Academic literature on the topic 'Lynden-Bell theory'

ABSTRACT Using the canonical Hamilton–Jacobi approach we study the Lynden-Bell concept of bar formation based on the idea of orbital trapping parallel to the long or short axes of the oval potential distortion. The concept considered a single parameter – a sign of the derivative of the precession rate over angular momentum, determining the orientation of the trapped orbits. We derived a perturbation Hamiltonian that includes two more parameters characterizing the background disc and the perturbation, which are just as important as the earlier known one. This allows us to link the concept with the matrix approach in linear perturbation theory, the theory of weak bars, and explain some features of the non-linear secular evolution observed in N-body simulations.

AbstractWe report the discovery that substructures/subhaloes of a galaxy-size halo tend to fall in together in groups in cosmological simulations, something that may explain the oddity of the MW satellite distribution. The original clustering at the time of infall is still discernible in the angular momenta of the subhaloes even for events which took place up to eight Gyrs ago, z ~ 1. This phenomenon appears to be rather common since at least 1/3 of the present-day subhaloes have fallen in groups in our simulations. Hence, this may well explain the Lynden-Bell & Lynden-Bell ghostly streams. We have also found that the probability of building up a flattened distribution similar to the MW satellites is as high as ~ 80% if the MW satellites were from only one group and ~ 20% when five groups are involved. Therefore, we conclude that the ‘peculiar’ distribution of satellites around the MW can be expected with the CDM structure formation theory. This non-random assignment of satellites to subhaloes implies an environmental dependence on whether these low-mass objects are able to form stars, possibly related to the nature of reionization in the early Universe.

AbstractWe model a massless viscous disk using smoothed particle hydrodynamics (SPH) and note that it evolves according to the Lynden-Bell & Pringle (1974) theory until a non-axisymmetric instability develops at the inner edge of the disk. This instability may have the same origin as the instability of initially axisymmetric viscous disks discussed by Lyubarskij, Postnov & Prokhorov (1994). To clarify the evolution we evolved single and double rings of particles. It is actually inconsistent with the SPH scheme to set up a single ring as an initial condition because SPH assumes a smoothed initial state. As would be expected from an SPH simulation, the ring rapidly breaks up into a band. We analyse the stability of the ring and show that the predictions are confirmed by the simulation.

The cosmological axion theory leads to the prediction of axionic mini-clusters of mass M ~ 10-9M⊙, which form at the time t e of equipartition of matter and radiation. By applying the two-body relaxation formula of Spitzer and Hart, we show, for the heterotic superstring theory of Gross et al., that these mini-clusters, considered as point masses, themselves cluster into axion mini-stars of mass [Formula: see text] within the age of the Universe t0 only if they are located within a distance R ~ 0.1 pc of the Galactic Center. Here, λ ≡ fB/fA is the ratio of the second to model-independent axion decay constants, assuming the QCD decay constant to be in the range [Formula: see text], and [Formula: see text] is the strong-interaction coupling parameter. Thus, if axion mini-stars are to explain the microlensing observations by the EROS and MACHO groups towards the Galactic Bulge and the Large and Small Magellanic Clouds, then a collisionless relaxation mechanism is required, as proposed by Seidel and Suen (essentially the violent relaxation of Lynden–Bell), or the four-axion self-interaction effect considered by Tkachev.

Joint Discussion 1 was supported by Division IV (Stars) and Commission 29 (Stellar Spectra), and co-supported by Commissions 28 (Galaxies), 36 (Theory of Stellar Atmospheres) and 37 (Stellar Clusters and Associations). Members of the scientific organizing committee were: N. Arimoto (Japan), B. Barbuy (Brazil), T. Beers (USA), J. Bergeron (Germany), M. Bessell (Australia), R. Cayrel (France), G. Gilmore (UK), B. Gustafsson (Sweden), F. Matteucci (Italy), P. Nissen (Den-mark), and M. Rich (USA).The inspiration for this meeting was the growing overlap and connections between previously separate areas of astrophysical research, namely, studies of stellar abundances, the bulges of galaxies, the gaseous components of nearby galaxies and the clouds (some of which may be primordial) responsible for the narrow absorption lines in quasars.The signature of the early chemical evolution of our Galaxy is imprinted in the abundance ratios of the oldest stars. We recall that element ratios are determined by a mix of the relative rates of different types of supernovae, the stellar IMF, and the relative histories of star formation rates and gaseous flows, and thus encapsulate much of the history of star formation and ISM evolution in galaxies. Hence, abundance ratios in stars are a primary probe for testing theories of galaxy formation and evolution.We do not know how the Galaxy formed: both the Eggen, Lynden-Bell & Sandage (1962) and the Searle & Zinn (1978) scenarios may be accommodated in the recent proposal of van den Bergh (1993) where the inner Galaxy follows ELS, whereas the outer Galaxy formation conforms to the Searle-Zinn proposition. A combination of abundance ratios, ages derived from colour-magnitude diagrams, and kinematical properties, can give us the required information to trace the past history of our Galaxy. We note here, that although stellar evolution and model atmospheres are not discussed in the proceedings both topics are of fundamental underlying importance. Model atmospheres are used to derive temperatures, colors and bolometric corrections of stars that are used not only in abundance analyses but also in deriving the ages of stars by comparing CM diagrams with HR diagrams. This process is under close scrutiny because of the apparent difference between the ages of the oldest stars and the expansion age of the universe.

