The entropic prior for distributions with positive and negative values

The maximum entropy method has been used to reconstruct images in a wide range of astronomical fields, but in its traditional form it is restricted to the reconstruction of strictly positive distributions. We present an extension of the standard method to include distributions that can take both positive and negative values. The method may therefore be applied to a much wider range of astronomical reconstruction problems. In particular, we derive the form of the entropy for positive/negative distributions and use direct counting arguments to find the form of the entropic prior. We also derive the measure on the space of positive/negative distributions, which allows the definition of probability integrals and hence the proper quantification of errors.     

Cosmological models with time-varying gravitational and cosmological “constants”

The evolution and dynamics of a locally-rotationally-symmetric (LRS) Bianchi type-V space-time cosmological models are discussed with variable gravitational and cosmological “constants” in context of the particle creation. We present the exact solutions of Einstein field equations by using a power-law form of the average scale factor of the metric in the case of the particle creation and in the absence of particle creation. The solution describes the particle and entropy generation in the anisotropic cosmological models. The particle creation rate is uniquely determined by the variation of gravitational and cosmological “constants”. We observe that the variable gravitational constant does not necessarily imply particle creation. In a generic situation, models can be interpolated between different phases of the universe. The dynamical behaviors of the solutions and kinematical parameters of the model are discussed in detail.     

Fermi acceleration in astrophysical jets

We consider the acceleration of energetic particles by Fermi processes (i.e., diffusive shock acceleration, second order Fermi acceleration, and gradual shear acceleration) in relativistic astrophysical jets, with particular attention given to recent progress in the field of viscous shear acceleration. We analyze the associated acceleration timescales and the resulting particle distributions, and discuss the relevance of these processes for the acceleration of charged particles in the jets of AGN, GRBs and microquasars, showing that multi-component powerlaw-type particle distributions are likely to occur.     

On the formation and unfolding of pulse height distributions

Spacecraft measurements of X-ray or particle pulse height distributions have become increasingly accurate during the last fifteen years, and they will continue to do so. The present paper deals with the question how one can reconstruct original photon or particle spectra from measured pulse height distributions. The statistical aspects of the formation of pulse height distributions are investigated. A method is presented that allows for a reliable reconstruction of the original spectrum. Its essentials are the formulation and subsequent solution of a matrix equation connecting pulse height distribution with photon/particle spectrum; an error analysis of the reconstructed spectrum is given. The present method has two advantages over the usualχ ²-minimum method: It is able to recover more spectral detail and it requires less computing time. Finally, a numerical example is given.     

Kappa Distributions: Theory and Applications in Space Plasmas

The plasma particle velocity distributions observed in the solar wind generally show enhanced (non-Maxwellian) suprathermal tails, decreasing as a power law of the velocity and well described by the family of Kappa distribution functions. The presence of non-thermal populations at different altitudes in space plasmas suggests a universal mechanism for their creation and important consequences concerning plasma fluctuations, the resonant and nonresonant wave – particle acceleration and plasma heating. These effects are well described by the kinetic approaches where no closure requires the distributions to be nearly Maxwellian. This paper summarizes and analyzes the various theories proposed for the Kappa distributions and their valuable applications in coronal and space plasmas.     

Fractal and entropy studies of Cherenkov arrival times

In this paper, time structure of simulated Cherenkov arrival times is explored by studying its multifractal/fractal and entropy properties. It is observed that the simulated Cherenkov arrival times are multifractal in nature. Its multifractal features do not show any dependence on the nature of the initiating particle and on the energy of arriving Cherenkov photons. However, the computed values of the entropy and Hausdorff dimension show consistent energy dependence on the energy of incoming γ-ray showers both for time arrivals as well for number of photons. Our results get partially validated by applying them to light curve of a gamma ray burst.     

Recovering 3D particle size distributions from 2D sections

We discuss different ways to convert observed, apparent particle size distributions from 2D sections (thin sections, SEM maps on planar surfaces, etc.) into true 3D particle size distributions. We give a simple, flexible, and practical method to do this; show which of these techniques gives the most faithful conversions; and provide (online) short computer codes to calculate both 2D‐3D recoveries and simulations of 2D observations by random sectioning. The most important systematic bias of 2D sectioning, from the standpoint of most chondrite studies, is an overestimate of the abundance of the larger particles. We show that fairly good recoveries can be achieved from observed size distributions containing 100–300 individual measurements of apparent particle diameter.     

Pitch angle and energy distributions of auroral electrons measured by the ESRO 4 satellite

Energy spectra and angular distributions of auroral electrons in the energy range 0.2–16 keV measured by the low-altitude polar orbiting satellite ESRO 4 are presented. The observations were made in the altitude range 800–1000 km near magnetic midnight. Energy-time spectrograms show inverted-V structures with peaked energy spectra. The inverted-V events are associated with anisotropic electron pitch angle distributions peaked at 0 deg. Frequently these distributions have a maximum also at 90 deg. Measurements of >43 keV electrons indicate that the acceleration probably occurs on closed field lines. It is found that many properties of the observed particle distributions can be explained by acceleration in an electric field parallel to the magnetic field lines, if trapping of particles under an increasing potential drop is included in the model.     

The lifetime of ice particles in the solar system

A new technique for the measurement of the sublimation rate of individual ice particles is described. With this technique experimental data obtained under simulated space conditions agree with the values computed from scattering theory. It is shown that under solar illumination the sublimation rate of water ice particles is most sensitively influenced by the absorption properties of ice in the near-infrared region. A comparison of experimental results and results calculated with the use of different choices for the complex index of refraction establishes a preference for the published data by J. E. Bertie, H. J. Labbe, and E. Whalley [J. Chem. Phys. 50, 4501–4520 (1969)]. Using these data the lifetimes of ice particles have been computed as a function of particle radius for solar distances of 0.5, 0.75, and 1.0 AU. If these results are applied to ice particle distributions, the distributions become drastically compressed and a quasi-stable particle radius of the order of 15 μm can be predicted for any solar distance.     

