Testing warm dark matter with kinematics of the smallest galaxies

TL;DR

This work proposes a novel WDM probe based on central prompt cusps with $\rho \propto r^{-1.5}$ by embedding the cusp-halo relation into the Galacticus model and comparing to kinematics of the faint Milky Way satellites Segue 1, Tri II, and Tuc V. By generating large ensembles of Galacticus analogues across DM masses $m_χ=3$–$40$ keV and comparing their predicted $v_{circ}(r_h)$ to observations, they derive a 95% confidence lower bound $m_χ>5.8$ keV (and $m_χ>9.4$ keV at 90%), competitive with other small-scale probes. The approach leverages the central-density enhancement from prompt cusps as a complementary, physically distinct test of WDM, and identifies observational and modeling improvements that could tighten the constraints further. The findings underscore the potential of high-precision kinematics of the smallest satellites, and of expanding the sample with additional ultra-faint systems, to sharpen WDM particle-mass limits.

Abstract

Every dark matter halo forms with a $ρ\propto r^{-1.5}$ density cusp at its center. For warm dark matter (WDM), these prompt cusps can be massive enough to influence the kinematics of dwarf galaxies. By implementing prompt cusps in the Galacticus galaxy formation model, we show that the measured velocity dispersions of Tucana V and Triangulum II are serious outliers for dwarf galaxies arising in WDM models. For thermal-relic dark matter, the three faintest Milky Way satellites together constrain the particle mass to be $m_χ>5.8$ keV at 95 percent confidence or $m_χ>9.4$ keV at 90 percent confidence. Improved velocity dispersion measurements for these systems could greatly refine this constraint, as could identification and kinematic characterization of more such galaxies.

Figures (11)

• Figure 1: Illustration of the analysis in this work. In color, we show radial profiles of the circular orbit velocity for satellite galaxies similar to Segue 1, Tri II, and Tuc V produced with Galacticus. We show the median and 68 percent scatter at each radius, and different colors correspond to different dark matter (DM) models. For the same galaxies, the points with error bars mark the observationally inferred circular orbit velocity at the half-light radius.
• Figure 2: Low-luminosity Milky Way satellites drawn from the LVDB (v1.0.6), shown in terms of absolute $V$-band magnitude $M_V$ and azimuthally averaged 2-dimensional half-light radius $r_\mathrm{h}^\mathrm{(2D)}$. In this work we consider Segue 1, Tri II, and Tuc V, which are the faintest and smallest confirmed Milky Way satellite galaxies.
• Figure 3: Cumulative posterior distributions of the line-of-sight velocity dispersion of the dwarf galaxies that we analyze. For Segue 1 and Tri II, we take the distributions directly from 2011ApJ...733...46S and 2022MNRAS.514.1706B, respectively. For Tuc V, the points correspond to the values reported by 2024ApJ...968...21H, and we adopt a closely matching log-normal distribution (green curve).
• Figure 4: Galacticus analogues of Segue 1, Tri II, and Tuc V for 10 keV WDM. We show their distribution in terms of the halo virial mass $M_\mathrm{ifl}$ at the infall redshift $z_\mathrm{ifl}$ (or scale factor $a_\mathrm{ifl}$). Darker symbols represent galaxy analogues that are drawn more times and hence weighted more strongly in our analysis.
• Figure 5: Distribution of the prompt cusp coefficients $A$ for Galacticus analogues of Segue 1, Tri II, and Tuc V in a 10 keV WDM scenario. The solid lines use the Galacticus prompt cusp prescription, which assigns the cusp at the mass $M_\mathrm{res}=10^7~\mathrm{M}_\odot$ and redshift $z_\mathrm{res}$ at which each halo crosses the resolution limit. These cusps are biased relative to those that would result from using the mass $M_\mathrm{ifl}$ and redshift $z_\mathrm{ifl}$ at subhalo infall, but we show in appendix \ref{['sec:simulations']} that this bias is physically correct.