The Observed properties of Dark Matter on small spatial scales

TL;DR

Gilmore et al. synthesize photometric and kinematic data for the most DM-dominated Local Group dwarfs and identify a robust size dichotomy between star clusters ($< 30$ pc) and dwarf galaxies ($> 120$ pc). They argue that dSph halos typically host cored DM density distributions with core scales $\gtrsim 100$ pc and a narrow range of central densities, yielding a nearly universal DM density within the stellar extent (≈$0.1\,M_\odot\,\mathrm{pc}^{-3}$) and a characteristic edge circular speed of about $15$ km s$^{-1}$. The total DM mass within the optical radii is similar across dSphs (the Mateo relation), and while cusps remain possible in some models, the data in well-studied systems prefer cores. These results have important implications for ΛCDM small-scale structure and DM physics, suggesting a small-scale power cutoff near $\sim 100$ pc and favoring light or self-interacting DM candidates over TeV-scale WIMPs.

Abstract

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.

Figures (5)

• Figure 1: Absolute magnitude ${\rm M_V}$ vs (logarithmic) half-light radius for well-studied stellar systems. The filled symbols are objects classed as galaxies, the open symbols and asterisks objects classed as star clusters of various types. Red colours indicate objects associated with the Milky Way Galaxy, blue colours are objects associated with M31 and green colours indicate more distant objects. Red filled triangles are the well-known dSph, red filled circles are those recently discovered, with in each case the photometry listed in Table 1 being adopted (references are given in the notes). The least-luminous M31 dSph (blue pentagons) are from Martin etal (2006), and have $\sim50\%$ uncertainties. Ringed circles highlight the probable star clusters Segue 1 and Willman 1, and the object ComaBer. Open red circles are Milky Way globular clusters, from the compilation of Harris (1996), except the two largest Galactic globular clusters (Pal 5 and Pal 14) which use the most recent data from Hilker (2006). The largest globular clusters in M31 are shown as blue open squares, with data from Mackey et al. (2006). Green pentagons are globular clusters in NGC 5128 (the peculiar elliptical galaxy Cen A; Harris et al. 2002, 2006; Gomez et al. 2006). Green crosses represent nuclear star clusters in a range of external galaxies (Bastian et al. 2006), open green triangles are young massive star clusters (Bastian et al. 2006; Seth et al. 2006). Asterisks are Ultra Compact Dwarfs (UCD) in the Fornax cluster of galaxies (De Propris et al. 2005; Mieske et al. 2002; Drinkwater et al. 2003), and in the Virgo cluster (Hasegan et al. 2005). For UCD3* in Fornax we adopt the most recent core measurement (22pc) by Drinkwater et al. 2003). Not shown individually are the "Faint Fluffy" star clusters found in the disks of lenticular galaxies (Brodie & Larsen 2002) which have absolute magnitudes M$_V\sim -7$, and sizes in the range ten to twenty pc (1.0-1.3 in log(r$_h$)). Sgr is not shown. Half-light size definitions and determinations are discussed further in the text.
• Figure 2: Observed line-of-sight velocity dispersion profiles for six dSph galaxies. Also shown (lower right) is the model predicted dispersion profile for a Plummer model in which mass follows light. The lower left panel shows the observed velocity dispersion profile for the globular cluster Omega Cen from Seitzer83. The similarity between the Plummer 'mass follows light' model and the data for Omega Cen is apparent, with a monotonic decrease in dispersion from a central maximum. In contrast, the dSph galaxies do not have their maximum dispersion value at the centre, and retain relatively high dispersions at large radii, indicating extended (dark) mass distributions.
• Figure 3: Functional fits to the surface brightness profile (top) and velocity dispersion profile (bottom) of the Draco (left panels) and Carina (right panels) dSphs used to derive mass profiles based on Jeans equations. Similar fits are used for the remaining four dSphs presented in Figure 4.
• Figure 4: Derived inner mass distributions from isotropic Jeans' equation analyses for six dSph galaxies. The modelling is reliable in each case out to radii of log (r)kpc$\sim0.5$. The unphysical behaviour at larger radii is explained in the text. The general similarity of the inner mass profiles is striking, as is their shallow profile, and their similar central mass densities. Also shown is an $r^{-1}$ density profile, predicted by many CDM numerical simulations (eg Navarro, Frenk & White 1997). The individual dynamical analyses are described in full as follows: Ursa Minor (W04); Draco (W04); LeoII (Koch07); LeoI (Koch06); Carina (W06a, and Wilkinson et al in preparation); Sextans (Kleyna04).
• Figure 5: An updated Mateo plot. Mass-to-light ratios are plotted versus absolute magnitudes for Local Group dwarf galaxies, following a style suggested by Mateo [Mateo etal (1993);(1998, his fig 9, lower panel)]. The solid line is the relation for a constant mass (dark) halo. The modern data shown here extend the original relation by three magnitudes in luminosity, and an order of magnitude in mass-to-light ratio, while reducing the scatter by an order of magnitude. Data are from the tables in the text. Values for Scl, AndII, AndIX, UMa and Boo are based on small kinematic samples, and are less certain than are the results for the other galaxies. We explain this correlation as a consequence of the characteristic minimum galaxy scale size shown in Figure 1 convolved with the narrow range of mass profiles and mean dark matter densities shown in Figure 4.