Abstract
We re-analyse the velocity-dispersion profile σ(r) at radii r > 10 kpc in the Galactic stellar halo, recently derived by Battaglia et al., who concluded that, for a constant velocity anisotropy of the tracers, these data rule out a flat circular-speed curve for the Milky Way. However, we demonstrate that if one makes the natural assumption that the tracer density is truncated at rt≳ 160 kpc and falls off significantly more steeply than r−3.5 at r≳ 80 kpc, then these data are consistent with a flat circular-speed curve and a constant velocity anisotropy comparable to that observed for halo stars in the solar neighbourhood. We also consider a more detailed mass model with an exponential stellar disc and an extended non-isothermal dark-matter halo. In this two-component model, the Milky Way's virial radius and mass are rvir≃ 200 kpc and Mvir≃ 1.5 × 1012 M⊙. Still assuming the tracers' velocity anisotropy to be constant (at β≃ 0.5), we again find good agreement with the observed σ(r), so long as the tracer density is truncated near the virial radius. These data by themselves do not allow to differentiate either between different dark-halo or total-mass models for the Milky Way, nor between different velocity-anisotropy profiles for the tracers.
Highlights
The case for dark-matter haloes around spiral galaxies is predominantly based on the flatness of the rotation curves observed for gas out to large radii
Since the velocity data from Battaglia et al reach more than halfway to the virial radius of the Galaxy – probing regions where the stellar density is unconstrained observationally, and even approaching what might be viewed as a natural ‘edge’ to the stellar halo – our ignorance of the detailed density distribution of the far stellar halo is at least as important as uncertainties in the tracers’ velocity anisotropy when attempting to use the observed σ (r) to infer anything about the mass profile of the Galaxy
These points reflect that the total circular speed given by equations (12) and (13) decreases monotonically with radius for r > 6.6 kpc, and is less than 220 km s−1 at all radii covered by the Battaglia et al (2005) or Harris (2001)
Summary
The case for dark-matter haloes around spiral galaxies is predominantly based on the flatness of the rotation curves observed for gas out to large radii. The projected velocity-dispersion profiles, σ (r), of planetary nebulae in four such galaxies have been measured to several effective radii by Mendez et al (2001) and Romanowsky et al (2003). These data probe regions that are expected to be dynamically dominated by dark matter, the dispersion profiles are found to decrease outwards in a manner consistent with the assumption that light traces mass, i.e. that there are no extended dark haloes. The importance of velocity anisotropy has been emphasized by Mamon & Lokas (2005) and Dekel et al (2005), who showed that falling dispersion profiles for elliptical galaxies are perfectly consistent with massive dark-matter haloes, in contrast to the original conclusion by Romanowsky et al (2003)
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