The spiral structure of the Galaxy revealed by CS sources and evidence for the 4:1 resonance

We present a map of the spiral structure of the Galaxy, as traced by molecular carbon monosulphide (CS) emission associated with IRAS sources which are believed to be compact H II regions. The CS line velocities are used to determine the kinematic distances of the sources in order to investigate their distribution in the galactic plane. This allows us to use 870 objects to trace the arms, a number larger than that of previous studies based on classical H II regions. The distance ambiguity of the kinematic distances, when it exists, is solved by different procedures, including the latitude distribution and an analysis of the longitude-velocity diagram. The study of the spiral structure is complemented with other tracers: open clusters, Cepheids, methanol masers and H II regions. The well-defined spiral arms are seen to be confined inside the corotation radius, as is often the case in spiral galaxies. We identify a square-shaped sub-structure in the CS map with that predicted by stellar orbits at the 4:1 resonance (four epicycle oscillations in one turn around the galactic centre). The sub-structure is found at the expected radius, based on the known pattern rotation speed and epicycle frequency curve. An inner arm presents an end with strong inwards curvature and intense star formation that we tentatively associate with the region where this arm surrounds the extremity of the bar, as seen in many barred galaxies. Finally, a new arm with concave curvature is found in the Sagitta to Cepheus region of the sky. The observed arms are interpreted in terms of perturbations similar to grooves in the gravitational potential of the disc, produced by crowding of stellar orbits.

Artificial satellites orbits in 2:1 resonance: GPS constellation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The Orbital Dynamics of Synchronous Satellites: Irregular Motions in the 2:1 Resonance

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

Resonance and chaos .1. First-order interior resonances

Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted three-body problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincare surfaces of section with a mass ratio of 10(-3) (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. on theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.

Relaxation-chaos phenomena in celestial mechanics. I. On wisdom's model for the 3/1 kirkwood gap

Sudden eccentricity increases of asteroidal motion in 3/1 resonance with Jupiter were discovered and explained by J. Wisdom through the occurrence of jumps in the action corresponding to the critical angle (resonant combination of the mean motions). We pursue some aspects of this mechanism, which could be termed relaxation-chaos: that is, an unconventional form of homoclinic behavior arising in perturbed integrable Hamiltonian systems for which the KAM theorem hypothesis do not hold. © 1987.

Dynamics of the 3:1 resonant planetary systems

Many of the discovered exoplanetary systems are involved inside mean-motion resonances. In this work we focus on the dynamics of the 3:1 mean-motion resonant planetary systems. Our main purpose is to understand the dynamics in the vicinity of the apsidal corotation resonance (ACR) which are stationary solutions of the resonant problem. We apply the semi-analytical method (Michtchenko et al., 2006) to construct the averaged three-body Hamiltonian of a planetary system near a 3:1 resonance. Then we obtain the families of ACR, composed of symmetric and asymmetric solutions. Using the symmetric stable solutions we observe the law of structures (Ferraz-Mello,1988), for different mass ratio of the planets. We also study the evolution of the frequencies of σ1, resonant angle, and Δω, the secular angle. The resonant domains outside the immediate vicinity of ACR are studied using dynamical maps techniques. We compared the results obtained to planetary systems near a 3:1 MMR, namely 55 Cnc b-c, HD 60532 b-c and Kepler 20 b-c.

Resonance and chaos: I. First-order interior resonances

Analytical models for studying the dynamical behaviour of objects near interior, mean motion resonances are reviewed in the context of the planar, circular, restricted threebody problem. The predicted widths of the resonances are compared with the results of numerical integrations using Poincaré surfaces of section with a mass ratio of 10-3 (similar to the Jupiter-Sun case). It is shown that for very low eccentricities the phase space between the 2:1 and 3:2 resonances is predominantly regular, contrary to simple theoretical predictions based on overlapping resonance. A numerical study of the 'evolution' of the stable equilibrium point of the 3:2 resonance as a function of the Jacobi constant shows how apocentric libration at the 2:1 resonance arises; there is evidence of a similar mechanism being responsible for the centre of the 4:3 resonance evolving towards 3:2 apocentric libration. This effect is due to perturbations from other resonances and demonstrates that resonances cannot be considered in isolation. On theoretical grounds the maximum libration width of first-order resonances should increase as the orbit of the perturbing secondary is approached. However, in reality the width decreases due to the chaotic effect of nearby resonances.

