Actions for axisymmetric potentials

We give an algorithm for the economical calculation of angles and actions for stars in axisymmetric potentials. We test the algorithm by integrating orbits in a realistic model of the Galactic potential, and find that, even for orbits characteristic of thick-disc stars, the errors in the actions are typically smaller than 2 percent. We describe a scheme for obtaining actions by interpolation on tabulated values that significantly accelerates the process of calculating observables quantities, such as density and velocity moments, from a distribution function.Comment: 5 pages accepted for publication in MNRA

The role of thermal evaporation in galaxy formation

In colour-magnitude diagrams most galaxies fall in either the ``blue cloud'' or the ``red sequence'', with the red sequence extending to significantly brighter magnitudes than the blue cloud. The bright-end of the red sequence comprises elliptical galaxies (Es) with boxy isophotes and luminosity profiles with shallow central cores, while fainter Es have disky isophotes and power-law inner surface-brightness (SB) profiles. An analysis of published data reveals that the centres of galaxies with power-law central SB profiles have younger stellar populations than the centres of cored galaxies. We argue that thermal evaporation of cold gas by virial-temperature gas plays an important role in determining these phenomena. In less massive galaxies, thermal evaporation is not very efficient, so significant amounts of cold gas can reach the galaxy centre and fill a central core with newly formed stars, consistent with the young stellar ages of the cusps of Es with power-law SB profiles. In more massive galaxies, cold gas is evaporated within a dynamical time, so star formation is inhibited, and a core in the stellar density profile produced by dissipationless dynamics cannot be refilled. The different observed properties of AGN in higher-mass and lower-mass ellipticals are also explained because in the former the central black holes invariably accrete hot gas, while in the latter they typically accrete cold gas. An important consequence of our results is that at the present time there cannot be blue, star-forming galaxies in the most massive galactic halos, consistent with the observed truncation of the blue cloud at L*. [abridged]Comment: MNRAS, accepted. Added discussion and references, conclusions unchanged. 14 pages, 6 figures (2 color

Modelling the Galaxy for GAIA

Techniques for the construction of dynamical Galaxy models should be considered essential infrastructure that should be put in place before GAIA flies. Three possible modelling techniques are discussed. Although one of these seems to have significantly more potential than the other two, at this stage work should be done on all three. A major effort is needed to decide how to make a model consistent with a catalogue such as that which GAIA will produce. Given the complexity of the problem, it is argued that a hierarchy of models should be constructed, of ever increasing complexity and quality of fit to the data. The potential that resonances and tidal streams have to indicate how a model should be refined is briefly discussed.Comment: 7 pages to appear in The Three Dimensional Universe with GAIA, eds M. Perryman & C. Turo

Self-consistent flattened isochrone models

We present a family of self-consistent axisymmetric stellar systems that have analytic distribution functions (DFs) of the form f(J), so they depend on three integrals of motion and have triaxial velocity ellipsoids. The models, which are generalisations of Henon's isochrone sphere, have four dimensionless parameters, two determining the part of the DF that is even in L_z, and two determining the odd part of the DF (which determines the azimuthal velocity distribution). Outside their cores, the velocity ellipsoids of all models tend to point to the model's centre, and we argue that this behaviour is generic, so near the symmetry axis of a flattened model, the long axis of the velocity ellipsoid is naturally aligned with the symmetry axis and not perpendicular to it as in many published dynamical models of well-studied galaxies. By varying one of the DF's parameters, the intensity of rotation can be increased from zero up to a maximum value set by the requirement that the DF be non-negative. Since angle-action coordinates are easily computed for these models, they are ideally suited for perturbative treatments and stability analysis. They can also be used to choose initial conditions for an N-body model that starts in perfect equilibrium and to model observations of early-type galaxies. The modelling technique introduced here is readily extended to different radial density profiles, more complex kinematics, and multi-component systems. A number of important technical issues surrounding the determination of the models' observable properties are explained in two appendices.Comment: 13 pages accepted by MNRA

