Observed Properties of Dark Matter: dynamical studies of dSph galaxies

TL;DR

This paper investigates how dark matter is distributed in Milky Way dwarf spheroidal galaxies by leveraging stellar kinematics as collisionless tracers. It combines Jeans-equation based mass estimates with full distribution-function modelling to overcome degeneracies between mass profile and orbital anisotropy, using Plummer-light profiles and multi-component DF frameworks. The main findings indicate predominantly core-like inner DM profiles with central densities of about $\sim 10$–$20\,\mathrm{GeV\,cm^{-3}}$, and a nearly constant enclosed DM mass of $\sim 4$–$5\times 10^{7} M_{\odot}$ within the stellar extent across dwarfs, with higher $M/L_V$ in the faintest systems. These results have significant implications for the nature of DM and the formation of small-scale structure, and they motivate further dynamical studies of newly discovered ultra-faint dSphs to test the generality of the trends.

Abstract

The Milky Way satellite dwarf spheroidal (dSph) galaxies are the smallest dark matter dominated systems in the universe. We have underway dynamical studies of the dSph to quantify the shortest scale lengths on which Dark Matter is distributed, the range of Dark Matter central densities, and the density profile(s) of DM on small scales. Current results suggest some surprises: the central DM density profile is typically cored, not cusped, with scale sizes never less than a few hundred pc; the central densities are typically 10-20 GeV/cc; no galaxy is found with a dark mass halo less massive than ~5.10^7 M_sun. We are discovering many more dSphs, which we are analysing to test the generality of these results.

Figures (5)

• Figure 1: Draco surface brightness profile, with a fitted Plummer model, and the observed line of sight velocity dispersion profile, from K01.
• Figure 2: An illustration of the possible effects of stellar orbital anistropy variations on kinematic modelling, from W04.
• Figure 3: Derived inner mass distributions from Jeans' eqn analyses for four dSph galaxies. Also shown is a predicted $r^{-1}$ density profile. 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 four inner mass profiles is striking.
• Figure 4: TOP: Result of search for kinematic sub-populations in UMi. Coutours are linearly spaced stellar isopleths; the second peak of UMi's stellar population is visible at ${\rm RA}=12^\prime, {\rm Dec}=8^\prime$ relative to UMi's center. Gray stars are UMi RGB member stars with measured velocities. The dots represent points where a model with a kinematically cold sub-population is at least 1000 times more likely than a model composed of a single $8.8\,\rm km\,s^{-1}$ Gaussian. BOTTOM: Simulation of an unbound clump in a dark matter halo. The halo has a density law $\rho(r)\propto(a^2+r^2)^{-1/2}$; the time $t$ is in units of Gyr. Top panel: a clump in a cored halo with $a=0.85$ persists for a Hubble time because the potential is nearly harmonic. Bottom panel: a clump in a cusped potential ($a=0$) disrupts in less than 1 Gyr. The histograms at the upper right corner of each snapshot show the distribution of total velocity $v=(v_x^2+v_y^2+v_z^2)^{1/2}$; tick marks are spaced 1 $\rm km\,s^{-2}$ apart. The stars in a cored halo remain coherent in velocity as well as in position. From K03.
• Figure 5: Mass to light ratios vs galaxy absolute V magnitude for some Local Group dSph galaxies. The solid curve shows the relation expected if all the dSph galaxies contain about $4\times10^7$ solar masses of dark matter interior to their stellar distributions.