Materia oscura escalar compleja (parte I): la versi\'on hidrodin\'amica

TL;DR

This paper models galactic halos using hydrodynamic equations derived from a complex scalar field, analyzing stability and structure formation through Jeans' instability, and revealing the presence of vorticity in the system.

Contribution

It introduces a hydrodynamic framework for complex scalar fields in galactic halos, providing new insights into structure formation and vorticity in such models.

Findings

Identification of a critical length scale for structure formation.

Demonstration of vorticity in the scalar field hydrodynamics.

Analysis of Jeans' instability in the complex scalar field context.

Abstract

In this work we use the Euler hydrodynamic equations of fluids to study a model of galactic halos minimally coupled to a complex scalar field, which in the Newtonian limit they become the Schr\"odinger-Poisson system. Applying a Madelung transformation, this system of equations takes the form of hydrodynamics equations, where there are a self-interacting potential and a kind of quantum potential that depends non-linearly on the density of the fluid. In this theoretical framework we analyze the Jeans' instability, which is useful for finding the scale length of perturbations of the scalar field that will form structures. In other words, perturbations of the scalar field with lengths less than this threshold length, can not lead to the formation of galactic structures. We also show that this scalar field hydrodynamic system has vorticity.