Gravitational collapse of Bose-Einstein condensate dark matter halos

Understand

We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive inter-particle interactions.

• By using a variational approach, and by choosing an appropriate trial wave function, we reformulate the Gross-Pitaevskii equation with spherical symmetry as Newton's equation of motion for a particle in an effective potential, which is determined by the zero point kinetic energy, the gravitational energy, and the particles interaction energy, respectively.
• The velocity of the condensate is proportional to the radial distance, with a time dependent proportionality function.
• The equation of motion of the collapsing dark matter condensate is studied by using both analytical and numerical methods.