Observations indicate that the Milky Way's known dSph satellites have masses 105 ≲ M(Rh) / M⊙ ≲ 107 and that dark matter dominates their internal kinematics at all radii, M / LV ≳ 10[M / LV]⊙ (Section 4.1). Current observations also provide direct and/or indirect constraints on the internal distributions of dark matter in three dSphs: Fornax, Sculptor and Ursa Minor (Section 4.2). For all three, the available evidence indicates central ‘cores’ of constant density on scales of a few hundred pc. 11 Taken at face value, these basic results have implications for broader areas of physics.
Observations of structure on large scales (e.g., as inferred from redshift surveys and anisotropy of the cosmic microwave background radiation) seem to require a significant contribution to the mass budget from non-baryonic dark matter, ΩDM ∼ 0.22 (e.g, Bennett et al., 2003, Spergel et al., 2003). The ‘cold dark matter’ (CDM) cosmological paradigm is built on the hypothesis that the dark matter consists of fundamental particles that act like a collisionless gas after decoupling from radiation at non-relativistic speeds shortly after the Big Bang. Small cross sections and low thermal velocities allow CDM structure to form and survive at high densities in small volumes, thereby enabling the growth of structure on small scales in the early universe.
Calculations of the matter power spectrum associated with popular ‘weakly interacting massive particle’ (WIMP) candidates for the dark matter (e.g., neutralinos with mass mχ ≳ 10 GeV) indicate P(k) ∝ k−3 at small scales until collisional damping and free streaming finally cause an exponential decline on sub-parsec (co-moving) scales (Green et al., 2004, Diemand et al., 2005a). The corresponding halo mass function would be approximately dN(M) / dM ∝ M−α with α ∼ 1.9, and a galaxy like the Milky Way would host roughly ∼ 1015 satellites in the form of individual, self-bound dark matter ‘subhalos’, ‘sub-subhalos’, ..., and ‘microhalos’ with masses ≳ 10−6 M⊙ (Hofmann et al., 2001, Diemand et al., 2005a, Springel et al., 2008).
Observational requirements derived from the current census of Milky Way satellites seem rather modest in this context. A viable dark matter particle needs to accommodate the formation and survival of only a few tens (or hundreds when correcting for incompleteness of sky surveys, Koposov et al. (2008), Tollerud et al. (2008)) of dark matter halos with masses M ≳ 105 M⊙ (Section 4) around the Milky Way. These constraints allow for significantly less massive, ‘warmer’ particle candidates (e.g., the sterile neutrino, Dodelson & Widrow (1994); see recent reviews and discussion by, e.g., Abazajian & Koushiappas (2006), Boyanovsky (2008), Boyarsky et al. (2009b), Kusenko (2009)) whose longer free-streaming lengths might naturally truncate the matter power spectrum at scales more similar to those that characterise the smallest galaxies (Gilmore et al., 2007, Bode et al., 2001, Macciò & Fontanot, 2010, Polisensky & Ricotti, 2011, Lovell et al., 2012).
Thus dark matter particle candidates and associated cosmologies can be classified in practicial terms according to whether the particles’ free streaming plays a significant role in galaxy formation (e.g., Bœhm et al., 2001). For sufficiently massive and ‘cold’ particles it does not, and other physical processes must be invoked to explain the suppression and/or truncation of galaxy formation in low-mass halos (e.g., Klypin et al., 1999, Koposov et al., 2009, Li et al., 2010, Macciò et al., 2010, Kravtsov, 2010, Font et al., 2011). The negligible thermal velocities invoked for ‘standard’ CDM particles also imply that N-body simulations can track the growth of structure accurately with relatively few particles, making CDM cosmological simulations the simplest, fastest and most widely practiced kind.
Cosmological simulations demonstrate that if gravitational interactions between standard CDM particles dominate the formation and evolution of galactic structure, then galaxies ought to be embedded in dark matter halos that have central cusps characterised by limr → 0 ρ(r) ∝ r−γ, with γ ≳ 1 (e.g., Dubinski & Carlberg, 1991, Navarro, Frenk & White, 1996, 1997, Moore et al., 1998, Klypin et al., 2001, Diemand et al., 2005b, Springel et al., 2008). Observations indicate that most individual galaxies with suitable measurements are not embedded in such halos. Instead, rotation curves of spiral and low surface brightness galaxies tend to favor dark matter halos with resolved ‘cores’ (γ ∼ 0) of constant density (e.g., Moore 1994, Flores & Primack 1994, de Blok & McGaugh 1997, Salucci & Burkert 2000, McGaugh et al. 2001, Simon et al. 2005, Kuzio de Naray et al. 2006, 2008, de Blok 2010, and references therein)). These results imply that (standard) gravitational interactions between CDM particles do not always dominate the formation and evolution of galactic structure.
