On particle scattering in Gross-Pitaevskii theory and implications for dark matter halos

TL;DR

This paper investigates the microphysical conditions of Bose-Einstein-condensed dark matter using the Gross-Pitaevskii framework, deriving bounds on particle properties and implications for dark matter halo structures.

Contribution

It derives constraints on BEC-DM particle mass and self-interaction strength from fundamental conditions and halo virial equilibrium, connecting microphysics to astrophysical observations.

Findings

GPP conditions are satisfied for relevant BEC-DM masses under virial equilibrium.

Derived bounds on particle mass and self-interaction coupling strength.

Implications for elastic scattering cross section vary widely depending on interaction regime.

Abstract

Bose-Einstein-condensed dark matter (BEC-DM), also called scalar field dark matter (SFDM), has become a popular alternative to the standard, collisionless cold dark matter (CDM) model, due to its long-held potential to resolve the small-scale crisis of CDM. Halos made of BEC-DM have been modelled using the Gross-Pitaevskii (GP) equation coupled to the Poisson equation; the so-called GPP equations of motion. These equations are based on fundamental microphysical conditions that need to be fulfilled in order for the equations to be valid in the first place, related to the diluteness of the DM gas and the nature of the particle scattering model. We use these conditions in order to derive the implications for the BEC-DM parameters, the 2-particle self-interaction coupling strength $g$ and the particle mass $m$. We compare the derived bounds with the constraint that results from the assumption of virial equilibrium of the central cores of halos, deriving a relationship that connects $g$ and $m$. We find that the GPP conditions are greatly fulfilled, for BEC-DM particle masses of interest, if such models also obey the virial condition that turns out to be the strongest constraint. We also derive the implications for the elastic scattering cross section (per particle mass) in BEC-DM halos, based on the scattering model of GPP, and find a huge range of possible values, depending on the self-interaction regime. We put our results into context to recent literature which predicts sub-kpc core size in BEC-DM halos.