[Paper Review] Dwarf galaxies imply dark matter is heavier than $\mathbf{2.2 imes 10^{-21}} \, \mathbf{eV}$

Tim Zimmermann, James Alvey+3 more|arXiv (Cornell University)|May 30, 2024

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper establishes a rigorous, model-independent lower bound on the mass of dark matter (DM) particles by analyzing stellar kinematics in the Milky Way's dwarf spheroidal galaxy Leo II. Using a self-consistent reconstruction of DM wavefunctions and a statistical comparison via maximum mean discrepancy, it finds $ m > 2.2 \times 10^{-21} \, \text{eV} $ at 95% confidence, independent of cosmology, microphysics, or dynamics—offering the strongest fundamental limit to date for bosonic DM.

ABSTRACT

It is widely established that a lower bound on the dark matter particle mass, $m$, can be obtained by demanding that the de Broglie wavelength in a given galaxy must be smaller than the virial radius of the galaxy, leading to $m\gtrsim 10^{-22} ext{ eV}$ when applied to typical dwarf galaxies. This lower limit has never been derived precisely or rigorously. We use stellar kinematical data for the Milky Way satellite galaxy Leo II to self-consistently reconstruct a statistical ensemble of dark matter wavefunctions and corresponding density profiles. By comparison to a data-driven, model-independent reconstruction, and using a variant of the maximum mean discrepancy as a statistical measure, we determine that a self-consistent description of dark matter in the local Universe requires $m>2.2 imes 10^{-21}\,\mathrm{eV}\;\mathrm{(CL>95\%)}$. This lower limit is free of any assumptions pertaining to cosmology, microphysics (including spin), or dynamics of dark matter, and only assumes that it is predominantly composed of a single bosonic particle species.

Motivation & Objective

• To derive a fundamental lower bound on the mass of dark matter particles using kinematic data from dwarf spheroidal galaxies.
• To overcome the limitations of heuristic 'folk wisdom' bounds that rely on crude estimates of de Broglie wavelength.
• To develop a statistically robust, model-independent method that avoids assumptions about cosmology, particle spin, or non-linear dynamics.
• To test whether a self-consistent description of dark matter as a single bosonic field can reproduce observed stellar kinematics in Leo II.
• To establish a limit that is independent of core-halo relations, baryonic physics, or long-term dynamical evolution.

Proposed method

• Reconstruct a statistical ensemble of 5,000 dark matter wavefunctions from stellar velocity dispersion data in Leo II using a Bayesian inference framework.
• Use the Schrödinger-Poisson system to model the self-consistent, spherically symmetric, stationary state of a bosonic dark matter halo.
• Compute the spherically averaged density profile $ \langle |\psi|^2 \rangle $ from the wavefunctions to compare with data-driven, model-independent reconstructions.
• Apply a variant of the maximum mean discrepancy (MMD) as a statistical test to compare the predicted and observed density profiles.
• Use a non-parametric, kernel-based statistical test to determine the confidence level at which the wavefunction-based model is consistent with observations.
• Perform a systematic scan over possible DM masses to identify the minimum mass consistent with the data at 95% confidence.

Figure 1: Direct comparison of different density ensembles for the Milky way dwarf Leo II. Black curves depict density samples generated by the Jeans code gravsphere and act as data-driven input set $X$ to our analysis pipeline. The pipeline output is a population $Y_{m_{22}}$ of reconstructed DM wa

Experimental results

Research questions

• RQ1 What is the minimum dark matter particle mass consistent with the kinematic data of the Leo II dwarf spheroidal galaxy?
• RQ2 Can a self-consistent, wavefunction-based model of bosonic dark matter reproduce the observed stellar velocity dispersion profile without assuming a specific halo profile?
• RQ3 How does the resulting lower bound on dark matter mass compare to existing heuristic limits derived from de Broglie wavelength considerations?
• RQ4 To what extent is the derived lower bound independent of cosmological models, particle spin, or baryonic physics?
• RQ5 Does the statistical consistency of the wavefunction reconstruction depend on the assumed dark matter particle mass?

Key findings

• The analysis establishes a lower bound of $ m > 2.2 \times 10^{-21} \, \text{eV} $ at 95% confidence level, significantly stronger than the commonly cited $ \sim 10^{-22} \, \text{eV} $ folk limit.
• The bound is derived without assumptions about cosmology, microphysics (including spin), or non-linear dynamics, relying only on the assumption of a single bosonic particle species.
• The method is robust to uncertainties in the core-halo relation and insensitive to baryonic effects such as stellar heating, which can alter cored profiles in other models.
• The statistical test using maximum mean discrepancy confirms that wavefunctions with $ m \leq 2.2 \times 10^{-21} \, \text{eV} $ are inconsistent with the data at 95% confidence.
• The result holds for both spin-0 and higher-spin bosonic dark matter, as the spherically averaged density profile remains unaffected by polarization states.
• The bound is stronger than previous limits from Lyman-alpha forest, galaxy counts, and dynamical heating in Eridanus II, which rely on additional astrophysical modeling.

Figure 2: Volume rendering of the total wave function density $|\psi|^{2}$ reconstructed from the average profile $\langle\rho_{\text{cNFWt}}\rangle$ of Fig. 1 for an excluded ( top ) and allowed ( bottom ) value of $m$ according to the hypothesis test in Fig. 3 . $J$ denotes the total number of rad