 50 keV less than or similar to mc(2) less than or similar to 345 keV, can be an alternative interpretation of the central compact object in Sgr A*, traditionally assumed to be a black hole (BH). We present in this work the gravitational lensing properties of this novel DM configuration in nearby Milky-Way-like spiral galaxies. We describe the lensing effects of the pure DM component both on halo scales, where we compare them to the effects of the Navarro-Frenk-White and the nonsingular isothermal sphere DM models, and near the galaxy center, where we compare them with the effects of a Schwarzschild BH. For the particle mass leading to the most compact DM core, mc(2) approximate to 10(2) keV, we draw the following conclusions. At distances r greater than or similar to 20 pc from the center of the lens the effect of the central object on the lensing properties is negligible. However, we show that measurements of the deflection angle produced by the DM distribution in the outer region at a few kpc, together with rotation curve data, could help to discriminate between different DM models. In the inner regions 10(-6) less than or similar to r less than or similar to 20 pc, the lensing effects of a DM quantum core alternative to the BH scenario becomes a theme of an analysis of unprecedented precision which is challenging for current technological developments. We show that at distances similar to 10(-4) pc strong lensing effects, such as multiple images and Einstein rings, may occur. Large differences in the deflection angle produced by a DM central core and a central BH appear at distances r less than or similar to 10(-6) pc; in this regime the weak-field formalism is no longer applicable and the exact general-relativistic formula has to be used for the deflection angle which may become bigger than 2 pi. An important difference in comparison to BHs is in the fact that quantum DM cores do not show a photon sphere; this implies that they do not cast a shadow (if they are transparent). Similar conclusions apply to the other DM distributions for other fermion masses in the above-specified range and for other galaxy types.