Self-Gravitating Scalar Field Configurations, Ultra Light Dark Matter and Galactic Scale Observations

TL;DR

This study investigates Ultra Light Dark Matter (ULDM) with spin-0 and mass around $m\sim 10^{-22}\,\text{eV}$, focusing on self-interactions characterized by $\lambda$. It leverages the nonrelativistic Gross-Pitaevskii-Poisson (GPP) framework to model stable soliton cores and explores how galactic-scale observations—central mass limits, rotation curves, and satellite tidal dynamics—constrain the ULDM mass and self-coupling in the $m$-$\lambda$ plane. The work shows that even tiny self-interactions, $|\lambda|\sim 10^{-90}-10^{-96}$, can significantly alter soliton properties and lifetimes, potentially reconciling ULDM with rotation curves (via repulsive SI) or extending satellite lifetimes (via attractive SI). It also demonstrates a machine-learning approach to infer density-profile and baryonic parameters from rotation curves, offering a data-driven path beyond traditional MCMC methods. Overall, the results underscore the pivotal role of self-interactions in ULDM phenomenology and showcase neural-network inference as a promising tool for galactic-scale DM parameter estimation.

Abstract

In this thesis, we investigate the possibility that dark matter consists of ultra light spin-zero particles with mass $m \sim 10^{-22}\ \text{eV}$. We focus on the role of self-interactions, assuming all other non-gravitational couplings to Standard Model particles are negligible. Such ultra light dark matter (ULDM) is expected to form stable self-gravitating scalar field configurations (solitons), whose properties depend on the particle mass and self-coupling $λ$. Using solutions of the Gross-Pitaevskii-Poisson equations, we explore how galactic-scale observations can constrain $m$ and $λ$. We show that observational upper limits on the mass enclosed in central galactic regions can probe both attractive and repulsive self-interactions with strengths $λ\sim \pm 10^{-96} - 10^{-95}$. We further demonstrate that self-interactions can allow ULDM to describe observed rotation curves as well as satisfy an empirical soliton-halo mass relation in low surface brightness galaxies for $m \sim 10^{-22}\ \text{eV}$ and $λ\gtrsim 10^{-90}$. We also study tidal effects in satellite dwarf galaxies and find that attractive self-interactions can extend their lifetimes over cosmological timescales, allowing ULDM to evade recent constraints derived for the non-interacting case. Finally, we explore machine learning based inference of dark matter and baryonic parameters from galaxy rotation curves, showing that neural networks can recover parameters consistent with observations.

Figures (42)

• Figure 1: Observed rotation curves for the following galaxies from the Spitzer Photometry & Accurate Rotation Curves (SPARC) catalogue Lelli_2016: Black - NGC 2366 (barred irregular dwarf galaxy), Green - NGC 6015 (spiral galaxy), Purple - NGC 2403 (intermediate spiral galaxy), Blue - NGC 4010 (barred spiral galaxy), Red - NGC 2915 (blue dwarf galaxy).
• Figure 2: Credit - X-ray: NASA/CXC/CfA/M.Markevitch, Optical and lensing map: NASA/STScI, Magellan/U.Arizona/D.Clowe, Lensing map: ESO WFI. A composite image of the Bullet Cluster.
• Figure 3: A schematic that illustrates a function $\varphi(t)$ undergoing fast oscillations shown in blue (which in our case are captured by the $e^{imt}$ term), along with a slow decay in amplitude with time shown by solid black curve (for our case, this is the scalar field $\Psi(t, \vec{x})$). We are only interested in the gross variation, i.e. time-dependence that is averaged over the fast oscillations.
• Figure 4: Example dimensionless ground state solutions (variables defined in eqs. (\ref{['eq:dimensions1']}) and (\ref{['eq:dimensions2']})) found using the shooting method shown for different values of $\hat{\lambda}$ with the boundary conditions: $\hat{\phi}'(0) = \hat{\Phi}'(0) = 0$, $\hat{\Phi}(0) = 0$ and $\hat{\phi}(0) = 1$.
• Figure 5: Blue curve denotes unscaled and dimensionless soliton mass and radius $\left(\hat{M}_\text{ini}, \hat{R}_\text{ini}\right)$ for various values of $\hat{\lambda}_\text{ini}$. Red curve shows the scaled mass-radius curve (dimensionless) for attractive self-interactions, while the green curve does the same for repulsive self-interactions, for a fixed $|\hat{\lambda}_\text{fin}| = 100$. Arrows denote transformation due to scaling from a fixed $s$ to a fixed $\hat{\lambda}_\text{fin}$ curve. NG corresponds to the non-gravitational regime, NI to the non-interaction regime, and TF (vertical dashed line) to the Thomas-Fermi regime. See section \ref{['sec:regimes']} for a discussion on different regimes.