Cores and Cusps in the Dwarf Spheroidals

We consider the problem of determining the structure of the dark halo of nearby dwarf spheroidal galaxies (dSphs) from the spherical Jeans equations. Whether the dark halos are cusped or cored at the centre is an important strategic problem in modern astronomy. The observational data comprise the line-of-sight velocity dispersion of a luminous tracer population. We show that when such data are analysed to find the dark matter density with the spherical Poisson and Jeans equations, then the generic solution is a dark halo density that is cusped like an isothermal. Although milder cusps (like the Navarro-Frenk-White 1/r cusp and even cores are possible, they are not generic. Such solutions exist only if the anisotropy parameter beta and the logarithmic slope of the stellar density gamma satisfy the constraint gamma = 2 x beta at the centre or if the radial velocity dispersion falls to zero at the centre. This surprisingly strong statement is really a consequence of the assumption of spherical symmetry, and the consequent coordinate singularity at the origin. So, for example, a dSph with an exponential light profile can exist in Navarro-Frenk- White halo and have a flat velocity dispersion, but anisotropy in general drives the dark halo solution to an isothermal cusp. The identified cusp or core is therefore a consequence of the assumptions (particularly of spherical symmetry and isotropy), and not the data.Comment: MNRAS, in pres

Observed Properties of Dark Matter: dynamical studies of dSph galaxies

The Milky Way satellite dwarf spheroidal (dSph) galaxies are the smallest dark matter dominated systems in the universe. We have underway dynamical studies of the dSph to quantify the shortest scale lengths on which Dark Matter is distributed, the range of Dark Matter central densities, and the density profile(s) of DM on small scales. Current results suggest some surprises: the central DM density profile is typically cored, not cusped, with scale sizes never less than a few hundred pc; the central densities are typically 10-20 GeV/cc; no galaxy is found with a dark mass halo less massive than ~5.10^7 M_sun. We are discovering many more dSphs, which we are analysing to test the generality of these results.Comment: Presented at UCLA Dark Matter 2006 conference, March 2006. In press in Nuclear Physics

The tidal stripping of satellites

We present an improved analytic calculation for the tidal radius of satellites and test our results against N-body simulations. The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and {\it the orbit of the star within the satellite}. We demonstrate that this last point is critical and suggest using {\it three tidal radii} to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically. Over short times (\simlt 1-2 Gyrs $\sim 1$ satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic.Comment: 10 pages, 5 figures. Final version accepted for publication in MNRAS. Some new fully analytic tidal radii have been added for power law density profiles (including the isothermal sphere) and some split power law

The mass of dwarf spheroidal galaxies and the missing satellite problem

We present the results from a suite of N-body simulations of the tidal stripping of two-component dwarf galaxies comprising some stars and dark matter. We show that recent kinematic data from the local group dwarf spheroidal (dSph) galaxies suggests that dSph galaxies must be sufficiently massive ($10^9 - 10^{10}$M$_\odot$) that tidal stripping is of little importance for the stars. We discuss the implications of these massive dSph galaxies for cosmology and galaxy formation.Comment: 4 pages, 1 figure, to appear in the proceedings of the IAUC198 "Near-Field Cosmology with Dwarf Elliptical Galaxies", H. Jerjen & B. Binggeli (eds.). Comments welcom

First Clear Signature of an Extended Dark Matter Halo in the Draco Dwarf Spheroidal

We present the first clear evidence for an extended dark matter halo in the Draco dwarf spheroidal galaxy based on a sample of new radial velocities for 159 giant stars out to large projected radii. Using a two parameter family of halo models spanning a range of density profiles and velocity anisotropies, we are able to rule out (at about the 2.5 sigma confidence level) haloes in which mass follows light. The data strongly favor models in which the dark matter is significantly more extended than the visible dwarf. However, haloes with harmonic cores larger than the light distribution are also excluded. When combined with existing measurements of the proper motion of Draco, our data strongly suggest that Draco has not been tidally truncated within ~1 kpc. We also show that the rising velocity dispersion at large radii represents a serious problem for modified gravity (MOND).Comment: to be published in ApJL; 5 pages, 4 figure

A Survey for Outer Satellites of Mars: Limits to Completeness

We surveyed the Hill sphere of Mars for irregular satellites. Our search covered nearly the entire Hill Sphere, but scattered light from Mars excluded the inner few arcminutes where the satellites Phobos and Deimos reside. No new satellites were found to an apparent limiting red magnitude of 23.5, which corresponds to radii of about 0.09 km using an albedo of 0.07.Comment: 5 figures (1 color), 2 Tables, to appear in AJ Nov. 200

Kinematically Cold Populations at Large Radii in the Draco and Ursa Minor Dwarf Spheroidals

We present projected velocity dispersion profiles for the Draco and Ursa Minor (UMi) dwarf spheroidal galaxies based on 207 and 162 discrete stellar velocities, respectively. Both profiles show a sharp decline in the velocity dispersion outside ~30 arcmin (Draco) and ~40 arcmin (UMi). New, deep photometry of Draco reveals a break in the light profile at ~25 arcmin. These data imply the existence of a kinematically cold population in the outer parts of both galaxies. Possible explanations of both the photometric and kinematic data in terms of both equilibrium and non-equilibrium models are discussed in detail. We conclude that these data challenge the picture of dSphs as simple, isolated stellar systems.Comment: 5 pages, accepted for publication in ApJ Letter

A Dynamical Fossil in the Ursa Minor Dwarf Spheroidal Galaxy

The nearby Ursa Minor dwarf spheroidal (UMi dSph) is one of the most dark matter dominated galaxies known, with a central mass to light ratio roughly equal to 70. Somewhat anomalously, it appears to contain morphological substructure in the form of a second peak in the stellar number density. It is often argued that this substructure must be transient because it could not survive for the > 10 Gyr age of the system, given the crossing time implied by UMi's 8.8 km/s internal velocity dispersion. In this paper, however, we present evidence that the substructure has a cold kinematical signature, and argue that UMi's clumpiness could indeed be a primordial artefact. Using numerical simulations, we demonstrate that substructure is incompatible with the cusped dark matter haloes predicted by the prevailing Cold Dark Matter (CDM) paradigm, but is consistent with an unbound stellar cluster sloshing back and forth within the nearly harmonic potential of a cored dark matter halo. Thus CDM appears to disagree with observation at the least massive, most dark matter dominated end of the galaxy mass spectrum.Comment: Astrophysical Journal (Letters), in pres