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     

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.     

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)     

Kinematics of hypervelocity stars in the triaxial halo of the Milky Way

Hypervelocity stars (HVSs) ejected by the massive black hole at the Galactic Centre have unique kinematic properties compared to other halo stars. Their trajectories will deviate from being exactly radial because of the asymmetry of the Milky Way potential produced by the flattened disc and the triaxial dark matter halo, causing a change of angular momentum that can be much larger than the initial small value at injection. We study the kinematics of HVSs and propose an estimator of dark halo triaxiality that is determined only by instantaneous position and velocity vectors of HVSs at large Galactocentric distances ( r ≳ 50 kpc). We show that, in the case of a substantially triaxial halo, the distribution of deflection angles (the angle between the stellar position and velocity vector) for HVSs on bound orbits is spread uniformly over the range 10°–180°. Future astrometric and deep wide-field surveys should measure the positions and velocities of a significant number of HVSs, and provide useful constraints on the shape of the Galactic dark matter halo.     

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.     

On the prospect of inferring the halo structure and the masses of dark objects through parallax microlensing

We study the proposed use of parallax microlensing in the direction of the Large Magellanic Cloud (LMC) to separate the effects of the mass function of dark massive halo objects (MHOs or 'machos') on the one hand, and their spatial distribution and kinematics on the other. This disentanglement is supposed to allow a much better determination of the two than could be achieved entirely on the basis of the durations of events. We restrict our treatment to the same class of power-law spherical models for the halo of MHOs studied in a previous paper by Marković 38 Sommer-Larsen, and assume that one can eliminate microlensing events caused by massive objects outside the halo (e.g., the LMC halo). Whereas the duration-based error in the average MHO mass, μ¯ ≡  M ¯/M, exceeds (at N  = 100 events) μ¯ by a factor of 2 or more, parallax microlensing remarkably brings it down to 15–20 per cent of μ¯, regardless of the shape of the mass function. In addition, the slope α of the mass function, d n /dμ ∝ μ^α, can be inferred relatively accurately (σ_α < 0.4) for a broader range, −3 < α < 0. The improvement in the inference of the halo structure is also significant: the index γ of the density profile ( ρ ∼  R ^−γ) can be obtained with the error σ_γ < 0.4. While in a typical situation the errors for the parameters specifying the velocity dispersion profile are of about the same magnitude as the parameters themselves, virtually all the uncertainty is 'concentrated' in linear combinations of the parameters that may have little influence on the profile, thus allowing its reasonably accurate inference.     

Infall of substructures on to a Milky Way-like dark halo

We analyse the dynamical properties of substructures in a high-resolution dark matter simulation of the formation of a Milky Way-like halo in a Λcold dark matter cosmology. Our goal is to shed light on the dynamical peculiarities of the Milky Way satellites. Our simulations show that about one-third of the subhaloes have been accreted in groups. We quantify this clustering by measuring the alignment of the angular momentum of subhaloes in a group. We find that this signal is visible even for objects accreted up to z ∼ 1, i.e. 8 Gyr ago, and long after the spatial coherence of the groups has been lost due the host tidal field. This group infall may well explain the ghostly streams proposed by Lynden-Bell & Lynden-Bell to orbit the Milky Way. Our analyses also show that if most satellites originate in a few groups, the disc-like distribution of the Milky Way satellites would be almost inevitable. This non-random assignment of satellites to subhaloes implies an environmental dependence on whether these low-mass objects are able to form stars, possibly related to the nature of reionization in the early Universe. With this picture, both the 'ghostly streams' and the 'disc-like configuration' are manifestations of the same phenomenon: the hierarchical growth of structure down to the smallest scales.