The Bar and Spiral Structure Legacy (BeSSeL) survey: Mapping the Milky Way with VLBI astrometry

Astrometric Very Long Baseline Interferometry (VLBI) observations of maser sources in the Milky Way are used to map the spiral structure of our galaxy and to determine fundamental parameters such as the rotation velocity (Θ₀) and curve and the distance to the Galactic center (R₀). Here, we present an update on our first results, implementing a recent change in the knowledge about the Solar motion. It seems unavoidable that the IAU recommended values for R₀ and Θ₀ need a substantial revision. In particular the combination of 8.5 kpc and 220 km s^–1 can be ruled out with high confidence. Combining the maser data with the distance to the Galactic center from stellar orbits and the proper motion of Sgr A* gives best values of R₀ = 8.3 ± 0.23 kpc and Θ₀ = 239 or 246±7 km s^–1, for Solar motions of V_⊙ = 12.23 and 5.25 km s^–1, respectively. Finally, we give an outlook to future observations in the Bar and Spiral Structure Legacy (BeSSeL) survey (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mass models of the Milky Way

A parametrized model of the mass distribution within the Milky Way is fitted to the available observational constraints. The most important single parameter is the ratio of the scalelength R _d* of the stellar disc to R ₀. The disc and bulge dominate v _c( R ) at R ≲ R ₀ only for R _d,*/ R ₀≲0.3. Since the only knowledge we have of the halo derives from studies like the present one, we allow it to contribute to the density at all radii. When allowed this freedom, however, the halo causes changes in assumptions relating to R  ≪  R ₀ to affect profoundly the structure of the best-fitting model at R  ≫  R ₀. For example, changing the disc slightly from an exponential surface-density profile significantly changes the form of v _c( R ) at R  ≫  R ₀, where the disc makes a negligible contribution to v _c. Moreover, minor changes in the constraints can cause the halo to develop a deep hole at its centre that is not physically plausible. These problems call into question the proposition that flat rotation curves arise because galaxies have physically distinct haloes rather than outwards-increasing mass-to-light ratios.   The mass distribution of the Galaxy and the relative importance of its various components will remain very uncertain until more observational data can be used to constrain mass models. Data that constrain the Galactic force field at z ≳ R and at R  >  R ₀ are especially important.     

Kinematics of SDSS subdwarfs: structure and substructure of the Milky Way halo

We construct a new sample of ∼1700 solar neighbourhood halo subdwarfs from the Sloan Digital Sky Survey (SDSS), selected using a reduced proper-motion diagram. Radial velocities come from the SDSS spectra and proper motions from the light-motion curve catalogue of Bramich et al. Using a photometric parallax relation to estimate distances gives us the full phase-space coordinates. Typical velocity errors are in the range  30–50 km s⁻¹  . This halo sample is one of the largest constructed to date and the disc contamination is at a level of ≲1 per cent. This enables us to calculate the halo velocity dispersion to excellent accuracy. We find that the velocity dispersion tensor is aligned in spherical polar coordinates and that  (σ _r , σ_φ, σ_θ) = (143 ± 2, 82 ± 2, 77 ± 2) km s⁻¹  . The stellar halo exhibits no net rotation, although the distribution of   v _φ  shows tentative evidence for asymmetry. The kinematics are consistent with a mildly flattened stellar density falling with distance like   r ^−3.75  .
Using the full phase-space coordinates, we look for signs of kinematic substructure in the stellar halo. We find evidence for four discrete overdensities localized in angular momentum and suggest that they may be possible accretion remnants. The most prominent is the solar neighbourhood stream previously identified by Helmi et al., but the remaining three are new. One of these overdensities is potentially associated with a group of four globular clusters (NGC 5466, NGC 6934, M2 and M13) and raises the possibility that these could have been accreted as part of a much larger progenitor.     

