Self-gravitating Superfluids: The Gross-Pitaevskii-Poisson Framework

TL;DR

This paper reviews the Gross-Pitaevskii-Poisson equation framework for modeling self-gravitating superfluid systems, including boson stars, dark matter halos, and neutron star interiors, incorporating vortices and flux tubes.

Contribution

It provides a comprehensive overview of the GPPE framework and extends it to include coupled models with vortices, flux tubes, and self-gravity in astrophysical superfluid systems.

Findings

GPPE effectively models self-gravitating superfluids.

Inclusion of vortices and flux tubes enhances astrophysical realism.

Framework applicable to boson stars, dark matter, and neutron stars.

Abstract

We provide an overview of the Gross-Pitaevskii-Poisson equation (GPPE) that is used to model self-gravitating superfluid systems, which include gravitationally collapsed boson and axion stars and dark-matter haloes. We outline how this framework can be used to develop minimal models for neutron stars and for pulsars and their glitches. We account not only for vortices in the neutron superfluid inside these stars, but also for the flux tubes in the proton-superconductor subsystem, using a coupled model with the neutron superfluid, proton superconductor, the Maxwell equations for the vector potential ${\bf A}$, and the Poisson equation for self-gravity.