Flux Enhancement of Slow-moving Particles by Sun or Jupiter: Can they be Detected on Earth?

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 are 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. We find that fluxes of such slow-moving and non-interacting particles must have speeds between ~0.01 and ~0.14 times the speed of light, $c$. Particles with speeds less than ~0.01 c 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 ~10E+6. We impose lensing constraints on the mass of these particles in order for them to be detected with large flux enhancements to be greater than E-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. As a special case, the perfect alignment of the planet Jupiter with the Sun is also considered.