Source-linked AI summary
The Observed properties of Dark Matter on small spatial scales
Gerard Gilmore, Mark I. Wilkinson, Rosemary F. G. Wyse, Jan T. Kleyna, Andreas Koch, N. Wyn Evans
TL;DR
The paper asks how star clusters and low-luminosity galaxies differ, and revisits their observed scaling relations using expanded photometric and kinematic data. It finds a size bimodality and interprets the galaxy results as evidence for shallow dark-matter cores, low mean densities, and model-dependent central densities.
Problem
The physical explanation for differences between star clusters and low-luminosity galaxies, including their discrepant scaling relations, remains a central question for identifying dark-matter physics.
Method
The paper synthesizes recent imaging and spatially resolved stellar-velocity data, revisits size and kinematic relations, and applies dynamical mass models to compare star clusters with dwarf spheroidal galaxies.
Results
Stable star clusters are smaller than ∼30pc while galaxies are larger than ∼120pc; dSph galaxies show shallow inner profiles, mean dark-matter density about 0.1 M⊙pc−3, and model-dependent central densities up to about 60 M⊙pc−3 for cusped models.
Takeaways & Limitations
The findings support dark matter halos with core scale lengths greater than about 100pc and indicate that smaller systems containing dark matter are not observed.
Takeaways & Limitations
Central dark-matter densities are less robust and model-dependent, while sufficiently small unresolved central cusps could remain undetected.
Abstract
from arXiv · showhide
We present a synthesis of recent photometric and kinematic data for several of the most dark-matter dominated galaxies. There is a bimodal distribution in half-light radii, with stable star clusters always being smaller than $\sim30$pc, while stable galaxies are always larger than $\sim120$pc. We extend the previously known observational relationships and interpret them in terms of a more fundamental pair of intrinsic properties of dark matter itself: dark matter forms cored mass distributions, with a core scale length of greater than about 100pc, and always has a maximum central massdensity with a narrow range. The dark matter in dSph galaxies appears to be clustered such that there is a mean volume mass density within the stellar distribution which has the very low value of about 0.1$\Msun$ pc$^{-3}$ (about 5GeV/c$^2$ cm$^{-3}$). All dSphs have velocity dispersions equivalent to circular velocities at the edge of their light distributions of $\sim 15$km s$^{-1}$. In two dSphs there is evidence that the density profile is shallow (cored) in the inner regions, and so far none of the dSphs display kinematics which require the presence of an inner cusp. The maximum central dark matter density derived is model dependent, but is likely to have a mean value (averaged over a volume of radius 10pc) of $\sim0.1\Msun$ pc$^{-3}$ (about 5GeV/c$^2$ cm$^{-3}$) for our proposed cored dark mass distributions (where it is similar to the mean value), or $\sim60\Msun$ pc$^{-3}$ (about 2TeV/c$^2$ cm$^{-3}$) if the dark matter density distribution is cusped. Galaxies are embedded in dark matter halos with these properties; smaller systems containing dark matter are not observed.
1. Introduction
The paper asks why star clusters and low-luminosity galaxies follow different structural and dynamical relations, using expanded photometric and kinematic data to interpret the distinction through dark matter properties.
- Observed structural differences: Star clusters and dwarf galaxies can overlap in luminosity and central stellar velocity dispersion, but galaxies have much larger half-light radii.Galaxies extend to ∼10^3 L⊙ and ∼10 km/s central line-of-sight dispersions, while their half-light radii are hundreds of parsecs versus tens of parsecs for clusters.
- Observed structural differences: A factor of ∼ten difference in half-light radii implies roughly two orders of magnitude lower phase-space density for galaxies at fixed stellar mass.The relevant phase-space-density measure combines central velocity dispersion and half-light radius.
- Motivation: Dark matter is the critical physical distinction because dSph galaxies are dark-matter dominated while star clusters show no corresponding evidence in the supplied discussion.This distinction motivates using dSph galaxies to investigate dark matter physics and small-scale clustering.
- Motivation: Dwarf galaxies provide a test of the smallest scales on which dark matter particles cluster because they appear to be the smallest dark-matter-dominated systems.The analysis aims to determine this smallest clustering scale from observed correlations and scaling relations.
