The outer rotation curve of the Milky Way

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 1.25 R0 are actually concentrated into a ring of radius ~1.6 R0.Comment: 3 pages, LaTeX, uses mn.sty, 5 .ps figures, submitted to MNRA

Dynamical Models for the Milky Way

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.Comment: 10 pages, LaTeX, style file and 4 figures included. Invited talk presented at the meeting ``Formation of the Galactic Halo ... Inside and Out'', Tucson, October 9-11. Full .ps file available at ftp://ftp.physics.ox.ac.uk/pub/local/users/dehnen/MilkyWayModels.ps.g

Mass models of the Milky Way

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 only for R_d*/R0< 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 << R0 to affect profoundly the structure of the best-fitting model 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.Comment: 10 pages, LaTeX, mn.sty, 5 .ps figures, accepted by MNRAS major revision involving new cepheid & hipparcos dat

Lyapunov Exponents for the Intermittent Transition to Chaos

The dependence of the Lyapunov exponent on the closeness parameter, $\epsilon$, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we develop theoretical expressions for an isolated tangency channel in which the Lyapunov exponent is defined on single channel passes. Numerical simulations were done to compare theory to measurement across a range of $\epsilon$ values. Next, as an illustration of defining the Lyapunov exponent on many channel passes, a simulation of the intermittent transition in the logistic map is described. The modified theory for the channels is explained and a simple model for the gate entrance rates is constructed. An important correction due to the discrete nature of the iterative flow is identified and incorporated in an improved model. Realistic fits to the data were made for the Lyapunov exponents from the logistic gate and from the full simulation. A number of additional corrections which could improve the treatment of the gates are identified and briefly discussed.Comment: 25 pages LaTeX and 12 separate ps figure

A Revised Parallax and its Implications for RX J185635-3754

New astrometric analysis of four WFPC2 images of the isolated neutron star RX J185635-3754 show that its distance is 117 +/- 12 pc, nearly double the originally published distance. At the revised distance, the star's age is 5 x 10^5 years, its space velocity is about 185 km/s, and its radiation radius inferred from thermal emission is approximately 15 km, in the range of many equations of state both with and without exotic matter. These measurements remove observational support for an extremely soft equation of state. The star's birthplace is still likely to be in the Upper Sco association, but a connection with zeta Oph is now unlikely.Comment: submitted to ApJ Letter

Axially Uniform Magnetic Field-Modulation Excitation for Electron Paramagnetic Resonance in Rectangular and Cylindrical Cavities by Slot Cutting

In continuous-wave (CW) Electron Paramagnetic Resonance (EPR) a low-frequency time-harmonic magnetic field, called field modulation, is applied parallel to the static magnetic field and incident on the sample. Varying amplitude of the field modulation incident on the sample has consequences on spectral line-shape and line-height over the axis of the sample. Here we present a method of coupling magnetic field into the cavity using slots perpendicular to the sample axis where the slot depths are designed in such a way to produce an axially uniform magnetic field along the sample. Previous literature typically assumes a uniform cross-section and axial excitation due to the wavelength of the field modulation being much larger than the cavity. Through numerical analysis and insights obtained from the eigenfunction expansion of dyadic Green’s functions, it is shown that evanescent standing-wave modes with complex cross-sections are formed within the cavity. From this analysis, a W-band (94 GHz) cylindrical cavity is designed where modulation slots are optimized to present a uniform 100 kHz field modulation over the length of the sample