The Cold Dark Matter Halos of Local Group Dwarf Spheroidals

TL;DR

The paper develops a two-component dynamical model for Local Group dwarf spheroidals, treating stars as King-profile tracers embedded in NFW CDM halos. By exploiting the King–NFW degeneracy and cosmological V_max–r_max relations, it derives robust constraints on the dark halos, finding that the mass within the luminous region is nearly constant across dwarfs and that V_max is about three times the central stellar velocity dispersion (V_max ≈ 3 σ_p(0)). The results alleviate the CDM substructure (missing satellites) problem by showing that observed dwarfs inhabit relatively dense halos with peak velocities in the 17–35 km/s range, and they predict that M31 dwarfs should have higher velocity dispersions than MW dwarfs if their halos are similar. The study also demonstrates that tidal stripping must be extreme (≳90% mass loss) to noticeably affect the stellar kinematics, reinforcing the resilience of dSph stellar systems within their halos and providing a concrete observational test for the CDM paradigm in the Local Group.

Abstract

We examine the dynamics of stellar systems embedded within cold dark matter (CDM) halos in order to assess observational constraints on the dark matter content of Local Group dwarf spheroidals (dSphs). Our analysis shows that the total mass within the luminous radius is reasonably well constrained and approximately independent of the luminosity of the dwarf, highlighting the poor correspondence between luminosity and halo mass. This result implies that the average density of dark matter is substantially higher in physically small systems such as Draco and Sculptor than in larger systems such as Fornax. For example, our results imply that Draco formed in a halo 5 times more massive than Fornax's despite being roughly 70 times fainter. Stellar velocity dispersion profiles, sigma_p(R), provide further constraints; flat sigma_p(R) profiles imply that stars are deeply embedded within their cold dark matter halos and so quite resilient to tidal disruption. We estimate that halos would need to lose more than 90% of their original mass before tides begin affecting the kinematics of stars. We estimate that V_max is about 3 times higher than the central velocity dispersion of the stars, which alleviates significantly the CDM ``substructure crisis''. We use these results to interpret the size differences between the M31 and Milky Way (MW) dSph population. Our modeling indicates that this difference should be reflected in their kinematics, and predicts that M31 dwarfs should have velocity dispersions up to a factor of ~ 2 higher than their MW counterparts. This CDM-motivated prediction may be verified with present observational capabilities.

Figures (11)

• Figure 1: Stellar surface density profile of King models with the same "concentration", $R_t/R_c=10$, and various degrees of spatial segregation relative to the dark matter. The segregation is measured by the ratio $R_c/r_s$, where $r_s$ is the scale radius of the NFW profile (shown by a dotted line in the figure) and $R_c$ is the stellar core radius, denoted with a dot in each profile. All radii have been scaled to the scale radius of the NFW profile. Units of surface density are arbitrary, since stars are assumed to contribute negligibly to the potential of the system.
• Figure 2: Stellar projected velocity dispersion profiles normalized to the halo maximum circular velocity for different values of $R_c/r_s$. The dotted line represents the projected velocity dispersion profile of the NFW halo. The solid circles indicate the core radius of the King model. Note that both the central velocity dispersion of the stars, as well as the shape of the velocity dispersion profile, depend on the degree of spatial segregation between stars and dark matter (quantified here by the ratio $R_c/r_s$).
• Figure 3: The King-NFW degeneracy. The thick lines show the halo peak circular velocity, $V_{\rm max}$, in units of the central velocity dispersion, and the radius of the peak, $r_{\rm max}$, in units of the King model core radius. Solid, dotted and dashed lines denote different King-model concentrations ($R_t/R_c$). Any NFW halo whose circular velocity peaks along this curve is consistent with the King model structure and kinematics. A few of these NFW models are shown for illustration by the thin curves. Note that all these NFW models cross each other at approximately $R\simeq R_c$ and $V_c \simeq 1.2 \, \sigma_p(0)$. This implies that, given our assumptions, the mass within the core radius of the stellar component is robustly constrained to be $M(R_c)\sim 1.44 \, R_c \,\sigma_p^2(0)/G$.
• Figure 4: Each panel shows, for the 8 Milky Way dwarfs in our sample, the King-NFW degeneracy (curved line), as well as the predictions for $\Lambda$CDM cosmogony (set of straight lines). Only NFW halos at the intersection of both sets of curves (marked by a red symbol) are consistent with both cosmological constraints and the structure and kinematics of the dwarfs. The three sets of cosmological curves correspond to NFW halos identified at various redshifts; we adopt the $z=0$ models here, but note that our conclusions are unlikely to be severely affected by this choice.
• Figure 5: Circular velocity profiles of NFW halo models consistent with the observed structure and kinematics of the stars and with the $\Lambda$CDM cosmological constraints. Blue symbols (on the left) denote the circular velocity at the core radius of each dwarf, where it is best constrained. Labels rank, from top to bottom, all dwarfs in decreasing order of halo mass.