Indeed galaxies contain baryons prone to interact via forces other than gravity. Many hydrodynamical simulations demonstrate that various poorly-understood baryon-physical mechanisms might influence the structure of galactic CDM halos (e.g., Blumenthal et al., 1986, Navarro et al., 1996, El-Zant et al., 2001, Gnedin et al., 2004, Tonini et al., 2006, Romano-Díaz et al., 2009, Del Popolo, 2010, Governato et al., 2010, Pontzen & Governato, 2011, Governato et al., 2012). Insofar as their baryons are dynamically negligible, dSphs and low surface brightness galaxies enable the most direct comparisons to structures formed in CDM-only simulations. In this context the available evidence against cusped dark matter halos in Fornax, Sculptor and Ursa Minor (Section 4.2) becomes particularly relevant: the viability of standard CDM now requires that baryon-driven mechanisms can have reduced the central dark matter densities in these galaxies to ρ0 ≳ 5 × 107 M⊙ kpc−3 while leaving behind stellar populations with low luminosities 105 ≲ LV / LV,⊙ ≲ 107 and central surface brightnesses 23 ≲ µ0 / (mag/arcsec2) ≲ 25. 12
Recent work identifies several mechanisms that might accomplish this feat on dSph scales by invoking either the dynamical coupling of the dark matter to energetic baryonic outflows (e.g., Read & Gilmore 2005, Mashchenko et al. 2006, 2008, de Souza et al. 2011) or the transfer of energy/angular momentum to dark matter from massive infalling objects (e.g., Sánchez-Salcedo et al. 2006, Goerdt et al. 2006, 2010, Cole et al. 2011). Hydrodynamical simulations by Sawala et al. (2010) and Parry et al. (2011) indicate that the former category of solutions has difficulty reproducing other dSph observables — specifically, star formation histories as well as luminosity functions and metallicity distributions. The latter category of solutions is difficult to evaluate observationally, as the evidence can literally be destroyed (e.g., by tidal disruption); furthermore it seems unlikely that such infall mechanisms generate cores of sufficient size. 13 Alternatively, cosmological simulations that consider ‘warmer’ particle candidates demonstrate that the associated suppression of small-scale power can naturally (i.e., without invoking baryon physics) produce halos with large cores; however, such scenarios seem to require fine tuning of the relative contributions from various production mechanisms in order to reproduce simultaneously the number of observed MW dSphs (Polisensky & Ricotti, 2011, Macciò et al., 2012a, b).
In any case, the emerging challenge for the standard CDM paradigm is not that empirical evidence against cusped dark matter halos necessarily rules out the hypothesis that CDM particles constitute the dark matter. The poorly understood complexities of baryon physics — along with the freedom to invoke other processes, e.g., self-scattering of CDM particles (Spergel & Steinhardt, 2000, Loeb & Weiner, 2011, Vogelsberger et al., 2012) — leave sufficient flexibility for CDM to be rendered consistent with virtually any realistic observation of galactic structure. In fact that is the problem. CDM escapes falsification of perhaps its most famous prediction only by withdrawing the prediction. While this circumstance does not imply that CDM is incorrect, it does mean that CDM currently fails to make accurate predictions regarding the stellar dynamics of galaxies, a primary piece of evidence for dark matter in the first place. In this context a decisive outcome favorable to standard CDM seems to require the detection of either 1) gravitational interactions involving dark matter halos on sub-galactic scales (e.g., via microlensing or perturbations of loosely bound luminous structure) or 2) nongravitational interactions involving cold dark matter particles.
It has long been recognised that the small sizes and large mass densities of dSphs place strong constraints on the particle nature of dark matter. For example, Liouville's theorem requires that the phase space densities of light, neutral lepton species do not increase after decoupling from radiation in the early Universe. Tremaine & Gunn (1979) point out that this constraint, combined with the necessity that Ων < Ωmatter, places a conservative upper limit on the neutrino mass that is summarily violated by lower limits from phase space densities inferred for galaxy halos. Therefore neutrinos are not the dark matter in galaxies. This exclusion is most evident on small scales, where small volumes demand heavy particles in order to satisfy phase-space requirements.
