The Modified Schrodinger Poisson Equation -- Quantum Polytropes

TL;DR

This paper introduces quantum polytropes, a new class of boson star solutions with non-minimal gravity coupling, supported by quantum pressure, and analyzes their stability based on the coupling exponent.

Contribution

It proposes a modified Schrödinger-Poisson equation with non-linear gravity coupling, leading to quantum polytrope solutions similar to classical polytropes, and establishes stability conditions.

Findings

Quantum polytropes resemble Newtonian polytropic stars.

Solutions are supported by non-local quantum pressure.

Stability depends on the coupling exponent, with instability for ta>8/3.

Abstract

Axions and axion-like 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 non-minimal 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 non-standard 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 non-local quantum pressure and follow an equation very similar to the Lane-Emden equation for classical polytropes. Furthermore, we derive a simple condition on the exponent of the non-linear gravitational coupling, $\alpha>8/3$, beyond which the equilibrium solutions are unstable.