Missing Satellites Problem: Completeness Corrections to the Number of Satellite Galaxies in the Milky Way are Consistent with Cold Dark Matter Predictions

A critical challenge to the cold dark matter (CDM) paradigm is that there are fewer satellites observed around the Milky Way than found in simulations of dark matter substructure. We show that there is a match between the observed satellite counts corrected by the detection efficiency of the Sloan Digital Sky Survey (for luminosities $L\gtrsim 340L_{\odot }$) and the number of luminous satellites predicted by CDM, assuming an empirical relation between stellar mass and halo mass. The “missing satellites problem,” cast in terms of number counts, is thus solved. We also show that warm dark matter models with a thermal relic mass smaller than 4 keV are in tension with satellite counts, putting pressure on the sterile neutrino interpretation of recent x-ray observations. Importantly, the total number of Milky Way satellites depends sensitively on the spatial distribution of satellites, possibly leading to a “too many satellites” problem. Measurements of completely dark halos below $10^8{M}_{\odot }$, achievable with substructure lensing and stellar stream perturbations, are the next frontier for tests of CDM.

Figure 1

Normalized radial distributions. The cumulative number of satellites within radius $r$, normalized to the total number of satellites at $R_{\mathrm{vir}}=300\mathrm{kpc}$, is shown. Distributions marked by dashed lines are expected when satellites survive extreme tidal stripping. The solid red lines are our fiducial radial distributions, matching the MW classical satellites. The dotted black line depicts the latter distribution depleted by Ref. [28]’s tidal stripping model. See text for details.

Figure 2

The number of completeness corrected luminous satellites (left) and the infall mass of the lowest mass subhalo hosting a $L>340L_{\odot }$ galaxy (right). Colors match those in Fig. 1; the dark red denotes results based on D17. The light colored bands denote the uncertainty due to anisotropy (based on Ref. [15]). Left: The gray-shaded region shows the predicted number of luminous satellites expected for the MW based on the calculation described below [Eqs. (7)–(9)]. If the completeness-corrected count falls within these bounds, there is no MSP. Right: The width of the dark bands is set by the uncertainty on the MW mass, $(1–2)\times {10}^{12}{M}_{\odot }$. The light bands denote uncertainties due to anisotropy. The bottom axis shows the subhalo mass at infall, and the top axis shows the average corresponding subhalo mass today [90].

Figure 3

The number of luminous (solid) and total (dashed) subhalos allowed by CDM and WDM mass functions for a given lower bound on the lowest mass subhalo, assuming a MW mass of $1.5\times {10}^{12}{M}_{\odot }$. The number of luminous subhalos is modeled as in D17, assuming a reionization redshift $z_{\text{re}}=9.3$ [110]. The grey band shows SHMH predictions for the infall mass of Segue I.