Instabilities and stickiness in a 3D rotating galactic potential

We study the dynamics in the neighborhood of simple and double unstable periodic orbits in a rotating 3D autonomous Hamiltonian system of galactic type. In order to visualize the four dimensional spaces of section we use the method of color and rotation. We investigate the structure of the invariant manifolds that we found in the neighborhood of simple and double unstable periodic orbits in the 4D spaces of section. We consider orbits in the neighborhood of the families x1v2, belonging to the x1 tree, and the z-axis (the rotational axis of our system). Close to the transition points from stability to simple instability, in the neighborhood of the bifurcated simple unstable x1v2 periodic orbits we encounter the phenomenon of stickiness as the asymptotic curves of the unstable manifold surround regions of the phase space occupied by rotational tori existing in the region. For larger energies, away from the bifurcating point, the consequents of the chaotic orbits form clouds of points with mixing of color in their 4D representations. In the case of double instability, close to x1v2 orbits, we find clouds of points in the four dimensional spaces of section. However, in some cases of double unstable periodic orbits belonging to the z-axis family we can visualize the associated unstable eigensurface. Chaotic orbits close to the periodic orbit remain sticky to this surface for long times (of the order of a Hubble time or more). Among the orbits we studied we found those close to the double unstable orbits of the x1v2 family having the largest diffusion speed.Comment: 29pages, 25 figures, accepted for publication in the International Journal of Bifurcation and Chao

Elliptical Galaxy Dynamics

A review of elliptical galaxy dynamics, with a focus on nonintegrable models. Topics covered include torus construction; modelling axisymmetric galaxies; triaxiality; collisionless relaxation; and collective instabilities.Comment: 97 Latex pages, 14 Postscript figures, uses aastex. To appear in Publications of the Astronomical Society of the Pacific, February 199

Estimation of the diffusion time in a triaxial galactic potential

In this work we apply the Shannon entropy based method to derive a diffusion or instability time in a triaxial model resembling an elliptical galaxy. We succeed in getting an accurate time-scale for diffusion using this no v el technique after adopting a particular initial starting space, the one defined by the unperturbed integrals of the system. Comparisons with other standard techniques, such as a least-squares fit on the variance evolution of the integrals and the straight numerical integrations of the equations of motion, are included. The physical results provided in this effort reveal that the role of chaotic motion in triaxial galactic models is almost irrele v ant in galactic time-scales, in agreement with previous qualitative approaches to this issue.Facultad de Ciencias Astronómicas y Geofísica

Comparative study of variational chaos indicators and ODEs' numerical integrators

The reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of Maffione et al. (2011a) for mappings, a detailed comparison among the widespread indicators of chaos in a general system is still lacking. Such a comparison could lead to select the most efficient algorithms given a certain dynamical problem. Furthermore, in order to choose the appropriate numerical integrators to compute them, more comparative studies among numerical integrators are also needed. This work deals with both problems. We first extend the work of Maffione et al. (2011) for mappings to the 2D H\'enon & Heiles (1964) potential, and compare several variational indicators of chaos: the Lyapunov Indicator (LI); the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI) and its generalized version, the Generalized Alignment Index (GALI); the Fast Lyapunov Indicator (FLI) and its variant, the Orthogonal Fast Lyapunov Indicator (OFLI); the Spectral Distance (D) and the Dynamical Spectras of Stretching Numbers (SSNs). We also include in the record the Relative Lyapunov Indicator (RLI), which is not a variational indicator as the others. Then, we test a numerical technique to integrate Ordinary Differential Equations (ODEs) based on the Taylor method implemented by Jorba & Zou (2005) (called taylor), and we compare its performance with other two well-known efficient integrators: the Prince & Dormand (1981) implementation of a Runge-Kutta of order 7-8 (DOPRI8) and a Bulirsch-St\"oer implementation. These tests are run under two very different systems from the complexity of their equations point of view: a triaxial galactic potential model and a perturbed 3D quartic oscillator.Instituto de Astrofísica de La Plat

Italian Science Case for ALMA Band 2+3

The Premiale Project "Science and Technology in Italy for the upgraded ALMA Observatory - iALMA" has the goal of strengthening the scientific, technological and industrial Italian contribution to the Atacama Large Millimeter/submillimeter Array (ALMA), the largest ground based international infrastructure for the study of the Universe in the microwave. One of the main objectives of the Science Working Group (SWG) inside iALMA, the Work Package 1, is to develop the Italian contribution to the Science Case for the ALMA Band 2 or Band 2+3 receiver. ALMA Band 2 receiver spans from ~67 GHz (bounded by an opaque line complex of ozone lines) up to 90 GHz which overlaps with the lower frequency end of ALMA Band 3. Receiver technology has advanced since the original definition of the ALMA frequency bands. It is now feasible to produce a single receiver which could cover the whole frequency range from 67 GHz to 116 GHz, encompassing Band 2 and Band 3 in a single receiver cartridge, a so called Band 2+3 system. In addition, upgrades of the ALMA system are now foreseen that should double the bandwidth to 16 GHz. The science drivers discussed below therefore also discuss the advantages of these two enhancements over the originally foreseen Band 2 system.Comment: 43 pages, 21 figure

Chirikov and Nekhoroshev diffusion estimates: bridging the two sides of the river

