The Capture and Escape of Stars

The shape of galaxies depends on their orbital populations. These populations change through capture into and escape from resonance. Capture problems fall into distinct cases depending upon the shape of the potential well. To visualise the effective potential well for orbital capture, a diagrammatic approach to the resonant perturbation theory of Born is presented. These diagrams we call equiaction sections. To illustrate their use, we present examples drawn from both galactic and Solar System dynamics. The probability of capture for generic shapes of the potential well is calculated. A number of predictions are made. First, there are barred galaxies that possess two outer rings of gas and stars (type R ′ 1R ′ 2). We show how to relate changes in the pattern speed and amplitude of the bar to the strength of the two rings. Secondly, under certain conditions, small disturbances can lead to dramatic changes in orbital shape. This can be exploited as a mechanism to pump counter-rotating stars and gas into the nuclei of disk galaxies. Tidal resonant forcing of highly inclined orbits around a central mass causes a substantial increase in the likelihood of collision. Thirdly, the angular momentum of a potential well is changed by the passage of stars across or capture into the well. This can lead to the creation of holes, notches and high velocity tails in the stellar distribution function, whose form we explicitly calculate.Peer reviewe

The Integrability of Pauli System in Lorentz Violating Background

We systematically analyze the integrability of a Pauli system in Lorentz violating background at the non-relativistic level both in two- and three-dimensions. We consider the non-relativistic limit of the Dirac equation from the QED sector of the so-called Standard Model Extension by keeping only two types of background couplings, the vector a_mu and the axial vector b_mu. We show that the spin-orbit interaction comes as a higher order correction in the non-relativistic limit of the Dirac equation. Such an interaction allows the inclusion of spin degree non-trivially, and if Lorentz violating terms are allowed, they might be comparable under special circumstances. By including all possible first-order derivative terms and considering the cases a\ne 0, b\ne 0, and b_0\ne 0 one at a time, we determine the possible forms of constants of motion operator, and discuss the existence or continuity of integrability due to Lorentz violating background.Comment: 19 page

Refinement of the standard halo model for dark matter searches in light of the Gaia Sausage

Predicting signals in experiments to directly detect dark matter (DM) requires a form for the local DM velocity distribution. Hitherto, the standard halo model (SHM), in which velocities are isotropic and follow a truncated Gaussian law, has performed this job. New data, however, suggest that a substantial fraction of our stellar halo lies in a strongly radially anisotropic population, the "Gaia sausage." Inspired by this recent discovery, we introduce an updated DM halo model, the SHM++, which includes a "sausage" component, thus better describing the known features of our Galaxy. The SHM++ is a simple analytic model with five parameters: the circular speed, local escape speed, and local DM density, which we update to be consistent with the latest data, and two new parameters: the anisotropy and the density of DM in the sausage. The impact of the SHM++ on signal models for weakly interacting massive particles (WIMPs) and axions is rather modest since the multiple changes and updates have competing effects. In particular, this means that the older exclusion limits derived for WIMPS are still reasonably accurate. However, changes do occur for directional detectors, which have sensitivity to the full three-dimensional velocity distribution

Proper Motions in the Andromeda Subgroup

This article presents results of VLBI observations of regions of H2O maser activity in the Local Group galaxies M33 and IC10. Since all position measurements were made relative to extragalactic background sources, the proper motions of the two galaxies could be measured. For M33, this provides this galaxy's three dimensional velocity, showing that this galaxy is moving with a velocity of 190 +/- 59 km\s relative to the Milky Way. For IC10, we obtain a motion of 215 +/- 42 km/s relative to the Milky Way. These measurements promise a new handle on dynamical models for the Local Group and the mass and dark matter halo of Andromeda and the Milky Way.Comment: 4 pages 1 figures, to appear in the proceedings of "Galaxies in the Local Volume", Astrophysics and Space Science, editors B. Koribalski and H. Jerjen also available at http://www.mpifr-bonn.mpg.de/staff/abrunthaler/pub.shtm

