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Abstract:

A parameterized 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 scale length R_d* of the stellar disk to R0. The disk and bulge dominate v_c(R) at R> R0. For example, changing the disk slightly from an exponential surface-density profile significantly changes the form of v_c(R) at R >> R0, where the disk 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 halos 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 > R0 are especially important.

Abstract:

A straightforward determination of the circular-speed curve vc(R) of the Milky Way suggests that near the Sun, vc starts to rise approximately linearly with R. If this result were correct, the Galactic mass density would have to be independent of radius at R ~> R0. We show that the apparent linear rise in v_c arises naturally if the true circular-speed curve is about constant or gently falling at R0 < R ~< 2 R0, but most tracers that appear to be at R ~> 1.25 R0 are actually concentrated into a ring of radius ~1.6 R0.

Abstract:

An algorithm is developed and tested for the problem posed by photometric observations of the bulge of the Milky Way. The latter subtends a non-trivial solid angle on the sky, and we show that this permits inversion of the projected brightness distribution under the assumption that the bulge has three orthogonal mirror planes of specified orientation. A serious error in the assumed orientation of the mirror planes should be detectable.

Abstract:

Axisymmetric density distributions are constructed which are invisible when viewed from a range of inclination angles $i$. By adding such distributions to a model galaxy, it can be made either disky or boxy without in any way affecting its projected image. As the inclination of a galaxy decreases from edge-on to face on, the range of `invisible' densities, the uncertainty in the deprojection, and the sensitivity of the deprojection to noise all increase. The relation between these phenomena is clarified by an analysis of Palmer's deprojection algorithm. These results imply that disk-to-bulge ratios are in principle ill-determined from photometry unless the disk is strong or the system is seen precisely edge-on. The uncertain role of third integrals in galaxies makes it unclear to what degree this indeterminacy can be resolved by kinematic studies.

Abstract:

The only way to map the Galaxy's gravitational potential $\Phi({\bf x})$ and the distribution of matter that produces it is by modelling the dynamics of stars and gas. Observations of the kinematics of gas provide key information about gradients of $\Phi$ within the plane, but little information about the structure of $\Phi$ out of the plane. Traditional Galaxy models {\em assume}, for each of the Galaxy's components, arbitrary flattenings, which together with the components' relative masses yield the model's equipotentials. However, the Galaxy's isopotential surfaces should be {\em determined\/} directly from the motions of stars that move far from the plane. Moreover, from the kinematics of samples of such stars that have well defined selection criteria, one should be able not only to map $\Phi$ at all positions, but to determine the distribution function $f_i({\bf x},{\bf v})$ of each stellar population $i$ studied. These distribution functions will contain a wealth of information relevant to the formation and evolution of the Galaxy. An approach to fitting a wide class of dynamical models to the very heterogeneous body of available data is described and illustrated.