Spherical solutions of the Schr\"odinger-Poisson system with core-tail structure

TL;DR

This paper constructs and analyzes spherically symmetric equilibrium solutions of the Schr"odinger-Poisson system with a core-tail structure, modeling Fuzzy Dark Matter halos, and investigates their evolution and scaling relations.

Contribution

It introduces a method to generate core-tail solutions of the Schr"odinger-Poisson system and studies their dynamical evolution and scaling properties.

Findings

Relaxed configurations oscillate around a virialized state.

Core-halo scaling exponent is 1/3 for equilibrium and 0.54 for relaxed states.

Tail perturbations induce oscillations in the core.

Abstract

We construct spherically symmetric equilibrium solutions of the Schr\"odinger-Poisson (SP) system of equations with a core-tail structure that could serve as models of Fuzzy Dark Matter (FDM) halos. The core is assumed to be a solitonic ground state equilibrium configuration of the SP equations, and the tail is integrated from a transition radius onwards. The total mass of the system parametrizes the family of solutions and constrains the tail density profile. The tail has a radial velocity profile, whereas the core is stationary. We investigate the evolution of these equilibrium configurations and find that the tail initially perturbs the core, and consequently, the whole solution oscillates around a virialized solution that we call 'relaxed', whose average also has a core-tail structure. We measure the departure of the relaxed configuration from the equilibrium solution in order to estimate the utility of the latter. We also find that the core-halo scaling relation of equilibrium configurations has an exponent $\alpha=1/3$, whereas relaxed configurations exhibit a scaling with $\alpha=0.54$.