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

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

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

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

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

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

On the impossibility of advection dominated accretion

Using only the assumption that all interactions between particles in an accretion flow are electromagnetically mediated, it is shown that the time to establish equipartition between ions and electrons is shorter than the characteristic accretion time. Consequently, two-temperature fits to the spectra of accreting objects are unphysical, and models in which significant thermal energy is carried across the event horizon are effectively ruled out.Comment: 3 pages submitted to MNRA

AGN and Cooling Flows

For two decades the steady-state cooling-flow model has dominated the literature of cluster and elliptical-galaxy X-ray sources. For ten years this model has been in severe difficulty from a theoretical point of view, and it is now coming under increasing pressure observationally. For two decades the steady-state cooling-flow model has dominated the literature of cluster and elliptical-galaxy X-ray sources. For ten years this model has been in severe difficulty from a theoretical point of view, and it is now coming under increasing pressure observationally. A small number of enthusiasts have argued for a radically different interpretation of the data, but had little impact on prevailing opinion because the unsteady heating picture that they advocate is extremely hard to work out in detail. Here I explain why it is difficult to extract robust observational predictions from the heating picture. Major problems include the variability of the sources, the different ways in which a bi-polar flow can impact on X-ray emission, the weakness of synchrotron emission from sub-relativistic flows, and the sensitivity of synchrotron emission to a magnetic field that is probably highly localized.Comment: 6 pages to appear in Particles and Fields in Radio Galaxies, eds R.A. Laing and K.M. Blundell, ASP Conf Se

The abundance of brown dwarfs

The amount of mass contained in low-mass objects is investigated anew. Instead of using a mass-luminosity relation to convert a luminosity function to a mass function, I predict the mass-luminosity relation from assumed mass functions and the luminosity functions of Jahreiss & Wielen (1997) and Gould et al (1997). Comparison of the resulting mass-luminosity relations with data from binary stars constrains the permissible mass functions. If the mass function is assumed to be a power law, the best fitting slope lies either side of the critical slope, -2, below which the mass in low-mass objects is divergent, depending on the luminosity function adopted. If these power-law mass functions are truncated at 0.001Msun, the contribution to the local density of stars lies between 0.016 and 0.039 Msun pc^-3, in conformity with the density measured dynamically from Hipparcos stars. If the mass function is generalized from a power law to a low-order polynomial in log(M), the mass in stars with M<0.1Msun is either negligible or strongly divergent, depending on the order of the polynomial adopted.Comment: Plain Te