The Modified Schrodinger Poisson Equation  Quantum Polytropes
Abstract
Axions and axionlike particles are a leading model for the dark matter in the Universe; therefore, dark matter halos may be boson stars in the process of collapsing. We examine a class of static boson stars with a nonminimal coupling to gravity. We modify the gravitational density of the boson field to be proportional to an arbitrary power of the modulus of the field, introducing a nonstandard coupling. We find a class of solutions very similar to Newtonian polytropic stars that we denote "quantum polytropes." These quantum polytropes are supported by a nonlocal quantum pressure and follow an equation very similar to the LaneEmden equation for classical polytropes. Furthermore, we derive a simple condition on the exponent of the nonlinear gravitational coupling, $\alpha>8/3$, beyond which the equilibrium solutions are unstable.
 Publication:

arXiv eprints
 Pub Date:
 September 2017
 arXiv:
 arXiv:1709.09291
 Bibcode:
 2017arXiv170909291H
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 7 pages, 3 figures, version accepted by Phys Rev D, added a relativistic generalization of the scalar field