Constraints on MACHO Dark Matter from Compact Stellar Systems in Ultra-Faint Dwarf Galaxies

TL;DR

The paper investigates whether dark matter could be composed entirely of massive compact halo objects (MACHOs) by studying dynamical heating of small star clusters in ultra-faint dwarfs. It develops a diffusion-based model of energy exchange between stars and MACHOs, deriving how heating drives cluster expansion and establishing two observable timescales. Applying the method to Eridanus II's central cluster and a population of compact ultra-faint dwarfs, it rules out MACHO dark matter across a broad mass range, from ~10^-7 M_sun to very high masses, under standard halo assumptions. These results provide robust, independent constraints that complement microlensing and wide-binary limits, with caveats tied to orbital histories and halo structure.

Abstract

I show that a recently discovered star cluster near the center of the ultra-faint dwarf galaxy Eridanus II provides strong constraints on massive compact halo objects (MACHOs) of >~5 M_sun as the main component of dark matter. MACHO dark matter will dynamically heat the cluster, driving it to larger sizes and higher velocity dispersions until it dissolves into its host galaxy. The stars in compact ultra-faint dwarf galaxies themselves will be subject to the same dynamical heating; the survival of at least ten such galaxies places independent limits on MACHO dark matter of masses >~10 M_sun. Both Eri II's cluster and the compact ultra-faint dwarfs are characterized by stellar masses of just a few thousand M_sun and half-light radii of 13 pc (for the cluster) and ~30 pc (for the ultra-faint dwarfs). These systems close the ~20--100 M_sun window of allowed MACHO dark matter and combine with existing constraints from microlensing, wide binaries, and disk kinematics to rule out dark matter composed entirely of MACHOs from ~10$^{-7}$ M_sun up to arbitrarily high masses.

Figures (4)

• Figure 1: Dynamical heating of a 6000 $M_\odot$ star cluster by 30 $M_\odot$ MACHOs at three fiducial densities, neglecting mass loss from the cluster. The cluster expands slowly until its mean density equals that of the MACHOs, and then expands as $r_h \sim \sqrt{t}$.
• Figure 2: MACHO constraints from the survival of the star cluster near the core of Eridanus II, assuming a cluster age of 3 Gyr (left panel) and 12 Gyr (right panel). The units for the dark matter density $\rho$ and velocity dispersion $\sigma$, are $M_\odot\,$pc$^{-3}$ and km s$^{-1}$, respectively. The limits come from requiring that the timescale to grow from $r_{h,0}= 2$ pc to the observed $r_h = 13$ pc is longer than the cluster age (red lines), or from requiring that the timescale to double in area (increase by $\sqrt{2}$ in $r_h$) is longer than the cluster age (blue lines).
• Figure 3: MACHO constraints from the observed sizes of compact ultra-faint dwarf galaxies, assuming a stellar mass of $3000$$M_\odot$, a current half-light radius $r_h=30$ pc, and an age of 10 Gyr. The units for the dark matter density $\rho$ and velocity dispersion $\sigma$, are $M_\odot\,$pc$^{-3}$ and km s$^{-1}$, respectively. The limits come from requiring that the timescale to grow from $r_{h,0}= 2$ pc to $r_h = 30$ pc is longer than 10 Gyr (red lines), or from requiring that the timescale to double in area (increase by $\sqrt{2}$ in $r_h$) is longer than 10 Gyr (blue lines).
• Figure 4: Constraints on MACHO dark matter from microlensing Alcock+Allsman+Alves+etal_2001Tisserand+LeGuillou+Afonso+etal_2007 and wide Galactic binaries Quinn+Wilkinson+Irwin+etal_2009, shown together with the constraints from the survival of compact ultra-faint dwarf galaxies and the star cluster in Eridanus II. I conservatively adopt a dark matter density of $0.02$$M_\odot$ pc$^{-3}$ in Eri II and $0.3$$M_\odot$ pc$^{-3}$ in the ultra-faint dwarfs, assume a three-dimensional velocity dispersion $\sigma=8$ km s$^{-1}$, and use two definitions of the heating timescale. A low-density halo and initially compact cluster weaken the constraints from Eri II. Even in this case, assuming dark matter halos to have the properties that are currently inferred, MACHO dark matter is excluded for all MACHO masses $\gtrsim$10$^{-7}$$M_\odot$.