Anisotropic quantum polytropes

TL;DR

This paper explores anisotropic quantum polytropes, analyzing how quantum effects and anisotropy influence the equilibrium configurations of boson stars and dark matter halos, revealing new types of hydrostatic equilibrium objects.

Contribution

It introduces a generalized Lane-Emden equation for anisotropic quantum boson stars, highlighting the opposing roles of anisotropy and gravity in quantum polytropes compared to classical models.

Findings

Quantum potential dominates equilibrium in quantum polytropes.

Anisotropy and gravity have opposite effects in quantum vs classical cases.

New classes of hydrostatic equilibrium objects are identified.

Abstract

The structure of astrophysical objects is usually modeled under the assumption of hydrostatic equilibrium. However, actual configurations may deviate from perfect spherical or isotropic properties. Consequently, cosmic objects are expected to exhibit some degree of anisotropy. This consideration also extends to hypothetical dark structures, such as dark stars and dark matter halos. Although the nature of dark matter remains unknown, axion-like particles (ALPs) are strong candidates, suggesting that dark matter halos may have originated from bosonic configurations undergoing gravitational collapse, sustained by boson-boson interactions in the condensate state. This system is described by the Gross-Pitaevskii-Poisson equation. Furthermore, within the framework of the Bohm-de Broglie approach, quantum effects,encapsulated in the so-called quantum potential, may play a significant role in equilibrium astrophysical configurations. In this study, we examine a class of static anisotropic boson stars which are non-minimally coupled to gravity. By including all these factors, we derive a generalized Lane-Emden-like equation and conduct a detailed analysis of the maximum degree of anisotropy that such systems can sustain, thereby identifying physically viable equilibrium configurations. Apart from focusing on the impact of anisotropic contributions, we find that for the so-called Quantum Polytropes (when the quantum potential is the main responsible for the equilibrium condition), the anisotropic factor and the gravitational field have opposite roles compared to the classical case. This leads to a new class of hydrostatic equilibrium objects.