Analytical Emulator for the Baryon Density Distribution inside the Fuzzy Dark Matter Soliton from Machine Learning

TL;DR

This paper develops a machine learning-based analytical emulator to predict baryon density distribution within fuzzy dark matter solitons, enabling efficient exploration of baryon effects on FDM dynamics.

Contribution

It introduces a novel machine learning emulator for baryon density distribution in FDM solitons, bypassing the need for complex equations of motion.

Findings

Emulator achieves fractional errors less than 4%

Successfully reproduces baryon effects on FDM soliton formation

Potentially applicable as a baryon equation of motion in FDM simulations

Abstract

An empirical baryon density profile can be included in the Schr\"odinger-Poisson (SP) equations to influence the fuzzy dark matter (FDM) soliton formation. However, to probe the effects of baryon on the other dynamical evolutions of the FDM soliton, its equation of motion (EoM) inside the corresponding FDM soliton is needed. In this paper, given an empirical baryon density profile, we first provide the cylindrical symmetric FDM soliton solution about the FDM density and the total potential of FDM and baryon. Then, instead of EoM, we build an analytical emulator (AE) for the baryon density distribution from the obtained FDM density and total potential by machine learning. Finally, we check that this AE works as well as an empirical baryon density profile for the FDM soliton formation, with the fractional errors $\lesssim0.04$. It should also work as a kind of baryon EoM for some other simple FDM soliton evolutions.