We present theoretical and numerical results pointing towards a strong connection between the estimates for the diffusion rate along simple resonances in multidimensional nonlinear Hamiltonian systems that can be obtained using the heuristic theory of Chirikov and a more formal one due to Nekhoroshev. We show that, despite a wide-spread impression, the two theories are complementary rather than antagonist. Indeed, although Chirikov's 1979 review has thousands of citations, almost all of them refer to topics such as the resonance overlap criterion, fast diffusion, the Standard or Whisker Map, and not to the constructive theory providing a formula to measure diffusion along a single resonance. However, as will be demonstrated explicitly below, Chirikov's formula provides values of the diffusion coefficient which are quite well comparable to the numerically computed ones, provided that it is implemented on the so-called optimal normal form derived as in the analytic part of Nekhoroshev's theorem. On the other hand, Chirikov's formula yields unrealistic values of the diffusion coefficient, in particular for very small values of the perturbation, when used in the original Hamiltonian instead of the optimal normal form. In the present paper, we take advantage of this complementarity in order to obtain accurate theoretical predictions for the local value of the diffusion coefficient along a resonance in a specific 3DoF nearly integrable Hamiltonian system. Besides, we compute numerically the diffusion coefficient and a full comparison of all estimates is made for ten values of the perturbation parameter, showing a very satisfactory agreement.Comment: 25 pages, 9 figures. NOTICE: this is the author's version of a work that was accepted for publication in Physica D. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publicatio

Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport

Comparing Hydrodynamics Codes for Modeling the Gas Flow in Barred Spiral Galaxies

Η κατανόηση και μοντελοποίηση της ροής του αερίου στους δίσκους ραβδωτών γαλαξιών είναι ένα σημαντικό βήμα προς την κατανόηση της μορφολογίας των περιοχών υψηλής πυκνότητας του αερίου, των ιδιοτήτων των σοκ καθώς και των κύριων περιοχών του δίσκου, όπου λαμβάνει χώρα η αστρογέννεση. Οι υδροδυναμικές προσομοιώσεις είναι ένα ισχυρό εργαλείο για την επίτευξη των παραπάνω στόχων. Παρόλα αυτά, διαφορετικές μέθοδοι αριθμητικής επίλυσης των υδροδυναμικών εξισώσεων οδηγούν συχνά σε ποσοτικά διαφορετικά αποτελέσματα και ιδιότητες εισροής του αερίου. Παρουσιάζουμε τη μελέτη μας πάνω σε αυτό το αντικείμενο με τη χρήση δύο υδροκωδίκων και τη σύγκριση των αντίστοιχων αποτελεσμάτων. Αρχικά χρησιμοποιούμε το καλά μελετημένο μοντέλο της ράβδου του Ferrers, για τη σύγκριση των αποτελεσμάτων Λαγκρανζιανών κωδικών και κωδίκων πλέγματος, σε προσομοιώσεις αυτού του δυναμικού. Αναλύουμε τη σχέση μεταξύ της δυναμικής των αστέρων και της ροής του αερίου. Παρουσιάζουμε, επίσης, αποτελέσματα από μια παρόμοια μελέτη εντός ραβδωτού δυναμικού, προερχόμενου από παρατηρήσεις, στο οποίο η μορφολογία που αποτελεί τον “σκελετό” των τροχιών του μοντέλου, διαφέρει σημαντικά από αυτή της ράβδου του Ferrers. Τέλος, δείχνουμε πώς σε αυτήν την περίπτωση η ροή του αερίου τείνει να αποφεύγει τις περιοχές των τροχιών με μεγάλους βρόχους κοντά στα άκρα της ράβδου.Understanding and modeling the flow of gas in galactic disks of barred galaxies is a key step towards understanding the morphology of their high gas density regions, the shock properties as well as the main locations on the disc, where global star formation is taking place. Hydrodynamic simulations are a powerful tool for reaching the above goals. However, different methods for solving numerically the hydrodynamics equations, lead frequently to different quantitative results and inflow properties. We present our study on this topic by means of two hydrocodes and the comparison of their respective results. Firstly, we use the well-studied Ferrers bar model in order to compare the results of Lagrangian and Mesh codes in simulations of this potential. We discuss the connection of the underlying stellar dynamics with the gas flow. We also present results from a similar study with a barred potential derived from observations, in which the morphology of the orbits that compose the orbital backbone of the model differs considerably from that of the Ferrers bar. Finally, we show how in this case the gas flow tends to avoid areas of orbits with big loops near the ends of the bar

Comparing real and synthetic observations of protostellar disks

Nascent envelope disk structures around protostars play a crucial role in the process of star and planet formation. As ALMA reveals unprecedented details of the envelope, disk, and outflow structures in nearby protostellar systems, a consistent interpretation for these observations remains absent, instead, highly simplified models are often adopted to partially fit the observed features. In this project, we aim to generate more realistic synthetic observations of the nascent protostellar disk and envelope system, using existing radiation and non-ideal magnetohydrodynamic simulations of protostellar collapse and disk formation. The main goal of the project is to provide multi-facet interpretation of the current continuum and polarization observations of protostellar sources at their earliest stages, and offer more realistic constraints on the dust growth in the early protoplanetary disks