Mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions: II. Numerical results

TL;DR

This paper numerically investigates the mass-radius relation of Newtonian self-gravitating Bose-Einstein condensates with short-range interactions, exploring various interaction regimes and comparing exact and approximate solutions.

Contribution

It provides a detailed numerical analysis of the mass-radius relation for BEC dark matter, including attractive interactions, and compares numerical results with analytical approximations.

Findings

Good agreement between numerical and analytical mass-radius relations.

Connection established between non-interacting and Thomas-Fermi limits.

Exploration of attractive self-interaction effects on condensate structure.

Abstract

We develop the suggestion that dark matter could be a Bose-Einstein condensate. We determine the mass-radius relation of a Newtonian self-gravitating Bose-Einstein condensate with short-range interactions described by the Gross-Pitaevskii-Poisson system. We numerically solve the equation of hydrostatic equilibrium describing the balance between the gravitational attraction and the pressure due to quantum effects (Heisenberg's uncertainty principle) and short-range interactions (scattering). We connect the non-interacting limit to the Thomas-Fermi limit. We also consider the case of attractive self-interaction. We compare the exact mass-radius relation obtained numerically with the approximate analytical relation obtained with a Gaussian ansatz. An overall good agreement is found.