Abstract
The Milky Way’s dwarf spheroidal satellites include the nearest, smallest, and least luminous galaxies known. They also exhibit the largest discrepancies between dynamical and luminous masses. This article reviews the development of empirical constraints on the structure and kinematics of dSph stellar populations and discusses how this phenomenology translates into constraints on the amount and distribution of dark matter within dSphs. Some implications for cosmology and the particle nature of dark matter are discussed and some avenues for future study are identified.
Notes
- 1.
As Fig. 20-1 and the terms themselves suggest, the distinction between “classical” and “ultrafaint” dSphs involves a mixture of intrinsic luminosity with sequence of discovery. Here, this distinction (which is meaningless in the sense that members of both classes trace smooth scaling relationships involving luminosity, size, metallicity, and stellar kinematics) is preserved only because observational studies of these objects – for both practical and accidental reasons – tend to be separable along the same lines. Following common practice, dSphs known before SDSS (Carina, Draco, Fornax, Leo I, Leo II, Sculptor, Sextans, Ursa Minor) are referred to as “classical,” and the rest as “ultrafaint.”
- 2.
In fact R K is usually referred to as a “tidal” radius and denoted r t . The adopted nomenclature and notation avoid confusion with the tidal radius defined in ( 20.4).
- 3.
Aaronson added to the final article proof a measurement of − 285. 6 ± 1. 1 km s− 1 for a fourth, non-carbon star, further supporting a large dispersion.
- 4.
M31 hosts several “extended” globular clusters with half-light radii as large as several tens of pc (e.g., Huxor et al. 2005), but no similar population within the Milky Way has yet been discovered.
- 5.
Some ambiguity regarding the masses of the smallest, faintest dSphs results from the convergence of three relevant quantities – the typical velocity measurement error, the measured velocity dispersions, and the potential contribution to the measured dispersions from binary orbital motions – on the same value, ∼ 3–4 km s− 1 (Koposov et al. 2011b; Martin et al. 2007; McConnachie and Côté 2010; Simon and Geha 2007; Simon et al. 2011). For some faint dSphs, the most compelling evidence for large amounts of dark matter comes from stellar chemistry rather than kinematics. The faintest objects classified as dSphs tend to have metallicity dispersions (σ [Fe∕H] ≳ 0. 4 dex, Geha et al. 2009; Kirby et al. 2011; Norris et al. 2010; Willman et al. 2011) indicative of prolonged and perhaps multiple episodes of star formation, thereby requiring gravitational potentials sufficiently deep to retain interstellar media despite pressures generated by stellar feedback. An adequate discussion of the relationships between dSph kinematics and stellar chemistry is beyond the scope of the present work; Tolstoy et al. (2009) provide an excellent, recent review.
- 6.
Equation 20.4 gives the tidal radius for the idealised case of point-mass potentials. Calculations and simulations by Read et al. (2006b) demonstrate that stars are actually lost from various depths depending on the internal mass distributions of satellite and parent, as well as on the properties of the stellar orbits themselves (e.g., prograde versus retrograde with respect to the orbit of the dSph about the Galaxy).
- 7.
The distribution function is defined such that \(f(\vec{r},\vec{v},t){d}^{3}\vec{x}{d}^{3}\vec{v}\) specifies the number of stars inside the volume of phase-space \({d}^{3}\vec{x}{d}^{3}\vec{v}\) centered on \((\vec{x},\vec{v})\) at time t.
- 8.
Łokas et al. (2005) develop a Jeans analysis that uses higher-order velocity moments (e.g., 〈v 4〉) in order to reduce degeneracy between anisotropy (assumed to be constant) and total mass (effectively normalizing a cusped mass profile assumed to have γ = 1 in the notation of Equation 20.12).
- 9.
Typical assumptions about anisotropy range in simplicity from β a = 0 or β a = constant to \(\beta _{a}(r) = (\beta _{\infty }-\beta _{0}){r}^{2}/(r_{\beta }^{2} + {r}^{2}) +\beta _{0}\) (e.g., Strigari 2010), introducing as many as three new free parameters.
- 10.
Chanamé et al. (2008) have formulated a Schwarzschild method that operates on discrete velocity measurements, avoiding the binning procedure altogether. Efforts to apply this method to dSph data are underway.
- 11.
Implicit in the estimation of M 300 is the assumption that the smallest dSphs, which have half-light radii R h ∼ 30 pc, have dark matter halos that extend beyond their most distant dynamical tracers.
- 12.
- 13.
For example, Goerdt et al. (2010) conclude that a sinking object of mass M s induces core formation inside a radius where the enclosed halo mass is M(r core) ∼ M s . In this scenario, the sinking of Fornax’s five surviving globular clusters (M s ∼ 105 M ⊙) cannot have formed the core inferred from estimates M( ∼ \(550\mathrm{pc}) \sim 5 \times 1{0}^{7}M_{\odot }\) and M( ∼ \(900\mathrm{pc}) \sim 2 \times 1{0}^{8}M_{\odot }\) (Walker and Peñarrubia 2011).
- 14.
Loewenstein and Kusenko (2010) interpret a Chandra detection of monochromatic ( ∼ 2.5 keV) emission from the direction of the Willman 1 satellite as a decay signal. However, Boyarsky et al. (2010b) argue that non-detections of this feature in the Galactic halo, M31, and several other dSphs rule out such an interpretation. Indeed, Loewenstein and 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.
- 15.
Charbonnier et al. (2011) use published kinematic data to estimate less stringent limits of 〈σv〉 ≲ 10− 25 cm3s− 1 (at m χ ∼ 10 GeV, cf. Figure Fig. 20-22 ) for individual dSphs. Possible reasons for this discrepancy include different assumptions about the dark matter halo profile (Geringer-Sameth and Koushiappas 2011 and Ackermann et al. 2011 adopt J values previously estimated under the assumption that dSph dark amtter halos follow NFW profiles; Charbonnier et al. 2011 estimate J values by marginalizing over uncertain halo shape parameters), different assumptions about the energy spectrum (Geringer-Sameth and Koushiappas 2011 and Ackermann et al. 2011 explicitly consider annihilation via b\bar{b} 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.
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Walker, M. (2013). Dark Matter in the Galactic Dwarf Spheroidal Satellites. In: Oswalt, T.D., Gilmore, G. (eds) Planets, Stars and Stellar Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5612-0_20
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