Milky Way Gas Dynamics

The Milky Way is made up of a central bar, a disk with embedded spiral arms, and a dark matter halo. Observational and theoretical constraints for the characteristic parameters of these components will be presented, with emphasis on the constraints from the dynamics of the Milky Way gas. In particular, the fraction of dark matter inside the solar radius, the location of the main resonances, and the evidence for multiple pattern speeds will be discussed.Invited talk at the AAS Division on Dynamical Astronomy meeting, Santa Barbara, April 2005     

The local density of matter mapped by Hipparcos

We determine the velocity distribution and space density of a volume-complete sample of A and F stars, using parallaxes and proper motions from the Hipparcos satellite. We use these data to solve for the gravitational potential vertically in the local Galactic disc, by comparing the Hipparcos measured space density with predictions from various disc models. We derive an estimate of the local dynamical mass density of 0.102±0.010 pc⁻³, which may be compared with an estimate of 0.095 M_⊙ pc⁻³ in visible disc matter. Our estimate is found to be in reasonable agreement with other estimates by Crézé et al. and Pham, also based on Hipparcos data. We conclude that there is no compelling evidence for significant amounts of dark matter in the disc.     

The pattern speed of the OH/IR stars in the Milky Way

We show how the continuity equation can be used to determine pattern speeds in the Milky Way Galaxy (MWG). This method, first discussed by Tremaine & Weinberg in the context of external galaxies, requires projected positions, ( l , b ), and line-of-sight velocities for a spatially complete sample of relaxed tracers. If the local standard of rest (LSR) has a zero velocity in the radial direction ( u _LSR), then the quantity that is measured is  Δ V ≡Ω_p R ₀- V _LSR  , where Ω_p is the pattern speed of the non-axisymmetric feature, R ₀ is the distance of the Sun from the Galactic centre and V _LSR is the tangential motion of the LSR, including the circular velocity. We use simple models to assess the reliability of the method for measuring a single, constant pattern speed of either a bar or spiral in the inner MWG. We then apply the method to the OH/IR stars in the ATCA/VLA OH 1612-MHz survey of Sevenster et al., finding  Δ V =252±41 km s^-1,  if   u _LSR=0  . Assuming further that   R ₀=8 kpc  and   V _LSR=220 km s^-1,  this gives  Ω_p=59±5 km s^-1 kpc^-1  with a possible systematic error of perhaps 10 km s⁻¹ kpc⁻¹. The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG.     

Weak Elliptical Distortion of the Milky Way Potential traced by Open Clusters

From photometric observations and star counts, the existence of a bar in the cen-tral few kpc of the Galaxy is suggested. It is generally thought that our Galaxy is surrounded by a massive invisible halo. The gravitational potential of the Galaxy is therefore made non-axisymmetric generated by the central tfiaxial bar, by the outer triaxial halo, and/or by the spiral structures. Selecting nearly 300 open clusters with complete spatial velocity measure-ments and ages, we were able to construct the rotation curve of the Milky Way within a range of 3 kpc of the Sun. Using a dynamic model for an assumed elliptical disk, a clear weak el-liptical potential of the disk with ellipticity of ε(R0) = 0.060 ± 0.012 is detected, the Sun is found to be near the minor axis, displaced by 30°± 3°. The motion of the clusters is suggested to be on an oval orbit rather than on a circular one.     

The fine-grained phase-space structure of cold dark matter haloes

We present a new and completely general technique for calculating the fine-grained phase-space structure of dark matter (DM) throughout the Galactic halo. Our goal is to understand this structure on the scales relevant for direct and indirect detection experiments. Our method is based on evaluating the geodesic deviation equation along the trajectories of individual DM particles. It requires no assumptions about the symmetry or stationarity of the halo formation process. In this paper we study general static potentials which exhibit more complex behaviour than the separable potentials studied previously. For ellipsoidal logarithmic potentials with a core, phase mixing is sensitive to the resonance structure, as indicated by the number of independent orbital frequencies. Regions of chaotic mixing can be identified by the very rapid decrease in the real-space density of the associated DM streams. We also study the evolution of stream-density in ellipsoidal NFW haloes with radially varying isopotential shape, showing that if such a model is applied to the Galactic halo, at least 10⁵ streams are expected near the Sun. The most novel aspect of our approach is that general non-static systems can be studied through implementation in a cosmological N -body code. Such an implementation allows a robust and accurate evaluation of the enhancements in annihilation radiation due to fine-scale structure such as caustics. We embed the scheme in the current state-of-the-art code gadget -3 and present tests which demonstrate that N -body discreteness effects can be kept under control in realistic configurations.