- Approach: The paper revisits established scaling relations using velocity data across several dSphs and newer imaging that strengthens evidence for a real size discontinuity.The authors interpret the findings through a more fundamental pair of intrinsic dark matter properties.
2. The sizes and internal kinematics of star clusters and galaxies
The section establishes a robust size dichotomy between star clusters and galaxies, while explaining how photometric definitions and observational biases affect the comparison.
- Size dichotomy: The size distribution spans roughly six orders of magnitude yet shows no known stable object between ∼30pc and ∼120pc, apart from the disrupted candidate ComaBer.Star clusters have a robust maximum radius, whereas dSph galaxies have a minimum characteristic radius more than four times larger.
- Size dichotomy: Intermediate sizes may occur transiently during dwarf-galaxy tidal disruption or globular-cluster evaporation, so the observed gap concerns stable objects.These processes can temporarily produce systems with properties lying within the size gap.
- Comparison systems: UCD dynamical mass-to-light ratios are consistent with simple stellar models, with no evidence for dark matter associated with these stellar clusters.The studied UCDs are presented as the high-mass, high-luminosity extreme of globular-cluster populations.
- Photometric definitions: For a Plummer model, the scale parameter a is a half-light radius, while core radii are only approximations or lower limits depending on the system.The analysis conservatively retains three dSph core radii at face value rather than converting them to more uncertain half-light radii.
- Systematic effects: Photometric sizes generally measure only the baryonic component and can underestimate total mass scale lengths because galaxies are embedded in extended dark matter halos.Recently discovered low-luminosity dSph sizes are also often revised upward as fainter members and kinematic membership become measurable.
3. Masses and mass distributions, cores and cusps
The analyses favor shallow, cored dark-matter distributions in dSph galaxies, while emphasizing that inner-profile inferences remain model-dependent and unresolved cusps may escape detection.
- Inner mass distributions: Velocity-anisotropy degeneracy makes general determinations of cored versus cusped inner profiles model-dependent.Breaking the degeneracy requires additional information or sufficiently large datasets for full distribution-function modelling.
- Inner mass distributions: Small unresolved central cusps might remain undetected, whereas mean enclosed density and total mass within the kinematic-data radius are more robustly determined.Central density estimates are less robust because central spatial sampling is limited and an underlying profile must be adopted.
- Inner mass distributions: Cored mass distributions are preferred where independent information is available, and no dSph requires a steep cusp.This motivates adopting cored profiles for the broader analysis, while acknowledging that Jeans analyses are not assumption-independent.
- King-model dynamical analyses: King-model analysis is inappropriate for dSph galaxies because their dynamical ages lie 3–4 orders of magnitude outside the method’s validity range.A representative dSph-like system would require about 5 × 10^10 stars and luminosity ≳10^10L⊙ for relaxation within a Hubble age.
- Outer mass distributions: Outer dSph mass distributions remain poorly constrained because few outer tracers probe unreliable distribution-function limits and may be affected by Galactic tides.Observed outer kinematics include cold populations and flat dispersion profiles, while the dynamical state of some nearby dSphs remains uncertain.
4. Discussion and Implications
The synthesis finds a sharp structural and dynamical distinction between star clusters and dark-matter-dominated galaxies, with dSphs showing shallow central profiles and characteristic dark-matter densities. These properties constrain interpretations of dark matter and small-scale galaxy formation, while the stellar size bimodality remains unexplained.
- 30 pc and 120 pc mark a clear size gap: smaller systems are star clusters, while larger luminous systems are galaxies.
- At fixed stellar luminosity, galaxies have phase-space densities two to three orders of magnitude lower than star clusters and are embedded in extended dark-matter halos.
- α ≲ 0.5 describes the inferred inner density slopes in two dSphs, with α consistent with zero, indicating shallow central dark-matter profiles.
- 0.1 M⊙ pc−3 is the derived mean dark-matter density within one to two half-light radii for the adopted shallow-profile model; cusped models allow about 60 M⊙ pc−3 within 10 pc.
- Similar scale sizes, mass-profile form, and normalization explain why dSph galaxies have similar total dark mass within their optical radii.
- The inferred small-scale dark-matter properties could reduce discrepancies in satellite counts and core–cusp comparisons within ΛCDM simulations, but the stellar size bimodality remains an unresolved astrophysical puzzle.