Orbital tori for non-axisymmetric galaxies

Our Galaxy's bar makes the Galaxy's potential distinctly non-axisymmetric. All orbits are affected by non-axisymmetry, and significant numbers are qualitatively changed by being trapped at a resonance with the bar. Orbital tori are used to compute these effects. Thick-disc orbits are no less likely to be trapped by corotation or a Lindblad resonance than thin-disc orbits. Perturbation theory is used to create non-axisymmetric orbital tori from standard axisymmetric tori, and both trapped and untrapped orbits are recovered to surprising accuracy. Code is added to the TorusModeller library that makes it as easy to manipulate non-axisymmetric tori as axisymmetric ones. The augmented TorusModeller is used to compute the velocity structure of the solar neighbourhood for bars of different pattern speeds and a simple action-based distribution function. The technique developed here can be applied to any non-axisymmetric potential that is stationary in a rotating from - hence also to classical spiral structure.Comment: 21 pp, 18 figs, accepted by MNRA

Dynamics for Galactic Archaeology

Our Galaxy is a complex machine in which several processes operate simultaneously: metal-poor gas is accreted, is chemically enriched by dying stars, and then drifts inwards, surrendering its angular momentum to stars; new stars are formed on nearly circular orbits in the equatorial plane and then diffuse through orbit space to eccentric and inclined orbits; the central stellar bar surrenders angular momentum to the surrounding disc and dark halo while acquiring angular momentum from inspiralling gas; the outer parts of the disc are constantly disturbed by satellite objects, both luminous and dark, as they sweep through pericentre. We review the conceptual tools required to bring these complex happenings into focus. Our first concern must be the construction of equilibrium models of the Galaxy, for upon these hang our hopes of determining the Galaxy's mean gravitational field, which is required for every subsequent step. Ideally our equilibrium model should be formulated so that the secular evolution of the system can be modelled with perturbation theory. Such theory can be used to understand how stars diffuse through orbit space from either the thin gas disc in which we presume disc stars formed, or the debris of an accreted object, the presumed origin of many halo stars. Coupling this understanding to the still very uncertain predictions of the theory of stellar evolution and nucleosynthesis, we can finally extract a complete model of the chemodynamic evolution of our reasonably generic Galaxy. We discuss the relation of such a model to cosmological simulations of galaxy formation, which provide general guidance but cannot be relied on for quantitative detail.Comment: 71 pages to appear in New Astron. Rev. (2013), http://dx.doi.org/10.1016/j.newar.2013.08.00

Components of the Milky Way and GAIA

The GAIA mission will produce an extraordinary database from which we should be able to deduce not only the Galaxy's current structure, but also much of its history, and thus cast a powerful light on the way in which galaxies in general are made up of components, and of how these formed. The database can be fully exploited only by fitting to it a sophisticated model of the entire Galaxy. Steady-state models are of fundamental importance even though the Galaxy cannot be in a steady state. A very elaborate model of the Galaxy will be required to reproduce the great wealth of detail that GAIA will reveal. A systematic approach to model-building will be required if such a model is to be successfully constructed, however. The natural strategy is to proceed through a series of models of ever increasing elaborateness, and to be guided in the specification of the next model by mismatches between the data and the current model. An approach to the dynamics of systems with steady gravitational potentials that we call the `torus programme' promises to provide an appropriate framework within which to carry out the proposed modelling programme. The basic principles of this approach have been worked out in some detail and are summarized here. Some extensions will be required before the GAIA database can be successfully confronted. Other modelling techniques that might be employed are briefly examined.Comment: Lecture at Les Houches summer school to appear in J.Phys IV Franc

Empire, Spectacle and the Patriot King: British Responses to Eighteenth-Century Russian Empire

