Turbulence and large-scale structures in self-gravitating superfluids

TL;DR

This paper investigates turbulence in self-gravitating superfluids using numerical simulations of the GPP equation, revealing structure formation, energy spectrum features, and inverse cascade mechanisms relevant to dark matter haloes.

Contribution

It demonstrates how self-gravity influences turbulence and structure formation in superfluids, providing insights into dark matter halo development.

Findings

Emergence of Kolmogorov $5/3$ scaling in non-self-gravitating case

Formation of diverse large-scale structures due to self-gravity

Evidence of inverse cascade leading to large-scale structure growth

Abstract

We study turbulence in self-gravitating superfluids by performing direct numerical simulations of the 3D Gross-Pitaevskii-Poisson (GPP) equation, which is also a model for dark matter haloes around galaxies. In the absence of self-gravity, the spectrally truncated Gross-Pitaevskii (GP) equation shows the emergence of Kolmogorov's $5/3$ scaling in the incompressible kinetic energy spectrum. Introducing self-gravity, we observe the formation of different structures, from sheet-like to spherically collapsed structures, which introduce a minimum in the kinetic energy spectrum that corresponds to the sizes of these structures. The system shows early convergence towards statistically stationary states, which we show by the onset of thermalisation in the compressible kinetic energy spectrum, where $E_{\rm kin}^c \propto k^2$. We also show that the formation of such large-scale structures suggests that the particles (bosons) move from small to large scales through an inverse cascade, supporting a mechanism for the formation of large-scale structures, such as dark matter haloes, around our galaxy Milky Way.