On turbulence in the quasi-perpendicular bow shock

In this paper we propose to review the fundamental aspects of turbulence theories and their relevance to particle distribution functions observed by the cluster satellites in the quasi-perpendicular shock. The paper focusses on the hierarchical model describing the different levels of plasma turbulence; from the linear theory, through the quasi-linear remedy, to strong turbulence theories in the context of the earth's bow shock. We will discuss very briefly the validity of these approximations, and their relevance as far as satellite observations are concerned. In particular, we will discuss the development of non-Gaussian features in the ion distribution functions through the evaluation of higher order moments such as the kurtosis or flatness and the skewness. We have found that the profile of the kurtosis versus skewness tends to collapse to a parabolic line. This in turn allows us to draw analogies with neutral fluid turbulence where such a collapse of the kurtosis-skewness profile has been observed.     

A Study of the Coefficient a in the Extended Nonlinear Guiding Center Theory

The diffusion mechanism of charged particles is one of the very im- portant problems in astrophysics. Recently, Matthaeus et al. (2003) developed a nonlinear guiding center theory (NLGC) of the perpendicular diffusion of en- ergetic charged particles with the parallel diffusion coefficient as an input. This theory agrees with the results of numerical simulations very well. In addition, Qin (2007) developed a nonlinear parallel diffusion theory (NLPA) following the idea of NLGC. Combining the NLGC with the NLPA, a new theory, NLGC-E was developed to solve the parallel and perpendicular diffusion coefficients simultaneously. In the NLGC theory, there is a coefficient a² which is selected to be 1/3 for the best agreement with the results of numerical simulations. In this work we tried the different values of a² for the NLGC-E theory to determine the optimal value which ?ts best the results of numerical simulations.     

Cosmic strings and strings in gravitational waves

We consider strings with the Nambu action as extremal surfaces in a given space-time, thus, we ignore their back reaction. Especially, we look for strings sharing one symmetry with the underlying space-time. If this is a non-null symmetry the problem of determining ihc motion of the string can be dimensionally reduced. We get exact solutions for the following cases: straight and circle-like strings in a Friedmann background, straight strings in an anisotropic Kasner background, different types of strings in the metric of a gravitational wave. The solutions will be discussed. Wir betrachten Strings mit der Nambu-Wirkung als Extremalflächen in einer gegebenen Raum-Zeit, d. h., wir ignorieren ihre Rückwirkung. Wir interessieren uns dabei besonders für solche Strings, die eine Isometrie mit der unterliegenden Raum-Zeit gemeinsam haben. Handelt es sich dabei um eine nicht-lichtartige Symmetrie, so läß Bt sich das Problem der Bestimmung der Stringbewegung dimensionsreduzieren. Wir erhalten exakte Lösungen für die folgenden Fälle: gerade und kreisrunde Strings im Friedmann-Hintergrund, gerade Strings im anisotropen Kasner-Hintergrund sowie verschiedene Stringtypen in der Metrik einer Gravitationswelle. Die Lösungen werden diskutiert.     

Canonical theory of perturbations using eccentric anomaly as independent variable

It is shown in this paper how to build a canonical transformation of variables, so that the eccentric anomaly becomes the new independent variable. In the case of eccentric elliptical orbits it changes the equations of motion so, that they can be integrated analytically to any order of approximation comparatively easy.     

Decoupling treatment of linear non-adiabatic non-radial pulsations of stars

A decoupling method is developed in this paper to deal with linear non-adiabatic non-radial pulsations of stars. The sixth order differential equation of linear pulsation is decomposed into a fourth order and a second order differential equations. The decoupling overcomes such difficulties encountered in the numerical solution as small domain and slowness of convergence and provides a natural guess solution needed in Henyey's method.     

The statistical properties of Λ cold dark matter halo formation

We present a comparison of the statistical properties of dark matter halo merger trees extracted from the Millennium Simulation with Extended Press–Schechter (EPS) formalism and the related galform Monte Carlo method for generating ensembles of merger trees. The volume, mass resolution and output frequency make the Millennium Simulation a unique resource for the study of the hierarchical growth of structure. We construct the merger trees of present-day friends-of-friends groups and calculate a variety of statistics that quantify the masses of their progenitors as a function of redshift, accretion rates, and the redshift distribution of their most recent major merger. We also look in the forward direction and quantify the present-day mass distribution of haloes into which high-redshift progenitors of a specific mass become incorporated. We find that the EPS formalism and its Monte Carlo extension capture the qualitative behaviour of all these statistics, but as redshift increases they systematically underestimate the masses of the most massive progenitors. This shortcoming is worst for the Monte Carlo algorithm. We present a fitting function to a scaled version of the progenitor mass distribution and show how it can be used to make more accurate predictions of both progenitor and final halo mass distributions.     

Neutralino annihilations and the gas temperature in the dark ages

Assuming that the dark matter is entirely made up of neutralinos, we re-visit the role of their annihilation on the temperature of diffuse gas in the high-redshift universe  ( z > 10)  , before the formation of luminous structures. We consider neutralinos of particle mass 36 and 100 GeV. The former is able to produce  ∼7  e ⁻ e ⁺  particles per annihilation through the fremionic channel, and the latter ∼53 particles assuming a purely bosonic channel. High-energy   e ⁻ e ⁺  particles up-scatter the cosmic microwave background (CMB) photons into higher energies via the inverse-Compton scattering. The process produces a power-law   e ⁻ e ⁺  energy spectrum of index −1 in the energy range of interest, independent of the initial energy distribution. The corresponding energy spectrum of the up-scattered photons is a power law of index −1/2, if absorption by the gas is not included. The scattered photons photoheat the gas by releasing electrons which deposit a fraction (14 per cent) of their energy as heat into the ambient medium. For uniformly distributed neutralinos, the heating is insignificant. The effect is greatly enhanced by the clumping of neutralinos into dense haloes. We use a time-dependent clumping model which takes into account the damping of density fluctuations on mass-scales smaller than  ∼10⁻⁶ M_⊙  . With this clumping model, the heating mechanism boosts the gas temperature above that of the CMB after a redshift of   z ∼ 30  . By   z ≈ 10  , the gas temperature is nearly 100 times its temperature when no heating is invoked. Similar increase is obtained for the two neutralino masses considered.     

The dependence of galaxy formation on cosmological parameters: can we distinguish between the WMAP1 and WMAP3 parameter sets?

We combine N -body simulations of structure growth with physical modelling of galaxy evolution to investigate whether the shift in cosmological parameters between the first- and third-year results from the Wilkinson Microwave Anisotropy Probe ( WMAP ) affects predictions for the galaxy population. Structure formation is significantly delayed in the WMAP3 cosmology, because the initial matter fluctuation amplitude is lower on the relevant scales. The decrease in dark matter clustering strength is, however, almost entirely offset by an increase in halo bias, so predictions for galaxy clustering are barely altered. In both cosmologies, several combinations of physical parameters can reproduce observed, low-redshift galaxy properties; the star formation, supernova feedback and active galactic nucleus feedback efficiencies can be played off against each other to give similar results. Models which fit observed luminosity functions predict projected two-point correlation functions which scatter by about 10–20 per cent on large scale and by larger factors on small scale, depending both on cosmology and on details of galaxy formation. Measurements of the pairwise velocity distribution prefer the WMAP1 cosmology, but careful treatment of the systematics is needed. Given present modelling uncertainties, it is not easy to distinguish between the WMAP1 and WMAP3 cosmologies on the basis of low-redshift galaxy properties. Model predictions diverge more dramatically at high redshift. Better observational data at   z > 2  will better constrain galaxy formation and perhaps also cosmological parameters.