Jeans instability and turbulent gravitational collapse of Bose-Einstein Condensate dark matter halos

TL;DR

This paper investigates the gravitational stability and collapse of rotating Bose-Einstein Condensate dark matter halos using quantum hydrodynamics, deriving conditions for collapse and exact solutions for their evolution.

Contribution

It introduces a detailed analysis of Jeans instability in BEC dark matter halos, including turbulence effects and semi-analytical solutions for their dynamics.

Findings

Derived dispersion relation including turbulence, quantum pressure, and quantum potential effects.

Identified critical Jeans scales for collapse of BEC dark matter halos.

Provided semi-analytical and numerical solutions for halo collapse and expansion profiles.

Abstract

We consider the Jeans instability and the gravitational collapse of the rotating Bose-Einstein Condensate dark matter halos, described by the zero temperature non-relativistic Gross-Pitaevskii equation, with repulsive inter-particle interactions. In the Madelung representation of the wave function, the dynamical evolution of the galactic halos is described by the continuity and the hydrodynamic Euler equations, with the condensed dark matter satisfying a polytropic equation of state with index $n=1$. By considering small perturbations of the quantum hydrodynamical equations we obtain the dispersion relation and the Jeans wave number, which includes the effects of the vortices (turbulence), of the quantum pressure and of the quantum potential, respectively. The critical scales above which condensate dark matter collapses (the Jeans radius and mass) are discussed in detail. We also investigate the collapse/expansion of rotating condensed dark matter halos, and we find a family of exact semi-analytical solutions of the hydrodynamic evolution equations, derived by using the method of separation of variables. An approximate first order solution of the fluid flow equations is also obtained. The radial coordinate dependent mass, density and velocity profiles of the collapsing/expanding condensate dark matter halos are obtained by using numerical methods.