Modelling the Galactic disc: perturbed distribution functions in the presence of spiral arms

Starting from an axisymmetric equilibrium distribution function (DF) in action space, representing a Milky Way thin disc stellar population, we use the linearized Boltzmann equation to explicitly compute the response to a three-dimensional spiral potential in terms of the perturbed DF. This DF, valid away from the main resonances, allows us to investigate a snapshot of the velocity distribution at any given point in three-dimensional configuration space. Moreover, the first order moments of the DF give rise to non-zero radial and vertical bulk flows -- namely breathing modes -- qualitatively similar to those recently observed in the extended Solar neighbourhood. We show that these analytically predicted mean stellar motions are in agreement with the outcome of test-particle simulations. Moreover, we estimate for the first time the reduction factor for the vertical bulk motions of a stellar population compared to the case of a cold fluid. Such an explicit expression for the full perturbed DF of a thin disc stellar population in the presence of spiral arms will be helpful in order to dynamically interpret the detailed information on the Milky Way disc stellar kinematics that will be provided by upcoming large astrometric and spectroscopic surveys of the Galaxy.Comment: 15 pages. Submitted on 2 December 2015 to MNRAS. Accepted for publication. Some typos corrected in v

The Galactic bar and the large scale velocity gradients in the Galactic disk

Aims: We investigate whether the cylindrical (galactocentric) radial velocity gradient of ~ -3 km/s/kpc, directed radially from the Galactic center and recently observed in the stars of the solar neighborhood with the RAVE survey, can be explained by the resonant effects of the bar near the solar neighborhood. Methods: We compared the results of test particle simulations of the Milky Way with a potential that includes a rotating bar with observations from the RAVE survey. To this end we applied the RAVE selection function to the simulations and convolved these with the characteristic RAVE errors. We explored different "solar neighborhoods" in the simulations, as well as different bar models Results: We find that the bar induces a negative radial velocity gradient at every height from the Galactic plane, outside the outer Lindblad resonance and for angles from the long axis of the bar compatible with the current estimates. The selection function and errors do not wash away the gradient, but often make it steeper, especially near the Galactic plane, because this is where the RAVE survey is less radially extended. No gradient in the vertical velocity ispresent in our simulations, from which we may conclude that this cannot be induced by the bar.Comment: 9 pages, 11 figures, v2. Accepted for publication on A&

State and parameter estimation approach to monitoring AGR nuclear core

This work concerns with the problem of monitoring an Advanced Gas-cooled Nuclear Reactor (AGR) core. This plant (figure 1) makes use of the heat given by the nuclear efficient reaction to produce electricity by means of steam turbines. These are driven by steam, which is heated, from the AGR gas using a heat exchanger. One of the advantages of a gas cooled reactor is the high temperature that the gas can achieve so that when it is used in conjunction with the heat exchanger and steamed turbine the thermal efficiency is very high

The vertical effects of disc non-axisymmetries from perturbation theory: the case of the Galactic bar

Evidence for non-zero mean stellar velocities in the direction perpendicular to the Galactic plane has been accumulating from various recent large spectroscopic surveys. Previous analytical and numerical work has shown that a "breathing mode" of the Galactic disc, similar to what is observed in the Solar vicinity, can be the natural consequence of a non-axisymmetric internal perturbation of the disc. Here we provide a general analytical framework, in the context of perturbation theory, allowing us to compute the vertical bulk motions generated by a single internal perturber (bar or spiral pattern). In the case of the Galactic bar, we show that these analytically predicted bulk motions are well in line with the outcome of a numerical simulation. The mean vertical motions induced by the Milky Way bar are small (mean velocity of less than 1 km/sec) and cannot be responsible alone for the observed breathing mode, but they are existing. Our analytical treatment is valid close to the plane for all the non-axisymmetric perturbations of the disc that can be described by small-amplitude Fourier modes. Further work should study how the coupling of multiple internal perturbers and external perturbers is affecting the present analytical results.Comment: 9 pages, 6 figures, accepted for publication in MNRAS. Error corrected, figures updated, added term in Eqs. 10 and 18 with no consequences on the conclusion

A de Finetti representation for finite symmetric quantum states

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.Comment: 22 pages, LaTe