Notes on the Missing Satellites Problem

Abstract

The Missing Satellites Problem (MSP) broadly refers to the overabundance of predicted Cold Dark Matter (CDM) subhalos compared to satellite galaxies known to exist in the Local Group. The most popular interpretation of the MSP is that the smallest dark matter halos in the universe are extremely inefficient at forming stars. The question from that standpoint is to identify the feedback source that makes small halos dark and to identify any obvious mass scale where the truncation in the efficiency of galaxy formation occurs. Among the most exciting developments in near-field cosmology in recent years is the discovery of a new population satellite galaxies orbiting the Milky Way and M31. Wide field, resolved star surveys have more than doubled the dwarf satellite count in less than a decade, revealing a population of ultrafaint galaxies that are less luminous that some star clusters. For the first time, there are empirical reasons to believe that there really are missing satellite galaxies in the Local Group, lurking just beyond our ability to detect them, or simply inhabiting a region of the sky that has yet to have been surveyed. Both kinematic studies and completeness-correction studies seem to point to a characteristic potential well depth for satellite subhalos that is quite close to the mass scale where photoionization and atomic cooling should limit galaxy formation. Among the more pressing problems associated with this interpretation is to understand the selection biases that limit our ability to detect the lowest mass galaxies. The least massive satellite halos are likely to host stealth galaxies with very-low surface brightness and this may be an important limitation in the hunt for low-mass fossils from the epoch of reionization.

Figures (14)

• Figure 1.1: Relationship between stellar mass $M_*$ and halo mass $M_{\rm h}$ as quantified by the abundance matching analysis of Behroozi et al. (2010), which includes uncertainties associated with observed stellar mass functions and possible scatter in the relationship between halo mass and stellar mass (shaded band). The lower dashed line is the extrapolated relationship that results from assuming the stellar mass function continues as a power law for $M_* < 10^{8.5} M_{\odot}$, using data from the full SDSS (Li & White 2009). The upper dashed line is extrapolated under the assumption that the slope of the stellar mass function has an upturn at low masses to $\alpha = -1.8$, as found by Baldry, Glazebrook, & Driver (2008).
• Figure 1.2: Cumulative subhalo $V_{\rm max}$ function within $R_{h} \simeq 400$ kpc for the three highest resolution simulations of Milky-Way size halos from Kuhlen (2010, private communication), shown here relative to the circular velocity of each host at its outer radius $V_{\rm h} \simeq 140 \, {\rm km}\,{\rm s}^{-1}$. The solid red line shows VL II subhalos from Diemand et al. (2008), the dashed black line shows Aq-A subhalos from Springel et al. (2008) and the solid blue line shows GHALO subhalos from Stadel et al. (2009). The shaded band provides an estimate of halo-to-halo scatter from a series of lower resolution halos (Aq suite, Springel et al. 2008). The small normalization difference between the GHALO/VL II and Aq halos is likely a result of their having different power spectrum normalizations (Zentner & Bullock 2003). The most recent determination of the normalization WMAP-7 (Komatsu et al. 2010) is intermediate between the adopted normalizations of the simulations shown here.
• Figure 1.3: Illustrative sketch of the expected cumulative CDM substructure abundance within the Milky Way's halo. The line is Equation \ref{['eq:nofv']} for a host halo of circular velocity $V_{\rm h} = 140 \, {\rm km}\,{\rm s}^{-1}$ at $R_{\rm h} = 400$ kpc (for which we would expect a maximum circular velocity of about 200 ${\rm km}\,{\rm s}^{-1}$). The line becomes dashed where we are extrapolating the power-law beyond the resolving power of state-of-the-art numerical simulations. The vertical red band provides an indication of where we expect this power-law to break for popular CDM dark matter candidates. The lower horizontal dashed line shows the number of Milky Way satellite galaxies known while the upper dashed line is an estimate of the total number of satellite galaxies that exist within 400 kpc of the Milky Way corrected for luminosity-bias and sky coverage limitations of current surveys (Tollerud et al. 2008). The fact that the upper horizontal line intersects the edge of the vertical blue band at about the location of the CDM prediction is quite encouraging for the theory.
• Figure 1.4: Left: The cumulative mass profile generated by analyzing the Carina dSph using four different constant velocity dispersion anisotropies. The lines represent the median cumulative mass value from the likelihood as a function of physical radius. Right: The cumulative mass profile of the same galaxy, where the black line represents the median mass from our full mass likelihood (which allows for a radially varying anisotropy). The different shades represent the inner two confidence intervals (68% and 95%). The green dot-dashed line represents the contribution of mass from the stars, assuming a stellar V-band mass-to-light ratio of 3 $M_{\odot} / L_{\odot}$. This figure is from Wolf et al. (2010).
• Figure 1.5: Observed circular velocities $V_c(r_{1/2})$ plotted versus $r_{1/2}$ for each of the Milky Way dSph galaxies discussed in Wolf et al. (2010). The circular velocity curve values for the data were determined using Equation \ref{['eq:vc']}. For reference, we plot $V(r)$ rotation curves for NFW subhalos obeying a median$V_{\rm max} - r_{\rm max}$ relationship given by Equation \ref{['eq:vm']}. Each curve is labeled by its $V_{\rm max}$ value (assumed to be in ${\rm km}\,{\rm s}^{-1}$). Dwarf galaxy points are color-coded by their luminosities (see legend). Notice that the least luminous dwarfs (red) seem to fall along similar $V(r)$ curves as the most luminous dwarfs (green).