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

An inefficient dwarf: Chemical abundances and the evolution of the Ursa Minor dwarf spheroidal galaxy

We present detailed chemical element abundance ratios of 17 elements in three metal poor stars in the Ursa Minor dwarf spheroidal galaxy, which we combine with extant data from the literature to assess the predictions of a novel suite of galaxy chemical evolution models. The spectroscopic data were obtained with the Keck/HIRES instrument and revealed low metallicities of [Fe/H]=-2.12, -2.13 and -2.67 dex. While the most metal poor star in our sample shows an overabundance of [Mn/Fe] and other Fe-peak elements, our overall findings are in agreement with previous studies of this galaxy: elevated values of the [alpha/Fe] ratios that are similar to, or only slightly lower than, the halo values but with SN Ia enrichment at very low metallicity, as well as an enhancement of the ratio of first to second peak neutron capture elements [Y/Ba] with decreasing metallicity. The chemical evolution models which were tailored to reproduce the metallicity distribution function of the dSph, indicate that UMi had an extended star formation which lasted nearly 5 Gyr with low efficiency and are able to explain the [Y/Ba] enhancement at low metallicity for the first time. In particular, we show that the present day lack of gas is probably due to continuous loss of gas from the system, which we model as winds.Comment: 10 pages, 7 figures, table

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

Two-body relaxation in modified Newtonian dynamics

A naive extension to MOND of the standard computation of the two-body relaxation time Tb implies that Tb is comparable to the crossing time regardless of the number N of stars in the system. This computation is questionable in view of the non-linearity of MOND's field equation. A non-standard approach to the calculation of Tb is developed that can be extended to MOND whenever discreteness noise generates force fluctuations that are small compared to the mean-field force. It is shown that this approach yields standard Newtonian results for systems in which the mean density profile is either plane-parallel or spherical. In the plane-parallel case we find that in the deep-MOND regime Tbb scales with N as in the Newtonian case, but is shorter by the square of the factor by which MOND enhances the gravitational force over its Newtonian value for the same system. Application of these results to dwarf galaxies and groups and clusters of galaxies reveals that in MOND luminosity segregation should be far advanced in groups and clusters of galaxies, two body relaxation should have substantially modified the density profiles of galaxy groups, while objects with masses in excess of ~10M_sun should have spiralled to the centres of dwarf galaxies.(Abridged)Comment: 8 pages, accepted by MNRA

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