A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates

We have established the exact expression for the gravitational potential of a homogeneous polar cell - an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any opening angle and radial extension of the cell. It is valid at any point in space, i.e. in the plane of the distribution (inside and outside) as well as off-plane, thereby generalizing the results reported by Durand (1953) for the circular disc. The three components of the gravitational acceleration are given. The mathematical demonstration proceeds from the "incomplete version of Durand's formula" for the potential (based on complete elliptic integrals). We determine first the potential due to the circular sector (i.e. a pie-slice sheet), and then deduce that of the polar cell (from convenient radial scaling and subtraction). As a by-product, we generate an integral theorem stating that "the angular average of the potential of any circular sector along its tangent circle is 2/PI times the value at the corner". A few examples are presented. For numerical resolutions and cell shapes commonly used in disc simulations, we quantify the importance of curvature effects by performing a direct comparison between the potential of the polar cell and that of the Cartesian (i.e. rectangular) cell having the same mass. Edge values are found to deviate roughly like 2E-3 x N/256 in relative (N is the number of grid points in the radial direction), while the agreement is typically four orders of magnitude better for values at the cell's center. We also produce a reliable approximation for the potential, valid in the cell's plane, inside and close to the cell. Its remarkable accuracy, about 5E-4 x N/256 in relative, is sufficient to estimate the cell's self-acceleration.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

Dark matter annihilation and non-thermal Sunyaev-Zel'dovich effect: II. dwarf spheroidal galaxy

We calculate the CMB temperature distortion due to the energetic electrons and positrons produced by dark matter annihilation (Sunyaev-Zel'dovich effect), in dwarf spheroidal galaxies (dSphs). In the calculation we have included two important effects which were previously ignored. First we show that the electron-positron pairs with energy less than GeV, which were neglected in previous calculation, could contribute a significant fraction of the total signal. Secondly we also consider the full effects of diffusion loss, which could significantly reduce the density of electron-positron pairs at the center of cuspy halos. For neutralinos, we confirm that detecting such kind of SZ effect is beyond the capability of the current or even the next generation experiments. In the case of light dark matter (LDM) the signal is much larger, but even in this case it is only marginally detectable with the next generation of experiment such as ALMA. We conclude that similar to the case of galaxy clusters, in the dwarf galaxies the SZ_2DM} effect is not a strong probe of DM annihilations.Comment: 22 pages, 9 figures, version accepted by JCA

Ferromagnetic models for cooperative behavior: Revisiting Universality in complex phenomena

Ferromagnetic models are harmonic oscillators in statistical mechanics. Beyond their original scope in tackling phase transition and symmetry breaking in theoretical physics, they are nowadays experiencing a renewal applicative interest as they capture the main features of disparate complex phenomena, whose quantitative investigation in the past were forbidden due to data lacking. After a streamlined introduction to these models, suitably embedded on random graphs, aim of the present paper is to show their importance in a plethora of widespread research fields, so to highlight the unifying framework reached by using statistical mechanics as a tool for their investigation. Specifically we will deal with examples stemmed from sociology, chemistry, cybernetics (electronics) and biology (immunology).Comment: Contributing to the proceedings of the Conference "Mathematical models and methods for Planet Heart", INdAM, Rome 201

Identification of high energy gamma-ray sources and source populations in the era of deep all-sky coverage

A large fraction of the anticipated source detections by the Gamma-ray Large Area Space Telescope (GLAST-LAT) will initially be unidentified. We argue that traditional approaches to identify individuals and/or populations of gamma ray sources will encounter procedural limitations. Those limitations are discussed on the background of source identifications from EGRET observations. Generally, our ability to classify (faint) source populations in the anticipated GLAST dataset with the required degree of statistical confidence will be hampered by sheer source wealth. A new paradigm for achieving the classification of gamma ray source populations is discussed.Comment: Comments: 6 pages, 2 figures, Accepted for publication in Astrophysics and Space Science, Proc. of "The Multi-Messenger Approach to High-Energy Gamma-ray Sources (Third Workshop on the Nature of Unidentified High-Energy Sources)", Barcelona, July 4-7, 200

Probing Ion-Ion and Electron-Ion Correlations in Liquid Metals within the Quantum Hypernetted Chain Approximation

We use the Quantum Hypernetted Chain Approximation (QHNC) to calculate the ion-ion and electron-ion correlations for liquid metallic Li, Be, Na, Mg, Al, K, Ca, and Ga. We discuss trends in electron-ion structure factors and radial distribution functions, and also calculate the free-atom and metallic-atom form-factors, focusing on how bonding effects affect the interpretation of X-ray scattering experiments, especially experimental measurements of the ion-ion structure factor in the liquid metallic phase.Comment: RevTeX, 19 pages, 7 figure