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.     

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 Milky Way Galaxy as a strong gravitational lens

We study the gravitational lensing effects of spiral galaxies by taking a model of the Milky Way and computing its lensing properties. The model is composed of a spherical Hernquist bulge, a Miyamoto–Nagai disc and an isothermal halo. As a strong lens, a spiral galaxy like the Milky Way can give rise to four different imaging geometries. They are (i) three images on one side of the galaxy centre ('disc triplets'), (ii) three images with one close to the centre ('core triplets'), (iii) five images and (iv) seven images. Neglecting magnification bias, we show that the core triplets, disc triplets and fivefold imaging are roughly equally likely. Even though our models contain edge-on discs, their image multiplicities are not dominated by disc triplets. The halo is included for completeness, but it has a small effect on the caustic structure, the time delays and brightnesses of the images.
The Milky Way model has a maximum disc (i.e. the halo is not dynamically important in the inner parts). Strong lensing by nearly edge-on disc galaxies breaks the degeneracy between the relative contributions of the disc and halo to the overall rotation curve. If a spiral galaxy has a submaximum disc, then the astroid caustic shrinks dramatically in size, whilst the radial caustic shrinks more modestly. This causes changes in the relative likelihood of the image geometries, specifically (i) core triplets are now ∼9/2 times more likely than disc triplets, (ii) the cross-section for threefold imaging is reduced by a factor of ∼2/3, whilst (iii) the cross-section for fivefold imaging is reduced by ∼1/2. Although multiple imaging is less likely (the cross-sections are smaller), the average total magnification is greater. The time delays are smaller, as the total projected lensing mass is reduced.     

Masses for the Local Group and the Milky Way

We use the very large Millennium Simulation of the concordance Λ cold dark matter cosmogony to calibrate the bias and error distribution of Timing Argument estimators of the masses of the Local Group and of the Milky Way. From a large number of isolated spiral–spiral pairs similar to the Milky Way/Andromeda system, we find the interquartile range of the ratio of timing mass to true mass to be a factor of 1.8, while the 5 and 95 per cent points of the distribution of this ratio are separated by a factor of 5.7. Here, we define true mass as the sum of the 'virial' masses, M ₂₀₀, of the two dominant galaxies. For present best values of the distance and approach velocity of Andromeda, this leads to a median likelihood estimate of the true mass of the Local Group of  5.27 × 10¹² M_⊙  or  log  M _LG/M_⊙= 12.72  , with an interquartile range of [12.58, 12.83] and a 5–95 per cent range of [12.26, 13.01]. Thus, a 95 per cent lower confidence limit on the true mass of the Local Group is  1.81 × 10¹² M_⊙  . A timing estimate of the Milky Way's mass based on the large recession velocity observed for the distant satellite Leo I works equally well, although with larger systematic uncertainties. It gives an estimated virial mass for the Milky Way of  2.43 × 10¹² M_⊙  with a 95 per cent lower confidence limit of  0.80 × 10¹² M_⊙  .     

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.     

Does the Milky Way launch a large-scale wind?

The ROSAT All-Sky Survey revealed soft X-ray emission on kiloparsec scales towards the Galactic center. Separately, it has also been observed that the cosmic ray intensity (measured via γ-ray emission) rises only very slowly towards the center of the Galaxy, counter to expectations based on the greater number of cosmic ray sources there. A thermal and cosmic-ray driven wind could potentially explain both of these observations. We find that a cosmic-ray and thermally driven wind fits the X-ray observations well; in fact, a wind fits significantly better than an earlier-proposed static-polytrope gas model.     

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)     

Simulations of minor mergers – II. The phase-space structure of thick discs

We analyse the phase-space structure of simulated thick discs that are the result of a 5:1 mass-ratio merger between a disc galaxy and a satellite. Our main goal is to establish what would be the imprints of a merger origin for the Galactic thick disc. We find that the spatial distribution predicted for thick-disc stars is asymmetric, seemingly in agreement with recent observations of the Milky Way thick disc. Near the Sun, the accreted stars are expected to rotate more slowly, to have broad velocity distributions and to occupy preferentially the wings of the line-of-sight velocity distributions. The majority of the stars in our model thick discs have low eccentricity orbits (in clear reference to the pre-existing heated disc) which give rise to a characteristic (sinusoidal) pattern for their line-of-sight velocities as a function of galactic longitude. The z -component of the angular momentum of thick-disc stars provides a clear discriminant between stars from the pre-existing disc and those from the satellite, particularly at large radii. These results are robust against the particular choices of initial conditions made in our simulations.     

A model for the Lin‐Shu type density‐wave structure of our Galaxy: Line‐of‐sight and transverse‐longitudinal velocities of 242 optically visible open clusters

In this paper, the fourth in a series, we examine again one of the implications of the Lin‐Shu density‐wave theory, specifically, the noncircular systematic motion of the Galactic objects. Our previous investigation is extended by analyzing simultaneously both the line‐of‐sight and transversal velocities of a sample of open clusters for which velocities, distances and ages are available. The ordinary equations of the Oort‐Lindblad theory of galactic differential rotation are used. The minor effects caused by the two‐dimensional tightly‐wound density waves are also taken into account. The published data of 242 currently known optically visible clusters having distances r < 3 kpc from the Sun and ‐200 < z < 200 pc from the Galactic plane, and ages 2 × 10⁸ < t < 2 × 10⁹ yr are collected from Dias et al. (2014), excluding extremely far, high‐velocity, young and old objects in our fitting. The most noteworthy result is the fact that the parameters of Lin–Shu type density waves estimated from two independent line‐of‐sight and transversal along the Galactic longitude velocities are nearly equal. We argue that the resemblance of these Galactic wave structures is so remarkable that no doubt is felt as to the theory's truth with respect to these data. The results obtained allow us to conclude that several low‐m trailing density‐wave patterns with different number of spiral arms m (say, m = 1, 2, 3, and 4), pitch angles (about 5°, 8°, 11°, and 14°, respectively) and amplitudes of the perturbed gravitational potential may coexist in the Galaxy. The latter suggests the asymmetric multiarm, not well‐organized (“flocculent”) spiral structure of the system. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)