2009/2010
In this Thesis we describe the theoretical-computational study performed on the behavior of isolated systems, far from thermodynamic equilibrium. Analyzing models well-known in literature we follow a path bringing to the classification of different behaviors in function of the interaction range of the systems' particles. In the case of systems with long-range interaction we studied the "Quasi-Stationary states" (QSSs) which emerge at short times when the system evolves with Hamiltonian dynamics. Their interest is in the fact that in many physical systems, such as self-gravitating systems, plasmas and systems characterized by wave-particle interaction, QSSs are the only experimentally accessible regime. QSS are defined as stable solutions of the Vlasov equation and, as their duration diverges with the system size, for large systems' size they can be seen as the true equilibria. They do not follow the Boltzmann statistics, and it does not exists a general theory which describes them. Anyway it is possible to give an approximate description using Lynden-Bell theory. One part of the thesis is devoted to shed light on the characteristics of the phase diagram of the "Hamiltonian mean field" model (HMF), during the QSS, calculated with the Lynden-Bell theory. The results of our work allowed to confirm numerically the presence of a phase re-entrance. In the Thesis is present also a detailed description on the system's caloric curves and on the metastability. Still in this context we show an analysis of the equivalence of the statistical ensembles, confirmed in almost the totality of the phase diagram (except for a small region), although the presence of negative specific heat in the microcanonical ensemble, which in Boltzmannian systems implies the non-equivalence of statistical ensembles. This result allowed us to arrive to a surprising conclusion: the presence of negative specific heat in the canonical ensemble. Still in the context of long-range interacting systems we analyze the linear stability of the non-homogeneous QSSs with respect to the Vlasov equation. Since the study of QSS find an application in the Free-electron laser (FEL) and other light sources, which are characterized by wave-particle interaction, we analyze, in the last chapter, the experimental perspectives of our work in this context. The other class of systems we studied are short-range interacting systems. Here the behavior of the components of the system is strongly influenced by the neighbors, and if one takes a system in a disordered state (a zero magnetization state for magnetic systems), which relaxes towards an ordered equilibrium state, one sees that the ordering process first develops locally and then extends to the whole system forming domains of opposed magnetization which grow in size. This process is called "coarsening". Our work in this field consisted in investigating numerically the laws of scale, and in the Thesis we characterize the temporal dependence of the domain sizes for different interaction ranges and we show a comparison between Hamiltonian and Langevin dynamics. This work inserts in the open debate on the equivalence of different dynamics where we found that, at least for times not too large, the two dynamics give different scaling laws.
In questa Tesi è stato fatto uno studio di natura teorico-computazionale sul comportamento dei sistemi isolati lontani dall'equilibrio termodinamico. Analizzando modelli noti in letteratura è stato seguito un percorso che ha portato alla classificazione di differenti comportamenti in funzione del range di interazione delle particelle del sistema. Nel caso di sistemi con interazione a lungo raggio sono stati studiati gli "stati quasi-stazionari" (QSS) che emergono a tempi brevi quando il sistema evolve con dinamica hamiltoniana. Il loro interesse risiede nel fatto che in molti sistemi fisici, come i sistemi auto-gravitanti, plasmi e sistemi caratterizzati da interazione onda-particella, i QSS risultano essere gli unici regimi accessibili sperimentalmente. I QSS sono definiti come soluzioni stabili dell'equazione di Vlasov, e visto che la loro durata diverge con la taglia del sistema, per sistemi di grandi dimensioni possono essere visti come i veri stati di equilibrio. Questi non seguono la statistica di Bolzmann, e non esiste una teoria generale che li descriva. E' tuttavia possibile fare una descrizione approssimata utilizzando la teoria di Lynden-Bell. Una parte della tesi è dedicata alla comprensione delle caratteristiche del diagramma di fase del modello "Hamiltonian mean field" (HMF) durante il QSS, calcolato con la teoria di Lynden-Bell. Il risultato del nostro lavoro ha permesso di confermare numericamente la presenza di fasi rientrati. E' inoltre presente un'analisi dettagliata sulle curve caloriche del sistema e sulla metastabilità. Sempre in questo contesto è stata fatto uno studio sull'equivalenza degli ensemble statistici, confermata nella quasi totalità del diagramma di fase (tranne in una piccola regione), nonostante la presenza di calore specifico negativo nell'insieme microcanonico, che in sistemi Boltzmanniani è sinonimo di non-equivalenza degli ensemble statistici. Questo risultato ci ha permesso di arrivare ad una sorprendente conclusione: la presenza di calore specifico negativo nell'insieme canonico. Sempre nel contesto dei sistemi con interazione a lungo range, è stata analizzata la stabilità lineare rispetto all'equazione di Vlasov degli stati quasi-stazionari non-omogenei. Poiché lo studio dei QSS trova applicazione nel Free-electron laser (FEL) e in altre sorgenti di luce, caratterizzate dall'interazione onda-particella, abbiamo analizzato anche le prospettive sperimentali del nostro lavoro in questo contesto. L'altra classe di sistemi che è stata studiata sono i sistemi con interazione a corto raggio. Qui il comportamento dei componenti del sistema è fortemente influenzato dai vicini, e se si prende un sistema in uno stato disordinato (a magnetizzazione nulla nei sistemi magnetici) che rilassa verso l'equilibrio ordinato, si vede che il processo di ordinamento si sviluppa prima localmente e poi si estende a tutto il sistema formando dei domini di magnetizzazione opposta che crescono in taglia. Questo processo si chiama "coarsening". Il nostro lavoro in questo contesto è consistito in una investigazione numerica delle leggi di scala, e nella tesi è stata caratterizzata la dipendenza temporale della taglia dei domini per differenti range di interazione ed è stato fatto un confronto fra dinamica hamiltoniana e dinamica di Langevin. Questi risultati si inseriscono nel dibattito aperto sull'equivalenza di differenti dinamiche, e si è mostrato che, almeno per tempi non troppo grandi, le due dinamiche portano a leggi di scala differenti.
XXIII Ciclo
1982