With the use of a detailed Milky Way nonaxisymmetric potential, observationally and dynamically constrained, the effects of the bar and the spiral arms in the Galaxy are studied in the disc and in the stellar halo. Especially the trapping of stars in
the disc and Galactic halo by resonances on the Galactic plane, induced by the Galactic bar, has been analysed in detail. To this purpose, a new method is presented to delineate the trapping regions using empirical diagrams of some orbital properties obtained in the Galactic potential. In these diagrams we plot in the inertial Galactic frame a characteristic orbital energy versus a characteristic orbital angular momentum, or versus the orbital Jacobi constant in the reference frame of the bar, when this is the only nonaxisymmetric component in the Galactic potential. With these diagrams some trapping regions are obtained in the disc and halo using a sample of disc stars and halo stars in the solar neighbourhood. We compute several families of periodic orbits on the Galactic plane, some associated with this resonant trapping. In particular, we find that the trapping effect of these resonances on the Galactic plane can extend several kpc from this plane, trapping stars in the Galactic halo. The purpose of our analysis is to investigate if the trapping regions contain some known moving groups in our Galaxy. We have applied our method to the Kapteyn group, a moving group in the halo, and we have found that this group appears not to be associated with a particular resonance on the Galactic plane.
Recent studies have presented evidence that the Milky Way global potential may be nonspherical. In this case, the assembling process of the Galaxy may have left long lasting stellar halo kinematic fossils due to the shape of the dark matter halo, pot
entially originated by orbital resonances. We further investigate such possibility, considering now potential models further away from $Lambda$CDM halos, like scalar field dark matter halos, MOND, and including several other factors that may mimic the emergence and permanence of kinematic groups, such as, a spherical and triaxial halo with an embedded disk potential. We find that regardless of the density profile (DM nature), kinematic groups only appear in the presence of a triaxial halo potential. For the case of a MOND like gravity theory no kinematic structure is present. We conclude that the detection of these kinematic stellar groups could confirm the predicted triaxiality of dark halos in cosmological galaxy formation scenarios.
We calculate orbits, tidal radii, and bulge-bar and disk shocking destruction rates for 63 globular clusters in our Galaxy. Orbits are integrated in both an axisymmetric and a non-axisymmetric Galactic potential that includes a bar and a 3D model for
the spiral arms. With the use of a Monte Carlo scheme, we consider in our simulations observational uncertainties in the kinematical data of the clusters. In the analysis of destruction rates due to the bulge-bar, we consider the rigorous treatment of using the real Galactic cluster orbit, instead of the usual linear trajectory employed in previous studies. We compare results in both treatments. We find that the theoretical tidal radius computed in the nonaxisymmetric Galactic potential compares better with the observed tidal radius than that obtained in the axisymmetric potential. In both Galactic potentials, bulge-shocking destruction rates computed with a linear trajectory of a cluster at its perigalacticons give a good approximation to the result obtained with the real trajectory of the cluster. Bulge-shocking destruction rates for clusters with perigalacticons in the inner Galactic region are smaller in the non-axisymmetric potential, as compared with those in the axisymmetric potential. For the majority of clusters with high orbital eccentricities (e > 0.5), their total bulge+disk destruction rates are smaller in the non-axisymmetric potential.
Using the most recent proper-motion determination of the old, Solar-metallicity, Galactic open cluster M 67, in orbital computations in a non-axisymmetric model of the Milky Way, including a bar and 3D spiral arms, we explore the possibility that the
Sun once belonged to this cluster. We have performed Monte Carlo numerical simulations to generate the present-day orbital conditions of the Sun and M 67, and all the parameters in the Galactic model. We compute 3.5 times 10^5 pairs of orbits Sun-M 67 looking for close encounters in the past with a minimum distance approach within the tidal radius of M 67. In these encounters we find that the relative velocity between the Sun and M 67 is larger than 20 km/s. If the Sun had been ejected from M 67 with this high velocity by means of a three-body encounter, this interaction would destroy an initial circumstellar disk around the Sun, or disperse its already formed planets. We also find a very low probability, much less than 10^-7, that the Sun was ejected from M 67 by an encounter of this cluster with a giant molecular cloud. This study also excludes the possibility that the Sun and M 67 were born in the same molecular cloud. Our dynamical results convincingly demonstrate that M67 could not have been the birth cluster of our Solar System.
Assuming the dark matter halo of the Milky Way as a non-spherical potential (i.e. triaxial, prolate, oblate), we show how the assembling process of the Milky Way halo, may have left long lasting stellar halo kinematic fossils only due to the shape of
the dark matter halo. In contrast with tidal streams, associated with recent satellite accretion events, these stellar kinematic groups will typically show inhomogeneous chemical and stellar population properties. However, they may be dominated by a single accretion event for certain mass assembling histories. If the detection of these peculiar kinematic stellar groups is confirmed, they would be the smoking gun for the predicted triaxiality of dark halos in cosmological galaxy formation scenarios.
We built models for low bulge mass spiral galaxies (late type as defined by the Hubble classification) using a 3-D self-gravitating model for spiral arms, and analyzed the orbital dynamics as a function of pitch angle, going from 10$deg$ to 60$deg$.
Testing undirectly orbital self-consistency, we search for the main periodic orbits and studied the density response. For pitch angles up to approximately $sim 20deg$, the response supports closely the potential permitting readily the presence of long lasting spiral structures. The density response tends to avoid larger pitch angles in the potential, by keeping smaller pitch angles in the corresponding response. Spiral arms with pitch angles larger than $sim 20deg$, would not be long-lasting structures but rather transient. On the other hand, from an extensive orbital study in phase space, we also find that for late type galaxies with pitch angles larger than $sim 50deg$, chaos becomes pervasive destroying the ordered phase space surrounding the main stable periodic and quasi-periodic orbits and even destroying them. This result is in good agreement with observations of late type galaxies, where the maximum observed pitch angle is $sim 50deg$.
In a previous work (Pichardo et al. 2005), we studied stable configurations for circumstellar discs in eccentric binary systems. We searched for invariant loops: closed curves (analogous to stable periodic orbits in time-independent potentials) that
change shape with the binary orbital phase, as test particles in them move under the influence of the binary potential. This approach allows us to identify stable configurations when pressure forces are unimportant, and dissipation acts only to prevent gas clouds from colliding with one another. We now extend this work to study the main geometrical properties of circumbinary discs. We have studied more than 100 cases with a range in eccentricity 0 .le. e .le. 0.9, and mass ratio 0.1 .le. q .le. 0.9. Although gas dynamics may impose further restrictions, our study sets lower stable bounds for the size of the central hole in a simple and computationally cheap way, with a relation that depends on the eccentricity and mass ratio of the central binary. We extend our previous studies and focus on an important component of these systems: circumbinary discs. The radii for stable orbits that can host gas in circumbinary discs are sharply constrained as a function of the binarys eccentricity. The circumbinary disc configurations are almost circular, with eccentricity e_d < 0.15, but if the mass ratio is unequal the disk is offset from the center of mass of the system. We compare our results with other models, and with observations of specific systems like GG Tauri A, UY Aurigae, HD 98800 B, and Fomalhaut, restricting the plausible parameters for the binary.
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary terms to give
a fairly good approximation that we compare with simulations, resulting in a simple set of analytical expressions that solve periodic orbits on discs of binary systems without the need of solving the motion equations by numerical integrations.
