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Constraining Ultra-Light Dark Matter mass with Dwarf Galaxy Rotation Curves

Tian-yao Fang, Ming-Chung Chu

TL;DR

This work addresses the outer-halo structure of ultra-light dark matter (ULDM) and seeks to constrain the ULDM particle mass. It introduces an analytic trial wavefunction to model the ULDM density outside the central Bose–Einstein condensate (BEC) core, derives the corresponding rotation curve (RC), and fits 12 dwarf spheroidal RCs, linking the RC shape to a single mass parameter. The fits yield a remarkably narrow mass range $m=(1.8-3.2)\times 10^{-23}$ eV across galaxies, supporting a universal scaling and the ULDM paradigm. The approach provides a fast, analytic framework for probing ULDM on galactic scales and complements full numerical Schrödinger–Poisson studies by enabling rapid mass constraints from outer-halo dynamics.

Abstract

While ultra-light bosonic dark matter (ULDM) in a Bose-Einstein condensate (BEC) state could naturally account for the central core in some galaxies and resolve the core-cusp problem, the dark matter density distribution in the outer regions of galaxies remains less explored. We propose a trial wavefunction to model the ULDM distribution beyond the BEC core. We derive the corresponding rotation velocity curve, which shows excellent agreement with those of 12 dwarf spheroidal galaxies. The best-fit ULDM particle mass for each dwarf galaxy falls within a strikingly narrow range of $m=(1.8-3.2)\times 10^{-23}\text{eV}$.

Constraining Ultra-Light Dark Matter mass with Dwarf Galaxy Rotation Curves

TL;DR

This work addresses the outer-halo structure of ultra-light dark matter (ULDM) and seeks to constrain the ULDM particle mass. It introduces an analytic trial wavefunction to model the ULDM density outside the central Bose–Einstein condensate (BEC) core, derives the corresponding rotation curve (RC), and fits 12 dwarf spheroidal RCs, linking the RC shape to a single mass parameter. The fits yield a remarkably narrow mass range eV across galaxies, supporting a universal scaling and the ULDM paradigm. The approach provides a fast, analytic framework for probing ULDM on galactic scales and complements full numerical Schrödinger–Poisson studies by enabling rapid mass constraints from outer-halo dynamics.

Abstract

While ultra-light bosonic dark matter (ULDM) in a Bose-Einstein condensate (BEC) state could naturally account for the central core in some galaxies and resolve the core-cusp problem, the dark matter density distribution in the outer regions of galaxies remains less explored. We propose a trial wavefunction to model the ULDM distribution beyond the BEC core. We derive the corresponding rotation velocity curve, which shows excellent agreement with those of 12 dwarf spheroidal galaxies. The best-fit ULDM particle mass for each dwarf galaxy falls within a strikingly narrow range of .
Paper Structure (7 sections, 21 equations, 5 figures, 1 table)

This paper contains 7 sections, 21 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Schrödinger-Poisson equation of ULDM
  3. Trial wavefunction and numerical results
  4. Comparison with the observed RCs
  5. Conclusion
  6. Wave function deviations and RCs result for different $t$
  7. Comparison with the RCs of the M31 and MW

Figures (5)

  • Figure 1: Deviation of the trial wave function from the eigen wave function (Eq.(\ref{['deviation']}), left panel), and the resulting RC (right panel), for $t = 10$ (upper panels) and $t = 15$ (lower panels).
  • Figure 2: RCs for different $t$ and appropriate rescaling of $R$ and $v_0$, showing a universal shape.
  • Figure 3: RC of M31 (left panel) and MW (right panel), compared to best-fit model (solid line). The best-fit parameters are shown in the legend.
  • Figure 4: Same as Fig.\ref{['t10']}, but for $t=20,30,50,100,200$, from top to bottom, respectively.
  • Figure 5: Same as Fig.\ref{['M31']}, but for dwarf galaxies.