Partial Reduction in the N-Body Planetary Problem using the Angular Momentum Integral

We present a new set of variables for the reduction of the planetary n-body problem, associated to the angular momentum integral, which can be of any use for perturbation theory. The construction of these variables is performed in two steps. A first reduction, called partial is based only on the fixed direction of the angular momentum. The reduction can then be completed using the norm of the angular momentum. In fact, the partial reduction presents many advantages. In particular, we keep some symmetries in the equations of motion (d'Alembert relations). Moreover, in the reduced secular system, we can construct a Birkhoff normal form at any order. Finally, the topology of this problem remains the same as for the non-reduced system, contrarily to Jacobi's reduction where a singularity is present for zero inclinations. For three bodies, these reductions can be done in a very simple way in Poincaré's rectangular variables. In the general n-body case, the reduction can be performed up to a fixed degree in eccentricities and inclinations, using computer algebra expansions. As an example, we provide the truncated expressions for the change of variable in the 4-body case, obtained using the computer algebra system TRIP.     

Analysis of the Space Debris Impacts Risk on the International Space Station

Öpik's analytical expressions relate in a simple way the semimajor axis, eccentricity and inclination of the projectile orbit to the magnitude and direction of the relative velocity vector at impact on a given target on circular orbit. These interesting quantities, along with the impact probability of any given projectile, can be all represented on a suitable projection giving a comprehensive picture of the impact risk on the selected target. By means of this theory a complete analysis of the impact risk on the International Space Station (ISS) is performed. It is found that the large majority of the debris population is on orbits such that a correlation exists between their impact velocity on the ISS and the angle between the velocity vector of the impactor and that of the ISS. The impactor population also is separated in terms of nature of the projectiles, with most of the low-medium velocity ones being particles related to solid rocket motor slag condensates. On the other hand, the highest velocity projectiles are composed mainly by fragments of past in-orbit explosions.The flux of projectiles on the ISS has been calculated for the planned operative lifetime of the Station, by assuming a realistic scenario of the future debris environment evolution and the actual planned altitude profile for the ISS mission. There is a factor 2-3 variation of the flux due to the changing ISS altitude. The most dangerous part of the mission appears to be the central one, when the ISS will orbit at about 450 km above the Earth.     

The klein–nishina Effects in Blazar Jets

Blazars are the only (with one or two exceptions) extragalactic objects which were detected and identified at gamma-ray energies so far. It is suspected that most of the unidentified gamma-ray sources may be the blazars as well. Because the entire electromagnetic spectrum of these objects is dominated by non-thermal radiation from relativistically moving jets, the effects such as the Klein–Nishina regime in the Compton scattering may play a major role in shaping some parts of the blazar spectrum. Within the framework of external radiation Compton model, we present how these effect influence the spectra of blazars for which the production of gamma rays is dominated by Comptonization of external radiation.     

Cosmological Scalar in the Jordan-Brans-Dicke Theory. I

A variant of the Jordan-Brans-Dicke (JBD) theory is examined which contains a cosmological scalar that is written so that on going to the Einstein representation it becomes the ordinary cosmological constant of general relativity theory. This paper is divided into two parts. In Part I we examine the cosmological solutions for the Einstein representation of the JBD theory, i.e., in the presence of a minimally coupled scalar field. In Part II we shall study the cosmological solutions in the proper representation of the JBD theory with a self consistent scalar field. The analysis of these solutions is of interest in connection with modern concepts of the evolution of the universe, in particular, with the observed acceleration of cosmological expansion and estimates of the density of dark matter and dark energy.__________Translated from Astrofizika, Vol. 48, No. 3, pp. 455–462 (August 2005).     

Contribution to diffuse gamma-rays in the Galactic Centre region from unresolved millisecond pulsars

Diffuse gamma-rays in the Galactic Centre region have been studied. We propose that there exists a population of millisecond pulsars in the Galactic Centre, which emit GeV gamma-rays through synchrotron-curvature radiation as predicted by outer gap models. These GeV gamma-rays from unresolved millisecond pulsars probably contribute to the diffuse gamma-ray spectrum detected by EGRET which displays a break at a few GeV. We have used a Monte Carlo method to obtain simulated samples of millisecond pulsars in the Galactic Centre region covered by EGRET  (∼ 15)  according to the different period and magnetic field distributions from observed millisecond pulsars in the Galactic field and globular clusters, and superposed their synchrotron-curvature spectra to derive the total GeV flux. Our simulated results suggest that there probably exist about 6000 unresolved millisecond pulsars in the region of angular resolution of EGRET, the emissions of which could contribute significantly to the observed diffuse gamma-rays in the Galactic Centre.     

Semi-analytic simulations of galactic winds: volume filling factor, ejection of metals and parameter study

We present a semi-analytic treatment of galactic winds within high-resolution, large-scale cosmological N -body simulations of a Λ cold dark matter (ΛCDM) universe. The evolution of winds is investigated by following the expansion of supernova-driven superbubbles around the several hundred thousand galaxies that form in an approximately spherical region of space with diameter 52  h ⁻¹ Mpc and mean density close to the mean density of the universe. We focus our attention on the impact of winds on the diffuse intergalactic medium. Initial conditions for mass loss at the base of winds are taken from Shu, Mo & Mao. Results are presented for the volume filling factor and the mass fraction of the intergalactic medium (IGM) affected by winds, and their dependence on the model parameters is carefully investigated. The mass-loading efficiency of bubbles is a key factor to determine the evolution of winds and their global impact on the IGM: the higher the mass loading, the later the IGM is enriched with metals. Galaxies with 10⁹ < M _★ < 10¹⁰ M_⊙ are responsible for most of the metals ejected into the IGM at   z = 3  , while galaxies with   M _★ < 10⁹ M_⊙   give a non-negligible contribution only at higher redshifts, when larger galaxies have not yet assembled. We find a higher mean IGM metallicity than Lyα forest observations suggest, and we argue that the discrepancy may be explained by the high temperatures of a large fraction of the metals in winds, which may not leave detectable imprints in absorption in the Lyα forest.     

Voids in a ΛCDM universe

We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular Λ cold dark matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of −0.8 or less – roughly the equivalent of using a spherical overdensity group finder for haloes. Each of the simulations contains thousands of voids. The distribution of void sizes in the different simulations shows good agreement when differences in particle and grid resolution are accounted for. Voids very clearly correspond to minima in the smoothed initial density field. Apart from a very weak dependence on the mass resolution, the rescaled mass profiles of voids in the different simulations agree remarkably well. We find a universal void mass profile of the form  ρ(< r )/ρ( r _eff) ∝ exp[( r / r _eff)^α]  , where r _eff is the effective radius of a void and  α∼ 2  . The mass function of haloes in voids is steeper than that of haloes that populate denser regions. In addition, the abundances of void haloes seem to evolve somewhat more strongly between redshifts ∼1 and 0 than the global abundances of haloes.