Resonance fluorescence spectrum of a \Lambda-type quantum emitter close to a metallic nanoparticle

We theoretically study the resonance fluorescence spectrum of a three-level quantum emitter coupled to a spherical metallic nanoparticle. We consider the case that the quantum emitter is driven by a single laser field along one of the optical transitions. We show that the development of the spectrum depends on the relative orientation of the dipole moments of the optical transitions in relation to the metal nanoparticle. In addition, we demonstrate that the location and width of the peaks in the spectrum are strongly modified by the exciton-plasmon coupling and the laser detuning, allowing to achieve controlled strongly subnatural spectral line. A strong antibunching of the fluorescent photons along the undriven transition is also obtained. Our results may be used for creating a tunable source of photons which could be used for a probabilistic entanglement scheme in the field of quantum information processing.

Physical and dynamical characterization of (5201) Ferraz-Mello, a possible extinct Jupiter family comet

Context. The subject of asteroids in cometary orbits (ACOs) has been of growing interest lately. These objects have the orbital characteristics typical of comets, but are asteroidal in appearance, i.e., show no signs of a coma at any part of their orbits. At least a fraction of these objects are thought to be comets that have either exhausted all their volatile content or developed a refractory crust that prevents sublimation. In particular, the asteroid ( 5201) Ferraz-Mello has, since its discovery, been suspected to be an extinct Jupiter family comet due to the peculiar nature of its orbit. Aims. The aim of this work is to put constraints on the possible origin of ( 5201) Ferraz-Mello by means of spectroscopic characterization and a study of the dynamics of this asteroid. Methods. We used the SOAR Optical Imager (SOI) to obtain observations of ( 5201) Ferraz-Mello using four SDSS filters. These observations were compared to asteroids listed in the Sloan Moving objects catalog and also to photometry of cometary nuclei, Centaurs, and TNOs. The orbital evolution of ( 5201) Ferraz-Mello and of a sample of asteroids and comets that are close to that object in the a - e plane were simulated using a pure N-body code for 4 000 years forward and 4 000 years backward in time. Results. The reflectance spectrum obtained from its colors in the SDSS system is unusual, with a steep spectral gradient that is comparable to TNOs and Centaurs, but with an increase in the reflectance in the g band that is not common in those populations. A similar behavior is seen in cometary nuclei that were observed in the presence of a faint dust coma. The dynamical results confirm the very chaotic evolution found previously and its dynamical similarity to the chaotic evolution of some comets. The asteroid is situated in the very stochastic layer at the border of the 2/1 resonance, and it has a very short Lyapunov time ( 30 - 40) years. Together, the spectral characteristcs and the dynamical evolution suggest that ( 5201) Ferraz-Mello is a dormant or extinct comet.

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

Chemically tagging the Hyades stream: does it partly originate from the Hyades cluster?

The Hyades stream has long been thought to be a dispersed vestige of the Hyades cluster. However, recent analyses of the parallax distribution, of the mass function, and of the action-space distribution of stream stars have shown it to be rather composed of orbits trapped at a resonance of a density disturbance. This resonant scenario should leave a clearly different signature in the element abundances of stream stars than the dispersed cluster scenario, since the Hyades cluster is chemically homogeneous. Here, we study the metallicity as well as the element abundances of Li, Na, Mg, Fe, Zr, Ba, La, Ce, Nd and Eu for a random sample of stars belonging to the Hyades stream, and compare them with those of stars from the Hyades cluster. From this analysis: (i) we independently confirm that the Hyades stream cannot be solely composed of stars originating in the Hyades cluster; (ii) we show that some stars (namely 2/21) from the Hyades stream nevertheless have abundances compatible with an origin in the cluster; (iii) we emphasize that the use of Li as a chemical tag of the cluster origin of main-sequence stars is very efficient in the range 5500 K <= T(eff) <= 6200 K, since the Li sequence in the Hyades cluster is very tight, while at the same time spanning a large abundance range; (iv) we show that, while this evaporated population has a metallicity excess of similar to 0.2 dex with respect to the local thin-disc population, identical to that of the Hyades cluster, the remainder of the Hyades stream population has still a metallicity excess of similar to 0.06-0.15 dex, consistent with an origin in the inner Galaxy and (v) we show that the Hyades stream can be interpreted as an inner 4:1 resonance of the spiral pattern: this then also reproduces an orbital family compatible with the Sirius stream, and places the origin of the Hyades stream up to 1 kpc inwards from the solar radius, which might explain the observed metallicity excess of the stream population.