For example, using Aaronson's (1983) initial measurement of Draco's velocity dispersion, Lin & Faber (1983) derive a lower limit of mν ≳ 500 eV. Lake (1989) points out that this constraint is sensitive to the dubious assumption that mass follows light (Section 4.1.1). Gerhard & Spergel (1992) strengthen the argument by turning it around, noting that for more viable neutrino masses of mν ∼ 30 eV, the core radii of dSph halos would need to be unrealistically large (≳ 10 kpc) to accommodate model-independent lower limits of ρ0 ≳ 0.05M⊙ pc−3 (Pryor & Kormendy, 1990) on their central densities. Generalising the phase-space argument of Tremaine & Gunn (1979) to relativistically decoupled warm dark matter candidates, Dalcanton & Hogan (2001) show that of all galaxies, dSphs provide the most stringent limits, mχ ≳ 700 eV and mχ ≳ 300 eV for thermal and degenerate fermions, respectively. Most recently and more specifically, Boyarsky et al. (2009a) use phase-space arguments to conclude that mχ ≳ 1.7 keV if the dark matter consists of sterile neutrinos produced via non-resonant mixing with active neutrinos.
Any positive identification of a dark matter particle will require the detection of its non-gravitational interactions. Experiments at the Large Hadron Collider might find evidence for such interactions, as might the various experiments designed to detect directly the scattering of dark matter particles in Earth's orbital path. Alternatively, high-energy photons might be released if dark matter self-annihilates (Gunn et al., 1978, Stecker, 1978) or decays (Pal & Wolfenstein, 1982, Boyarsky et al., 2006, Kusenko, 2006), providing an opportunity for indirect detection.
Their large mass-to-light ratios, low astrophysical backgrounds and close proximities make the Milky Way's dSph satellites popular targets in the search for annihilation and/or decay products (e.g., Evans et al., 2004, Strigari et al., 2008b, Kuhlen, 2010). For annihilation, the differential γ-ray flux (units cm−2 s−1 sr−1 GeV−1) received on Earth in solid angle ΔΩ is given by
 |
(17) |
where mχ is the particle mass, ⟨σ v⟩ is the (velocity-averaged) cross section, dNγ / dEγ is the energy spectrum of products and
 |
(18) |
This ‘J-factor’ represents the astrophysical contribution to the signal and is specified by the integral of the squared dark matter density, ρ2(l, Ω), over line of sight l and solid angle Ω. The equation for the flux due to decay events is similar, except that the integral is taken over the dark matter density raised only to the first power. Published constraints on J come directly from constraints on ρ(r) obtained in parametric Jeans analyses of the sort described in Section 4.1.3 and demonstrated in Figure 18 (e.g., Strigari et al., 2007b, Martinez et al., 2009, Charbonnier et al., 2011).
At present, dSph surveys conducted with atmospheric Cherenkov telescopes (e.g., Pieri et al., 2009, Essig et al., 2009, H. E. S. S. Collaboration et al., 2011, the VERITAS collaboration: Vivier et al., 2011, Aleksić et al., 2011), x-ray (e.g., Boyarsky et al., 2007, Loewenstein et al., 2009, Riemer-Sørensen & Hansen, 2009, Loewenstein & Kusenko, 2010, Boyarsky et al., 2010b, Loewenstein & Kusenko, 2012) and gamma-ray telescopes (e.g., Abdo et al., 2010, Scott et al., 2010, Ackermann et al., 2011) yield no unambiguous detections. 14 From Equation 17, upper limits on photon flux translate into upper limits on the cross section ⟨σ v⟩ for a given particle mass and annihilation channel. For example, Figure 22 plots 95% upper limits on ⟨σ v⟩ derived from Fermi-LAT observations of Milky Way dSphs, based on two years of data from the planned five-year mission (Geringer-Sameth & Koushiappas (2011), Ackermann et al. (2011)). Dotted lines at ⟨σ v⟩ ∼ 3 × 10−26 cm3s−1 mark the ‘generic’ cross section expected for WIMPs with mass mχ ∼ 0.1−1 TeV (e.g., Jungman et al., 1996, Feng, 2010). WIMPs having this combination of mass and cross section would have decoupled from radiation with relic abundance ΩWIMP ∼ 0.2, the value cosmology requires of the dark matter (a coincidence sometimes referred to as the ‘WIMP miracle’). For particle masses below mχ ≲100 GeV, the combination of kinematic and high-energy data available for dSphs is now encroaching upon the cross section most readily associated with WIMPs. 15 Over the next decade, searches for dark matter and/or its byproducts will intensify with large-scale efforts at existing facilities and with new instrumentation that will provide unprecedented sensitivity (e.g., CTA Consortium, 2010).
