Not too big, not too small: the dark halos of the dwarf spheroidals in the Milky Way

TL;DR

This study reevaluates the compatibility of LCDM subhalos with the Milky Way’s dwarf spheroidal satellites by combining Aquarius dark-matter halos with a semi-analytic galaxy formation model. It finds that subhalo mass profiles are better described by Einasto profiles with shape parameter $\alpha$ typically in $0.2$–$0.5$, rather than the standard NFW form, and that tidal stripping drives higher $\alpha$, aligning simulated halos with observed dSph kinematics. When the Milky Way’s mass is set to around $M_{\rm MW} \approx 8\times10^{11}\,M_\odot$, the predicted satellites reproduce the observed mass within the half-light radius and circular-velocity constraints, and no missing population of massive subhalos is required; this also extends to the dwarf systems of M31. The results underscore the sensitivity of satellite statistics to host halo mass and dynamical history, supporting LCDM predictions at the dwarf-galaxy scale while highlighting substantial stochasticity in satellite counts.

Abstract

We present a new analysis of the Aquarius simulations done in combination with a semi-analytic galaxy formation model. Our goal is to establish whether the subhalos present in LCDM simulations of Milky Way-like systems could host the dwarf spheroidal (dSph) satellites of our Galaxy. Our analysis shows that, contrary to what has been assumed in most previous work, the mass profiles of subhalos are generally not well fit by NFW models but that Einasto profiles are preferred. We find that for shape parameters alpha = 0.2 - 0.5 and Vmax = 10 - 30 km/s there is very good correspondence with the observational constraints obtained for the nine brightest dSph of the Milky Way. However, to explain the internal dynamics of these systems as well as the number of objects of a given circular velocity the total mass of the Milky Way should be ~ 8x10^11 Msun, a value that is in agreement with many recent determinations, and at the low mass end of the range explored by the Aquarius simulations. Our simulations show important scatter in the number of bright satellites, even when the Aquarius Milky Way-like hosts are scaled to a common mass, and we find no evidence for a missing population of massive subhalos in the Galaxy. This conclusion is also supported when we examine the dynamics of the satellites of M31.

Figures (5)

• Figure 1: Spherically averaged circular velocity profiles $v_c^2 (r) = Gm(r)/r$ for the subhalos that are predicted to host stars by our semi-analytic model. Velocities have been scaled to $v_{-2}^2 \equiv 4\pi G \rho_{-2} r_{-2}^2$. As already reported in Stoehr2002 the velocity profiles of subhalos tend to be more narrowly peaked than in the NFW form. The sample of subhalos has been grouped according to the best fit value of $\alpha$, and plotted with different colors. The number of objects in each $\alpha$-bin is 154. An Einasto profile with the average value of $\alpha$ for each bin is overplotted, while the median $v_{\rm max}$ in each $\alpha$-bin is 13.6, 20.3 and 27 km s$^{-1}$ from left to right, and the $v_{\rm max}$ ranges given by the 68% percentiles for each panel are (10, 26.2), (15.9, 26.2) and (20.5, 44.8) km s$^{-1}$, respectively. The residuals from the best-Einasto (NFW) fits are shown in the middle (bottom) panel, and in general are consistent with zero for the Einasto profile and exhibit systematic deviations from zero for the NFW case. In the column $\langle\alpha\rangle = 0.24$ both models yield similar results, which is naturally expected since the NFW equivalent is reached with $\alpha=0.22$. The systematic change of $r_{\rm conv}/r_{-2}$ with $\alpha$ is a consequence of setting the convergence parameter $\kappa$ to a fixed value.
• Figure 2: Constraints for the MW's dwarf spheroidals using NFW (gray band) and Einasto (blue curves) profiles. Points are the results from the six Aquarius halos, colored according to their predicted luminosity and sized using the fraction of mass retained after infall. The cyan point at $v_{\rm max} \sim 50$ km s$^{-1}$ represents a subhalo that underwent a merger with another substructure after infall, therefore increasing its mass. The black dots correspond to isolated halos in the simulations.
• Figure 3: Luminosity function for the original Aquarius simulations (top) and once they have scaled to the mass of Aq-B-2 (bottom). For reference we have added the luminosity function derived by Koposov2008 for the Milky Way. This takes into account incompleteness issues for satellites with $M_V > -11$ and, for brighter objects it considers the average for the Milky Way and M31. Although in the scaled version the simulations follow much more closely the observations, some differences remain in the number of satellites of a given luminosity.
• Figure 4: Circular velocity profiles for scaled subhalos in three different luminosity bins, following the absolute magnitudes of the nine classical dSph of the Milky Way. The subhalos are colored according to the host halo they are associated with. This figure shows that the number of satellites per bin, as well as the velocities profiles are consistent with the measurements obtained for the dSph.
• Figure 5: Circular velocities for the subhalos present in halo Aq-C-2 associated to satellites with luminosities $M_{V}\leq -12$. The symbols represent observations of the satellites of M31 in the same luminosity range. Open symbols represent the estimated dark matter contribution to $v_c(r)$ when the decomposition is available (see text for details).