2.5. Central Densities of Dwarf Spheroidal and Irregular Galaxies

The smallest dSph galaxies allow us to greatly increase our leverage on correlations of DM parameters with galaxy luminosity. Note that only the halo central density can be measured. Pioneering observations by Aaronson (1983) and by Aaronson & Olszewski (1987) showed that the stellar velocity dispersions in Draco and UMi are ~ 10 km s^-1, much larger than expected if the galaxies are in equilibrium and if they consist only of old, metal-poor stars (M / L_V 2.5). High dispersions imply mass-to-light ratios M / L_V ~ 10². Moreover, the central DM densities ₀ ~ 0.6 to 1 M pc^-3 are "shockingly high. ... Indeed, these are the highest central DM densities seen in any galaxy so far" (Kormendy 1987a). The latter result was an early sign of the correlations in Figures 2 - 4.

DM in dSph galaxies has important implications, so considerable effort has gone into trying to find some escape. Early worries included small-number statistics, measurement errors, atmospheric velocity jitter in the most luminous AGB stars, and especially unrecognized binary stars. These have largely been laid to rest as more and fainter stars have been measured, as the time baseline on measurements of individual stars has increased beyond a decade, and as different authors have proved to agree (e.g., Armandroff, Olswezski, & Pryor 1995; Olszewski, Pryor, & Armandroff 1996, see Tremaine 1987; Pryor 1992; Mateo 1994, 1997, 1998 for reviews). As the number of dSph galaxies with dispersion measurements has increased (above reviews and Mateo et al. 1998; Cook et al. 1999; Côté et al. 1999; and Gallart et al. 2001), escape routes that depend on rare events have become implausible. These include the suggestion (Kuhn & Miller 1989; Kuhn 1993) that the stars formerly in dSph galaxies are unbound because of Galactic tides, so we overestimate the masses of systems that are far from equilibrium. The required orbital resonance works best if the dispersion is only marginally larger than the escape velocity and if not too many systems need special engineering. But M / L ratios of 10 - 100 (not 2.5!) imply velocities that are inflated by factors of ~ 2 - 6. Piatek & Pryor (1995), Oh, Lin, & Aarseth (1995), Sellwood & Pryor (1998), Klessen, Grebel, & Harbeck (2003), and Wilkinson (2004) argue convincingly that tides do not inflate velocity dispersions this much, especially not without producing velocity gradients across the galaxies that would have been seen. This remains true even though apparently extratidal stars have been seen in some dSphs (e.g., Irwin & Hatzidimitriou 1995; Piatek et al. 2001, 2002; Palma et al. 2003). In addition, some dSph galaxies are too far from our Galaxy to be affected by tides (Mateo 1998). All nine dSph galaxies with dynamical analyses appear DM dominated. It has become difficult to argue that we get fooled by special circumstances.

One DM alternative is not addressed by the above arguments: Modified Newtonian Dynamics (Milgrom 1983a, b, c; Milgrom & Bekenstein 1987). MOND has been much debated in recent years and will be revisited during this conference. Thirty years of failure to identify all constituents of DM persuade us to treat even exotic alternatives with respect. However, while the jury is out, we assume conventional gravity and treat measurements of high velocity dispersions in dSph galaxies as detections of DM.

Accordingly, Figures 2 and 4 include DM central densities for all galaxies with ₀ tabulated in Mateo (1998) plus And II (Côté et al. 1999). This includes four dI galaxies with virial measurements of ₀; three of these are based on HI and one (LGS3) is based on stellar dynamics (Cook et al. 1999). The central mass density has been corrected for visible matter by subtracting 2.5 times the central, V-band volume brightness. For all galaxies except Fornax, the correction is small. In Fornax (M_B = - 12.6), visible matter accounts for approximately half of the central density. For this galaxy, ₀ is very uncertain.

The "error bars" on ₀ require discussion. The plotted densities are derived by assuming that r_c is the same for the visible and dark matter. If r_{c, DM} >> r_{c, vis} as in the other galaxies in the figures, then ₀ is smaller by a factor of 0.46 (Pryor & Kormendy 1990; Lake 1990). Anisotropic velocity dispersions reduce ₀ estimates by as much as an order of magnitude over the isotropic case (Pryor & Kormendy 1990; Mateo et al. 1993), although the extreme models are not good fits to the data. Finally, model-independent lower limits to the DM density (Merritt 1987) are typically _{0, min} 10^-2.2±0.17 M pc^-3. These limits are mostly too weak to be interesting. However, for Leo II, UMi, and Draco, they are log _{0, min} / (1 M pc^-3) = - 1.55, -1.38, and -1.26, respectively. Even these low values are reasonably consistent with the extrapolation of the DM correlations to low luminosities.