Fuzzy dark matter dynamics and the quasi-particle hypothesis

Abstract

ABSTRACT Dark matter may be composed of ultralight bosons whose de Broglie wavelength in galaxies is $\lambda \sim 1\, {\rm kpc}$. The standard model for this fuzzy dark matter (FDM) is a complex scalar field that obeys the Schrödinger–Poisson equations. The wavelike nature of FDM leads to fluctuations in the gravitational field that can pump energy into the stellar components of a galaxy. Heuristic arguments and theoretical analyses suggest that these fluctuations can be modelled by replacing FDM with a system of quasi-particles (QPs). We test this hypothesis by comparing self-consistent simulations of a Schrödinger field with those using a system of QPs in one spatial dimension. Simulations of pure FDM systems allow us to derive a phenomenological relation between the number of QPs that is required to model FDM with a given de Broglie wavelength. We also simulate systems of FDM and stars and find that the FDM pumps energy into the stars whether it is described by QPs or a Schrödinger field with the FDM adiabatically contracting and the stellar system adiabatically expanding. However, we find that QPs overestimate dynamical heating.