Models for the 3-D axisymmetric gravitational potential of the Milky Way Galaxy - A detailed modelling of the Galactic disk

Aims. Galaxy mass models based on simple and analytical functions for the density and potential pairs have been widely proposed in the literature. Disk models constrained by kinematic data alone give information on the global disk structure only very near the Galactic plane. We attempt to circumvent this issue by constructing disk mass models whose three-dimensional structures are constrained by a recent Galactic star counts model in the near-infrared and also by observations of the hydrogen distribution in the disk. Our main aim is to provide models for the gravitational potential of the Galaxy that are fully analytical but also with a more realistic description of the density distribution in the disk component. Methods. From the disk model directly based on the observations (here divided into the thin and thick stellar disks and the HI and H$_2$ disks subcomponents), we produce fitted mass models by combining three Miyamoto-Nagai disk profiles of any "model order" (1, 2, or 3) for each disk subcomponent. The Miyamoto-Nagai disks are combined with models for the bulge and "dark halo" components and the total set of parameters is adjusted by observational kinematic constraints. A model which includes a ring density structure in the disk, beyond the solar Galactic radius, is also investigated. Results. The Galactic mass models return very good matches to the imposed observational constraints. In particular, the model with the ring density structure provides a greater contribution of the disk to the rotational support inside the solar circle. The gravitational potential models and their associated force-fields are described in analytically closed forms, and in addition, they are also compatible with our best knowledge of the stellar and gas distributions in the disk component. The gravitational potential models are suited for investigations of orbits in the Galactic disk.Comment: 22 pages, 13 figures, 11 tables, accepted for publication in A&

Comments on the Quantum Potential Approach to a Class of Quantum Cosmological Models

In this comment we bring attention to the fact that when we apply the ontological interpretation of quantum mechanics, we must be sure to use it in the coordinate representation. This is particularly important when canonical tranformations that mix momenta and coordinates are present. This implies that some of the results obtained by A. B\l aut and J. Kowalski-Glikman are incorrect.Comment: 7 pages, LaTe

Modelling resonances and orbital chaos in disk galaxies. Application to a Milky Way spiral model

Context: Resonances in the stellar orbital motion under perturbations from spiral arms structure play an important role in the evolution of the disks of spiral galaxies. The epicyclic approximation allows the determination of the corresponding resonant radii on the equatorial plane (for nearly circular orbits), but is not suitable in general. Aims: We expand the study of resonant orbits by analysing stellar motions perturbed by spiral arms with Gaussian-shaped profiles without any restriction on the stellar orbital configurations, and we expand the concept of Lindblad (epicyclic) resonances for orbits with large radial excursions. Methods: We define a representative plane of initial conditions, which covers the whole phase space of the system. Dynamical maps on representative planes are constructed numerically, in order to characterize the phase-space structure and identify the precise location of resonances. The study is complemented by the construction of dynamical power spectra, which provide the identification of fundamental oscillatory patterns in the stellar motion. Results: Our approach allows a precise description of the resonance chains in the whole phase space, giving a broader view of the dynamics of the system when compared to the classical epicyclic approach, even for objects in retrograde motion. The analysis of the solar neighbourhood shows that, depending on the current azimuthal phase of the Sun with respect to the spiral arms, a star with solar kinematic parameters may evolve either inside the stable co-rotation resonance or in a chaotic zone. Conclusions: Our approach contributes to quantifying the domains of resonant orbits and the degree of chaos in the whole Galactic phase-space structure. It may serve as a starting point to apply these techniques to the investigation of clumps in the distribution of stars in the Galaxy, such as kinematic moving groups.Comment: 17 pages, 15 figures. Matches accepted version in A&

A new model for gravitational potential perturbations in disks of spiral galaxies. An application to our Galaxy

We propose a new, more realistic, description of the perturbed gravitational potential of spiral galaxies, with spiral arms having Gaussian-shaped groove profiles. We investigate the stable stellar orbits in galactic disks, using the new perturbed potential. The influence of the bulge mass on the stellar orbits in the inner regions of a disk is also investigated. The new description offers the advantage of easy control of the parameters of the Gaussian profile of its potential. We find a range of values for the perturbation amplitude from 400 to 800 km^2 s^{-2} kpc^{-1} which implies a maximum ratio of the tangential force to the axisymmetric force between 3% and 6%, approximately. Good self-consistency of arm shapes is obtained between the Inner Lindblad resonance (ILR) and the 4:1 resonance. Near the 4:1 resonance the response density starts to deviate from the imposed logarithmic spiral form. This creates bifurcations that appear as short arms. Therefore the deviation from a perfect logarithmic spiral in galaxies can be understood as a natural effect of the 4:1 resonance. Beyond the 4:1 resonance we find closed orbits which have similarities with the arms observed in our Galaxy. In regions near the center, in the presence of a massive bulge, elongated stellar orbits appear naturally, without imposing any bar-shaped potential, but only extending the spiral perturbation a little inward of the ILR. This suggests that a bar is formed with a half-size around 3 kpc by a mechanism similar to that of the spiral arms. The potential energy perturbation that we adopted represents an important step in the direction of self-consistency, compared to previous sine function descriptions of the potential. Our model produces a realistic description of the spiral structure, able to explain several details that were not yet understood.Comment: 12 pag., 11 fig. Accepted for publication in A&A, 2012 December 1

Persistence on airline accidents

This paper analyses airline accidents data from 1927-2006. The fractional integration methodology is adopted. It is shown that airline accidents are persistent and (fractionally) cointegrated with airline traffic. Thus, there exists an equilibrium relation between air accidents and airline traffic, with the effect of the shocks to that relationship disappearing in the long run. Policy implications are derived for countering accidents events.