2014ApJ...780..158P

Slow-moving particles capable of interacting solely with gravity might be detected on Earth as a result of the gravitational lensing induced focusing action of the Sun. The deflection experienced by these particles is inversely proportional to the square of their velocities, and as a result their focal lengths will be shorter. We investigate the velocity dispersion of these slow-moving particles, originating from distant point-like sources, for imposing upper and lower bounds on the velocities of such particles in order for them to be focused onto Earth. Stars, distant galaxies, and cluster of galaxies, etc., may all be considered as point-like sources. We find that fluxes of such slow-moving and non-interacting particles must have speeds between ∼0.01 and.14 times the speed of light, c. Particles with speeds less than ∼0.01c will undergo way too much deflection to be focused, although such individual particles could be detected. At the caustics, the magnification factor could be as high as ∼10⁶. We impose lensing constraints on the mass of these particles in order for them to be detected with large flux enhancements that are greater than 10^–9 eV. An approximate mass density profile for Jupiter is used to constrain particle velocities for lensing by Jupiter. We show that Jupiter could potentially focus particles with speeds as low as ∼0.001c, which the Sun cannot.