 |
Figure 22. Exclusion of WIMP self-annihilation cross sections, based on Fermi-LAT non-detections (2-year data) of gamma-rays in the Milky Way's dSph satellites (reprinted with permission from Geringer-Sameth & Koushiappas, Phys. Rev. Lett. 107, 241303 (2011; left) and Ackermann et al. (The Fermi Collaboration), Phys. Rev. Lett. 107, 241302 (2011; right), Copyright 2011 by the American Physical Society). |
The status of dark matter as a particle will depend critically on the outcomes of direct and indirect dark matter detection experiments that are either ongoing or planned for the near future. Also at stake is the motivation and context for studying dark matter phenomenology in dSphs. An unambiguous, positive detection of dark matter byproducts emitted from dSphs would establish the existence of a new particle and would provide a unique means for measuring its mass and cross section; via Equation 17, constraints on such parameters would be only as good as dynamical constraints on the dark matter density profile. In case of detections in other objects, e.g., the Galactic center (see Hooper & Linden, 2011) or galaxy clusters (see Han et al., 2012), high-energy and dynamical constraints from dSphs would provide important consistency checks in the regime of minimal astrophysical background. In the case of direct detection and characterisation of a new particle in the laboratory, dSph phenomenology would help to establish or rule out association with cosmological dark matter. In case of failure to detect non-gravitational interactions involving dark matter particles, consideration of the extreme phenomenology exhibited by dSphs would help to inform alternative explanations for dark matter.
11 In a recent preprint, Wolf & Bullock (2012) argue that the situation is more ambiguous, and specifically that the Sculptor data of Walker, Mateo & Olszewski (2009) favor a dark matter halo that is centrally cusped (γ = 1) rather than cored (γ = 0). Their Figure 1 demonstrates that this conclusion — and more generally the ability of their Jeans analysis to yield an apparent constraint on γ — depends critically on their assumption that the data sample a single stellar population with isotropic (βa = 0 in the notation of Equation 11) velocity distribution. This assumption is incompatible with the multi-component structure that is present in the spectroscopic data (Tolstoy et al., 2004, Battaglia et al., 2006, Walker & Peñarrubia, 2011, see Sections 2.2.4 and 4.2). Back.
12 Boylan-Kolchin et al. (2011) identify a similar (perhaps the same) structural problem, noting that the most massive ‘subhalos’ produced in the Aquarius CDM simulation (Springel et al., 2008) have central densities larger than those estimated for any of the known dSphs. Back.
13 For example, Goerdt et al. (2010) conclude that a sinking object of mass Ms induces core formation inside a radius where the enclosed halo mass is M(rcore) ∼ Ms. In this scenario the sinking of Fornax's five surviving globular clusters (Ms ∼ 105 M⊙) cannot have formed the core inferred from estimates M( ∼ 550 pc) ∼ 5 × 107M⊙ and M( ∼ 900 pc) ∼ 2 × 108M⊙ (Walker & Peñarrubia, 2011). Back.
14 Loewenstein & Kusenko (2010) interpret a Chandra detection of monochromatic ( ∼ 2.5 keV) emission from the direction of the Willman 1 satellite as a possible signal of sterile neutrino decay. However, Boyarsky et al. (2010b) argue that non-detections of this feature in the Galactic halo, M31 and several other dSphs rule out a dark matter origin. Indeed, Loewenstein & Kusenko (2012) report no detection of the ∼ 2.5 keV feature in follow-up XMM-Newton observations of Willman 1; corresponding limits on the mass/mixing angle of sterile neutrinos depend on how reliably the ‘irregular’ stellar kinematics of Willman 1 (Willman et al., 2011, Section 2.2.4) trace its mass. Back.
15 Charbonnier et al. (2011) use published kinematic data to estimate less stringent limits of ⟨σv⟩ ≲ 10−25 cm3 s−1 (at mχ ∼ 10 GeV, cf. Figure 22) for individual dSphs. Possible reasons for this discrepancy include different assumptions about the dark matter halo profile (Geringer-Sameth & Koushiappas (2011) and Ackermann et al. (2011) adopt J values previously estimated under the assumption that dSph dark matter halos follow NFW (γ = 1 in the notation of Equation 12) profiles; Charbonnier et al. (2011) estimate J values by marginalising over uncertain halo shape parameters), different assumptions about the energy spectrum (Geringer-Sameth & Koushiappas (2011) and Ackermann et al. (2011) explicitly consider annihilation via bb and τ+τ− mechanisms; Charbonnier et al. (2011) consider a conservative spectrum averaged over a variety of plausible annihilation channels) and/or different assumptions about detector sensitivity. Back.