Ultra-Light Dark Matter Simulations and Stellar Dynamics: Tension in Dwarf Galaxies for $m < 5\times10^{-21} $ eV

TL;DR

This work tests ultra-light dark matter (ULDM) in dwarf galaxies by simulating the coupled Schrödinger-Poisson dynamics of ULDM and a stellar tracer population, focusing on Fornax, Leo II, and Carina. The authors find that ULDM induces dynamical heating that drives secular growth of the stellar half-light radius and generates distinctive LOS velocity dispersion features, with the inner soliton core often in tension with observed kinematics. Across the mass range studied, they conclude that $m$ in the interval $5\times10^{-22}$ eV to $5\times10^{-21}$ eV is disfavored, since heating disrupts the observed stellar structure on Gyr timescales, though tidal effects can mitigate heating at the low-mass end. The results emphasize that non-equilibrium ULDM+stellar dynamics must be accounted for in interpreting dwarf-galaxy data and motivate extending the analysis to include stellar self-gravity, cosmological contexts, and higher-spin ULDM scenarios. All mathematical expressions are presented in $...$ notation where appropriate, e.g., $m$, $M_{200}$, and $r_{half}$ are used in conjunction with their physical units and scaling relations.

Abstract

We present numerical simulations of dark matter and stellar dynamics in ultra light dark matter halos tailored to mimic dwarf galaxies. An important effect we observe is the dynamical evolution of the stellar half-light radius and velocity dispersion, which makes previous equilibrium models significantly incomplete. Based on half-light radius dynamical evolution, as well as velocity peaks due to soliton core condensation, we show that data from the Fornax, Carina, and Leo II dwarf galaxies disfavores particle masses in the range $ 5\times 10^{-22} \text{ eV} \lesssim m \lesssim 5\times10^{-21}$ eV. Smaller boson masses, around $m\approx1\times10^{-22}$ eV, could cause strong dynamical heating, but we caution that tidal stripping by the Milky Way could moderate the effect. A caveat in our analysis is the omission of stellar self-gravity, which could affect extrapolation back in time if the stellar body was much more compact in the past.

Figures (19)

• Figure 1: Simulation results for $m=1e-21eV$, with $L=12$ kpc. Left. LOSVD data for Fornax (purple) is compared to the simulation at time 0 (red) and at time $t\approx9.9G\years$ (blue). Every bin has the same number of stars. Black line is the $\sigma_{\rm los}$ predicted by a Jeans analysis. Notice that LOSVD data are difficult to reconcile with ULDM for $r\lesssim0.5$ kpc. Right. Red lines: half-light radius $r_{\rm half}$ evolution over time. Solid and dotted refer to two simulations, with the same ULDM halo but different initial distribution of stars. The stellar kinematics analysis of the left plot is done for the lowest initial $r_{\rm half}$ simulation. Grey band indicates the observed half-light radius of Fornax reported in Tab. I of Ref. 2009ApJ...704.1274W, $r_{\rm half} = 0.668 \pm 0.034 \,\mathrm{kpc}$, while grey dashed line shows the half-light radius from Ref. DES:2018jtu (see discussion in App. \ref{['s:data']}). Blue line shows the soliton core radius $r_{\rm c}$. Dashed blue line shows the expectation from the soliton-halo relation of Ref. Schive:2014hza. Vertical dashed line highlights $t=10$ Gyr, which is the typical age of the systems we consider. Notice that fine-tuned initial conditions allow to reproduce the half-light radius from DES:2018jtu (albeit not from 2009ApJ...704.1274W).
• Figure 2: Simulation for a Fornax-like system for $m=1e-22eV$, with $L=40k\parsec$. Panels explanation is the same as in the caption of Fig. \ref{['fig:NFW_1em21_main']}. The rapid increase of stellar $r_{\rm half}$ makes matching both stellar kinematics and surface brightness profile difficult for a $10G\years$ old system.
• Figure 3: Simulation of a halo resembling Leo II and Carina, with $m=5e-21eV$, $L=5k\parsec$. Legend as in Fig. \ref{['fig:NFW_1em21_main']}. The stellar kinematics analysis in the left plot relates to the simulation with smaller $r_{\rm half}$. Note the tension between simulated stellar $r_{\rm half}$ and data. For Leo II we derived LOSVD and $r_{\rm half}$ from Ref. Koch:2007ye, finding $r_{\rm half} = 0.21 \pm 0.02 \, \rm kpc$ with uncertainty determined via bootstrap resampling. For Carina we use data from Ref. Walker:2009zp; in this case $r_{\rm half} = 0.24 \pm 0.02 \, \rm kpc$.
• Figure 4: Example of radially averaged density profile (with $r$ measured from the maximum density point) of a NFW profile, designed to roughly match Fornax at $m=1\times10^{-21}$ eV. We show different snapshots, including initialization (thick red) together with the target NFW density profile (thick blue) and the moment at which star particles are inserted, $t=2$ Gyr (dashed purple). The dynamical formation and growth of the soliton is manifest.
• Figure 5: Evolution of the anisotropy parameter for a simulation of a halo initialized as NFW, with $L=12k\parsec$, $m=1e-21eV$, and initial $\beta = -0.3$. As noted in the main text, $\beta$ evolves towards positive values due to ULDM dynamical heating.