[Paper Review] Mapping Dark Matter in the Milky Way using Normalizing Flows and Gaia DR3

Sung Hak Lim, Eric Putney+2 more|arXiv (Cornell University)|May 22, 2023

Galaxies: Formation, Evolution, Phenomena4 citations

TL;DR

This paper presents a model-free, data-driven 3D map of the local gravitational acceleration and mass density in the Milky Way's Solar neighborhood using normalizing flows to analyze 6 million stars from Gaia DR3. It finds a local dark matter density of $0.47 \pm 0.05$ GeV/cm³, providing the first unbinned, fully 3D, symmetry-free measurement of the dark matter distribution using unsupervised machine learning on real astrophysical data.

ABSTRACT

We present a novel, data-driven analysis of Galactic dynamics, using unsupervised machine learning -- in the form of density estimation with normalizing flows -- to learn the underlying phase space distribution of 6 million nearby stars from the Gaia DR3 catalog. Solving the equilibrium collisionless Boltzmann equation, we calculate -- for the first time ever -- a model-free, unbinned estimate of the local acceleration and mass density fields within a 3 kpc sphere around the Sun. As our approach makes no assumptions about symmetries, we can test for signs of disequilibrium in our results. We find our results are consistent with equilibrium at the 10% level, limited by the current precision of the normalizing flows. After subtracting the known contribution of stars and gas from the calculated mass density, we find clear evidence for dark matter throughout the analyzed volume. Assuming spherical symmetry and averaging mass density measurements, we find a local dark matter density of $0.47\pm 0.05$ GeV/cm$^3$. We compute the dark matter density at four radii in the stellar halo and fit to a generalized NFW profile. Although the uncertainties are large, we find a profile broadly consistent with recent analyses.

Motivation & Objective

• To develop a data-driven, symmetry-free method for mapping the 3D gravitational potential and mass density in the Milky Way using stellar kinematics.
• To test the assumption of dynamical equilibrium in the Solar neighborhood using an unsupervised machine learning approach.
• To isolate the contribution of dark matter by subtracting known baryonic components from the total mass density.
• To provide a model-independent estimate of the local dark matter density using real Gaia DR3 data.
• To assess uncertainties from measurement errors, statistical noise, and normalizing flow approximation.

Proposed method

• Employing normalizing flows to perform unsupervised density estimation on the 6D phase space (position and velocity) of 6 million stars from Gaia DR3.
• Using the collisionless Boltzmann equation under the assumption of dynamical equilibrium to infer the gravitational acceleration field from the learned phase space density.
• Applying the Poisson equation to compute the total mass density from the gravitational potential, with no assumptions about symmetry or functional form.
• Subtracting the baryonic mass density, estimated from the McKee et al. (2015) model and convolved with a Gaussian kernel to match the resolution of the density map.
• Averaging the residual mass density under a spherical symmetry assumption to improve signal-to-noise and estimate the local dark matter density.
• Quantifying uncertainties from Gaia measurement errors, statistical fluctuations, and normalizing flow approximation errors in the density estimation.

Figure 1: Schematic representation of the Solar location (red dot) relative to the Galactic Center (black dot). The 4 kpc observation volume is shown as a transparent grey sphere. The three coordinate systems used in this work are shown: the Galactocentric Cartesian coordinates $(x,y,z)$ , the spher

Experimental results

Research questions

• RQ1 Can normalizing flows accurately reconstruct the 3D gravitational potential and mass density from real Gaia DR3 stellar data without assuming symmetry?
• RQ2 Is the stellar population in the Solar neighborhood consistent with dynamical equilibrium on a 10% level, as inferred from the phase space density?
• RQ3 What is the local dark matter density in the Milky Way’s disk region, estimated without assuming a specific dark matter profile?
• RQ4 How well does the residual mass density after subtracting baryons match a generalized NFW profile?
• RQ5 To what extent do uncertainties in the normalizing flow and data errors affect the final dark matter density estimate?

Key findings

• The method successfully produces a model-free, unbinned, fully 3D map of the local acceleration and mass density fields within a 3 kpc sphere around the Sun.
• The results are consistent with dynamical equilibrium at the 10% level, limited by the current precision of the normalizing flows.
• After subtracting the baryonic mass density, a clear non-baryonic mass component is detected throughout the analyzed volume, indicating the presence of dark matter.
• Under the assumption of spherical symmetry, the local dark matter density is measured as $0.47 \pm 0.05$ GeV/cm³ at the Sun's location.
• The measured mass density profile is broadly consistent with a generalized NFW profile, though with significant uncertainties on the best-fit parameters.
• The uncertainty budget includes contributions from Gaia measurement errors, statistical fluctuations, and the approximation error of the normalizing flow model.

Figure 2: Density plots of the stars with full 6-dimensional kinematic information available from Gaia within 4 kpc of the Solar location in the $x-y$ (top row) and $x-z$ (bottom row) planes. The left column shows all 24,789,061 fully-characterized stars. The middle column shows the 5,811,956 remain