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Register a new userDark Matter in Dwarf Spheroidals II: Observations and Modelling of Draco
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J.T. Kleyna
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We present stellar radial velocity data for the Draco dwarf spheroidal galaxy obtained using the AF2/WYFFOS instrument combination on the William Herschel Telescope. Our dataset consists of 186 member stars, 159 of which have good quality velocities, extending to a magnitude V=19.5 with a mean velocity precision of 2 km/s. We find statistically strong evidence of a rising velocity dispersion consistent with a dark matter halo with gently rising rotation curve. There is a <2 sigma signature of rotation about the long axis, inconsistent with tidal disruption being the source of the rising dispersion. By comparing our dataset with earlier velocities, we find that Draco probably has a binary distribution and fraction comparable to those in the solar neighbourhood. We apply a novel maximum likelihood algorithm and fit the velocity data to a two parameter spherical model with an adjustable dark matter content and velocity anisotropy. Draco is best fit by a weakly tangentially anisotropic distribution of stellar orbits in a dark matter halo with a very slowly rising rotation law. We are able to rule out both a mass-follows-light distribution and an extended halo with a harmonic core at the 2.5 to 3 sigma significance level, depending on the details of our assumptions about Dracos stellar binary population. Our modelling lends support to the idea that the dark matter in dwarf spheroidals is distributed in the form of massive, nearly isothermal haloes.
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This paper introduces a new two-parameter family of dwarf spheroidal (dSph) galaxy models. The density distribution has a Plummer profile and falls like the inverse fourth power of distance in projection, in agreement with the star-count data. The first free parameter controls the velocity anisotropy, the second controls the dark matter content. The dark matter distribution can be varied from one extreme of mass-follows-light through a near-isothermal halo with flat rotation curve to the other extreme of an extended dark halo with harmonic core. This family of models is explored analytically in some detail -- the distribution functions, the intrinsic moments and the projected moments are all calculated. For the nearby Galactic dSphs, samples of hundreds of discrete radial velocities are becoming available. A technique is developed to extract the anisotropy and dark matter content from such data sets by maximising the likelihood function of the sample of radial velocities. This is constructed from the distribution function and corrected for observational errors and the effects of binaries. Tests on simulated data sets show that samples of 1000 discrete radial velocities are ample to break the degeneracy between mass and anisotropy in the nearby dSphs. Interesting constraints can already be placed on the distribution of the dark matter with samples of 160 radial velocities (the size of the present-day data set for Draco).
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.
Self-Interacting Dark Matter is an attractive alternative to the Cold Dark Matter paradigm only if it is able to substantially reduce the central densities of dwarf-size haloes while keeping the densities and shapes of cluster-size haloes within current constraints. Given the seemingly stringent nature of the latter, it was thought for nearly a decade that SIDM would be viable only if the cross section for self-scattering was strongly velocity-dependent. However, it has recently been suggested that a constant cross section per unit mass of sigma_T/m~0.1cm^2/g is sufficient to accomplish the desired effect. We explicitly investigate this claim using high resolution cosmological simulations of a Milky-Way size halo and find that, similarly to the Cold Dark Matter case, such cross section produces a population of massive subhaloes that is inconsistent with the kinematics of the classical dwarf spheroidals, in particular with the inferred slopes of the mass profiles of Fornax and Sculptor. This problem is resolved if sigma_T/m~1cm^2/g at the dwarf spheroidal scales. Since this value is likely inconsistent with the halo shapes of several clusters, our results leave only a small window open for a velocity-independent Self-Interacting Dark Matter model to work as a distinct alternative to Cold Dark Matter.
We present an F606W-F814W color-magnitude diagram for the Draco dwarf spheroidal galaxy based on Hubble Space Telescope WFPC2 images. The luminosity function is well-sampled to 3 magnitudes below the turn-off. We see no evidence for multiple turnoffs and conclude that, at least over the field of the view of the WFPC2, star formation was primarily single-epoch. If the observed number of blue stragglers is due to extended star formation, then roughly 6% (upper limit) of the stars could be half as old as the bulk of the galaxy. The color difference between the red giant branch and the turnoff is consistent with an old population and is very similar to that observed in the old, metal-poor Galactic globular clusters M68 and M92. Despite its red horizontal branch, Draco appears to be older than M68 and M92 by 1.6 +/- 2.5 Gyrs, lending support to the argument that the ``second parameter which governs horizontal branch morphology must be something other than age. Dracos observed luminosity function is very similar to that of M68, and the derived initial mass function is consistent with that of the solar neighborhood.
We examine the dark matter content of satellite galaxies in Lambda-CDM cosmological hydrodynamical simulations of the Local Group from the APOSTLE project. We find excellent agreement between simulation results and estimates for the 9 brightest Galactic dwarf spheroidals (dSphs) derived from their stellar velocity dispersions and half-light radii. Tidal stripping plays an important role by gradually removing dark matter from the outside in, affecting in particular fainter satellites and systems of larger-than-average size for their luminosity. Our models suggest that tides have significantly reduced the dark matter content of Can Ven I, Sextans, Carina, and Fornax, a prediction that may be tested by comparing them with field galaxies of matching luminosity and size. Uncertainties in observational estimates of the dark matter content of individual dwarfs have been underestimated in the past, at times substantially. We use our improved estimates to revisit the `too-big-to-fail problem highlighted in earlier N-body work. We reinforce and extend our previous conclusion that the APOSTLE simulations show no sign of this problem. The resolution does not require `cores in the dark mass profiles, but, rather, relies on revising assumptions and uncertainties in the interpretation of observational data and accounting for `baryon effects in the theoretical modelling.
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