The article was submitted on 11.05.2016.Обращаясь к описаниям представлений, устраиваемых русскими царями, в трудах британских путешественников, автор показывает противоречивый характер британского взгляда на Российскую империю XVIII в. Россия традиционно изображалась как «чужая» империя, а приверженность Британии свободе и разуму противопоставлялась духу несвободы самодержавного государства и иррациональной тяге русского народа к традициям. Однако британские авторы рассказывали в своих отзывах о русских царях, таких как Петр I и его последователи, изображая их как просвещенных монархов. Впечатления британцев о зрелищах, устраиваемых царями, с одной стороны, акцентируют внимание на личностях русских монархов и их реформах и, с другой, иллюстрируют ограниченность народа и его неспособность рассуждать здраво и бороться за свободу. Автор утверждает, что это противоречие сформировалось в представлении британцев о России под влиянием идей Болингброка о царе-реформаторе и России как стране, занимающей промежуточное положение между Востоком и Западом.The author uses examples of British travellers’ responses to Russian tsars’ spectacles to argue that the British view of the Russian Empire in the eighteenth century fosters a contradiction. Traditionally Russia was depicted as an imperial Other in which British liberty and its attachment to reason is contrasted with Russian servility within the autocratic state and Russian citizens’ irrational attachment to tradition. Yet British writers complicate this depiction with Peter the Great, and later tsars, who are depicted frequently as enlightened reformers. Indeed, British travellers’ depictions of tsars’ spectacles at once foreground the tsar’s enlightened reforms and the tsar’s person, but also are characterized as limiting the spectators’ capacity to reason and to pursue liberty. The author maintains that this contradiction is accommodated in the British thought by Bolingbroke’s notion of a reform-minded patriot king and Russia’s often-portrayed middle position between East and West

Microlensing and Galactic Structure

Because we know little about the Galactic force-field away from the plane, the Galactic mass distribution is very ill-determined. I show that a microlensing survey of galaxies closer than 50 Mpc would enable us to map in three dimensions the Galactic density of stellar mass, which should be strictly less than the total mass density. A lower limit can be placed on the stellar mass needed at R<R_0 to generate the measured optical depth towards sources in the bulge. If the Galaxy is barred, this limit is lower by a factor of up to two than in the axisymmetric case. Even our limited knowledge of the Galactic force field suffices to rule out the presence of the amount of mass an axisymmetric Galaxy needs to generate the measured optical depth. Several lines of argument imply that the Galaxy is strongly barred only at R < 4 kpc, and if this is the case, even barred Galaxy models cannot generate the measured optical depth without violating some constraint on the Galactic force-field. Galactic mass models that are based on the assumption that light traces mass, for which there is significant support in the inner Galaxy, yield microlensing optical depths that are smaller than the measured value by a factor of more than 2.5.Comment: 12 pages to appear in Microlensing 2000, A New Era of Microlensing Astrophysics J.W. Menzies and P.D. Sackett, ed

Modelling the Galaxy in the era of Gaia

The body of photometric and astrometric data on stars in the Galaxy has been growing very fast in recent years (Hipparcos/Tycho, OGLE-3, 2-Mass, DENIS, UCAC2, SDSS, RAVE, Pan Starrs, Hermes, ...) and in two years ESA will launch the Gaia satellite, which will measure astrometric data of unprecedented precision for a billion stars. On account of our position within the Galaxy and the complex observational biases that are built into most catalogues, dynamical models of the Galaxy are a prerequisite full exploitation of these catalogues. On account of the enormous detail in which we can observe the Galaxy, models of great sophistication are required. Moreover, in addition to models we require algorithms for observing them with the same errors and biases as occur in real observational programs, and statistical algorithms for determining the extent to which a model is compatible with a given body of data. JD5 reviewed the status of our knowledge of the Galaxy, the different ways in which we could model the Galaxy, and what will be required to extract our science goals from the data that will be on hand when the Gaia Catalogue becomes available.Comment: Proceedings of Joint Discussion 5 at IAU XXVII, Rio de Janeiro, August 2009; 31 page