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

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 V and I CCD Mosaic Survey of the Ursa Minor Dwarf Spheroidal Galaxy

We discuss a Johnson-Cousins V- and I-band CCD mosaic survey of the Ursa Minor dwarf spheroidal galaxy (dSph) to V ~ 22. We covered UMi with 27 105 × 105 overlapping CCD frames, each frame consisting of two 300 s exposures in each of V and I. We also observed several regions ~3° from UMi to obtain an estimate of contamination by galaxies and Galactic stars. We report the first H-R diagram of an entire dSph. Separation of dwarf stars from foreground stars by color allows a robust estimation of the structural parameters of UMi. We examine earlier evidence of two lumps in the UMi stellar distribution. We detect a statistically significant asymmetry in the stellar distribution of UMi along the major axis. Structure in the stellar distribution of UMi might indicate a tidal origin for UMi\u27s high observed mass-to-light ratio. We demonstrate a technique for obtaining the absolute magnitude of UMi from horizontal-branch star counts compared with M92; this method of luminosity estimation is independent of the distance to UMi. We obtain MV = -8.87 ± σ , where σ = 0.14 if M92 is a perfect calibrator and σ 0.35 is an upper bound on the error arising from differences in stellar populations. Our value for MV is consistent with earlier measurements and has a smaller uncertainty

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

A photometrically and kinematically distinct core in the Sextans dwarf spheroidal galaxy

We present the line of sight radial velocity dispersion profile of the Sextans dwarf spheroidal galaxy (dSph), based on a sample of 88 stars extending to about 1 degree (about 1.5 kpc). Like the Draco and Ursa Minor dSphs, Sextans shows some evidence of a fall-off in the velocity dispersion at large projected radii, with significance p=0.96. Surprisingly, the dispersion at the very centre of Sextans is close to zero (with significance p=0.96). We present evidence which suggests that this latter change in the stellar kinematics coincides with changes in the stellar populations within the dSph. We discuss possible scenarios which could lead to a kinematically and photometrically distinct population at the centre of Sextans.Comment: 7 pages, 9 figures, accepted for publication in MNRA

The importance of tides for the Local Group dwarf spheroidals

There are two main tidal effects which can act on the Local Group dwarf spheroidals (dSphs): tidal stripping and tidal shocking. Using N-body simulations, we show that tidal stripping always leads to flat or rising projected velocity dispersions beyond a critical radius; it is $\sim 5$ times more likely, when averaging over all possible projection angles, that the cylindrically averaged projected dispersion will rise, rather than be flat. In contrast, the Local Group dSphs, as a class, show flat or falling projected velocity dispersions interior to $\sim 1$ kpc. This argues for tidal stripping being unimportant interior to $\sim 1$ kpc for most of the Local Group dSphs observed so far. These results have important implications for the formation of the dSphs and for cosmology. A tidal origin for the formation of these Local Group dSphs (in which they contain no dark matter) is strongly disfavoured. In the cosmological context, a naive solution to the missing satellites problem is to allow only the most massive substructure dark matter halos around the Milky Way to form stars. It is possible for dSphs to reside within these halos ($\sim 10^{10}$M$_\odot$) and have their velocity dispersions lowered through the action of tidal shocks, but only if they have a central density core in their dark matter, rather than a cusp. dSphs can reside within cuspy dark matter halos if their halos are less massive ($\sim 10^{9}$M$_\odot$) and therefore have smaller central velocity dispersions initially (abridged).Comment: 15 pages, 9 figures. Accepted for publication in MNRAS. No change from previous versio

Chemical Evolution in the Carina Dwarf Spheroidal

We present metallicities for 487 red giants in the Carina dwarf spheroidal (dSph) galaxy that were obtained from FLAMES low-resolution Ca triplet (CaT) spectroscopy. We find a mean [Fe/H] of -1.91 dex with an intrinsic dispersion of 0.25 dex, whereas the full spread in metallicities is at least one dex. The analysis of the radial distribution of metallicities reveals that an excess of metal poor stars resides in a region of larger axis distances. These results can constrain evolutionary models and are discussed in the context of chemical evolution in the Carina dSph.Comment: 3 pages, 2 figures, to be published in the proceedings of the ESO/Arcetri-workshop on "Chemical Abundances and Mixing in Stars", 13.-17. Sep. 2004, Castiglione della Pescaia, Italy, L. Pasquini, S. Randich (eds.