Redefining the Missing Satellites Problem

TL;DR

This work reframes the Missing Satellites Problem by deriving robust constraints on the mass within a fixed radius, $M_{0.6}$, for nine Milky Way dwarf spheroidals using Jeans modeling and flexible anisotropy, circumventing the uncertainties of $V_{max}$. The observed $M_{0.6}$ function is roughly flat across $10^7$–$10^8$ M_sun, in contrast to the steeply rising subhalo $M_{0.6}$ function from the Via Lactea CDM simulation, which rules out a simple one-to-one mapping between the brightest dwarfs and the most massive subhalos. Incorporating a cosmology-informed prior on the $r_{max}$–$V_{max}$ relation, the authors obtain realistic $V_{max}$ bounds and show that MSP solutions based on reionization or pre-accretion characteristic halo masses remain viable. The $M_{0.6}$ framework thus provides a powerful avenue to probe the CDM small-scale power spectrum and to test warm dark matter scenarios with current and future MW dwarf observations.

Abstract

Numerical simulations of Milky-Way size Cold Dark Matter (CDM) halos predict a steeply rising mass function of small dark matter subhalos and a substructure count that greatly outnumbers the observed satellites of the Milky Way. Several proposed explanations exist, but detailed comparison between theory and observation in terms of the maximum circular velocity (Vmax) of the subhalos is hampered by the fact that Vmax for satellite halos is poorly constrained. We present comprehensive mass models for the well-known Milky Way dwarf satellites, and derive likelihood functions to show that their masses within 0.6 kpc (M_0.6) are strongly constrained by the present data. We show that the M_0.6 mass function of luminous satellite halos is flat between ~ 10^7 and 10^8 M_\odot. We use the ``Via Lactea'' N-body simulation to show that the M_0.6 mass function of CDM subhalos is steeply rising over this range. We rule out the hypothesis that the 11 well-known satellites of the Milky Way are hosted by the 11 most massive subhalos. We show that models where the brightest satellites correspond to the earliest forming subhalos or the most massive accreted objects both reproduce the observed mass function. A similar analysis with the newly-discovered dwarf satellites will further test these scenarios and provide powerful constraints on the CDM small-scale power spectrum and warm dark matter models.

Figures (6)

• Figure 1: The likelihood functions for the mass within 0.6 kpc for the nine dSphs, normalized to unity at the peak.
• Figure 2: The velocity dispersion for Ursa Minor as a function of radial distance, along with the model that maximizes the likelihood function.
• Figure 3: The mass within 0.6 kpc (upper) and the mass-to-light ratios within the King tidal radius (lower) for the Milky Way dSphs as a function of dwarf luminosity. The error-bars here are defined as the locations where the likelihoods fall to $40\%$ of the peak values (corresponding to $\sim 1 \sigma$ errors). The lines denote, from top to bottom, constant values of mass of $10^7, 10^8, 10^9 \, M_\odot$.
• Figure 4: The mass within 0.6 kpc versus the maximum circular velocity for the mass ranges of Via Lactea subhalos corresponding to the population of satellites we study.
• Figure 5: The $M_{0.6}$ mass function of Milky Way satellites and dark subhalos in the Via Lactea simulation. The red (short-dashed) curve is the total subhalo mass function from the simulation. The black (solid) curve is the median of the observed satellite mass function. The error-bars on the observed mass function represent the upper and lower limits on the number of configurations that occur with a probability of $> 10^{-3}$.