Fuzzy Dark Matter and the Impact of Core-Halo Diversity on Its Particle Mass Constraints

Abstract

We investigate how diversity in the core-halo mass relation affects constraints on the fuzzy dark matter particle mass $m_ψ$ inferred from the internal kinematics of dwarf galaxies. Using stellar line-of-sight velocities and projected positions for eight Milky Way dwarf spheroidal galaxies, we model their dark matter halos as solitonic cores embedded within outer NFW envelopes. We apply both second- and fourth-order Jeans analyses to derive the posterior distribution of $m_ψ$. Our results show that there are two ranges of $m_ψ$ consistent with the observed kinematics: $-20.3 < \log_{10}(m_ψ/\mathrm{eV}) < -19.2$, and a narrower small-mass window $-22.1 < \log_{10}(m_ψ/\mathrm{eV}) < -21.5$, both within the 68\% credible intervals. The latter becomes prominent only if core-halo diversity is taken into account. These constraints pose a challenge to fuzzy dark matter, as the small-$m_ψ$ window is in conflict with Milky Way satellite abundances, and our upper bound largely excludes the parameter space permitted by Lyman-$α$ forest constraints.

Figures (7)

• Figure 1: The estimated $m_\psi$ from this work for each galaxy. There are two high-probability regions, which correspond to two different DM core radii. Thick (thin) error bars indicate 68% (95%) credible interval.
• Figure 2: Core radius $r_c$ of the small-$m_\psi$ solutions as a function of the median projected galactocentric distance of the kinematic samples. Error bars denote the 68% credible intervals. The solid gray line represents $r_c = \mathrm{median}(R)$ to guide the readers. For the small-$m_\psi$ solution, the dark matter (DM) core radius must be sufficiently large to encompass most of the kinematic tracers within the core region, which gives rise to the observed correlation.
• Figure 3: Upper panel: MCMC samples of the estimated $\log_{10}(M_{200})$ versus $\log_{10}(m_\psi/\textrm{eV})$ for Draco as representative. The colors are coded based on the slope of the CHR $\eta$. Lower panel: similar to the upper panel but for $r_t/r_c$ versus $\log_{10}(m_\psi/\textrm{eV})$ with the colors coded by $\log_{10}(r_s/\textrm{kpc})$.
• Figure 4: Constraints on the fuzzy dark matter particle mass. The shaded bands indicate excluded ranges of $m_\psi$. The upper section, in cyan and brown, shows constraints derived from this work and from other kinematic analyses of dwarf galaxies, respectively. Darker and lighter shades show exclusion at 95% and 68% credible intervals, respectively. The lower part, in gray, summarizes constraints obtained from a variety of independent astrophysical and cosmological probes as indicated. Different tones of gray in the same row correspond to different works.
• Figure 5: The posterior distributions of the model parameters for Carina, Draco, Fornax, and Leo I. Although $r_c$ is not treated as a free parameter in the model, it is included here for reference.