The temporal development of microcrater and accretionary grain populations on lunar rocks subjected to meteoroid and solar wind bombardment—II. Observations on the lunar surface and Apollo samples

The development, with time, of microcrater and accretionary particle distributions is investigated for lunar rocks subjected to meteoroid and solar wind bombardment. Experimental observations of the impact crater size distributions and accretionary particle populations on specially selected areas of Apollo Lunar Samples are used to derive incident fluxes for the theory of topological development described in Paper I. (ibid.). Observations show that a delineation and quantitative characterisation of erosion by impact, solar wind sputter and accretionary build-up leads to features typical of lunar surface rocks. The dominance of specific erosion mechanisms is shown to be size dependent. Monte Carlo simulations of these processes are developed to mimic the surface development of populations under arbitrary exposure conditions. Surface dust and splash (accreta) build-up significantly affects observed parameters; it may be used also as a sample surface exposure age indicator. Sputter by the solar wind is shown to modify both accreta and microcrater populations up to dimensions of one micron.     

Formation of proton fluxes under the radiation belts during geomagnetic disturbances

The fluxes of energetic particles under the radiation belts are studied using data obtained in the experiments onboard the CORONAS-I and CORONAS-F satelites. The spatial structure of the distributions of proton fluxes with E _p > 1 MeV both near the geomagnetic equator on L ≤ 1.2 and at high latitudes on L ～ 3.5–6.5 as well as the particle flux variations with geomagnetic activity are analyzed. The scattering processes that lead to particle precipitation and, in particular, the scattering of protons as they interact with VLF emission and the scattering when the particle motion becomes nonadiabatic are considered. We compare the data on particle dynamics during geomagnetic disturbances of various kinds to determine whether the physical processes that lead to particle precipitation are a manifestation of the geoefficiency of a given magnetic storm or they are controlled by internal magnetospheric conditions.     

The atmosphere of Io

Observations of Io suggest that it may have an atmosphere in which sodium vapor, ammonia, and nitrogen are important constituents. Several atmospheric models consisting of these gases are treated here. These are tested as a function of total content against the Pioneer 10 observations and for stability against escape. The results suggest that the atmosphere is very tenuous and that the interpretation of the ionosphere detected by Pioneer 10 by a static model may be inconsistent with the sodium cloud observations. It is postulated that ionization may also be escaping and that sodium may be comparable in content in the atmosphere with some molecular constituent such as NH₃ or N₂. Sodium and this molecular component then dominate the atmosphere. It is also suggested that particle precipitation contributes to heating of the atmosphere and to the production of ionization; furthermore, the difference between day- and nighttime ionospheres and possible trailing and leading side effects may relate to the nature of the particle energy distributions. These distributions may be the result of the peculiar interaction of Io with the Jovian magnetosphere.     

Partial reconstruction of the initial conditions for streams of energetic electrons associated with a solar type III burst

A simple test of the applicability of quasilinear theory is presented to be applied to measured velocity distributions of energetic electrons associated with solar type III bursts or similar particle streams: it consists in taking the time integral of these distributions after removing the background. If quasilinear diffusion of weak plasma turbulence applies to the particle dynamics and if all other losses are neglected, the time integral of the distributions injected at the source of the streaming particles is recovered. In particular, if these distributions are approximated by hot Maxwellian ones, direct estimates of the initial temperatures are retrieved. Further analysis might even permit an experimental evaluation of the relative effects of collision and scattering losses.     

Hawking radiation of Dirac particles via tunneling from a black plane

Extending Kerner and Mann’s fermion tunneling, we investigate the Dirac particle’s tunneling radiation from a black plane in Anti-de Sitter space-time. The result shows that the tunneling probability is related to the change of Bekenstein-Hawking entropy.     

A calculation of the Rosseland mean opacity of dust grains in primordial solar system nebulae

The Rosseland mean opacity was determined for an ensemble of dust grain species though to have been present in the early solar nebula, as well as in the primordial nebulae that helped to form the outer planets. In performing these calculations, we have derived and used more general equation for the Rosseland opacity that allows for anisotropic scattering. The identity of the major particle species and their relative abundances were found from thermodynamic equilibrium and solar elemental abundances. The optical constants of these materials were defined at wavelengths ranging from near-UV to the radio domain. Calculations were performed for a very wide range of particle size distributions, including a nominal one based on that of interstellar dust grains. In addition, asymptotic expressions for the Rosseland opacity are derived in the limits of very small and very large sized particles. Results are presented for nebular temperatures varying from 10 to 2500°K and for nebular gas densities varying from 10^?14 to 1 g/cm³. The values of the Rosseland mean opacity do not depend sensitively on the choice of the particle size distribution function, provided that there are few particles having sizes in excess of several tens of microns. At low temperatures that lie within the stability field of condensed water (?200°K), this opacity varies approximately as the square of the temperature for the nominal size distribution and for all distributions having few particles larger than several tens of microns. However, the Rosseland opacity has a much weaker temperature dependence at higher temperatures for this class of size distributions and at all temperatures for size distributions containing numerous particles larger than several tens of microns. As a result, thermal convection in primordial nebulae occurs over broader ranges of altitudes at low temperatures and for size distributions for which extensive aggregation has not yet occurred.     

Lunar soil grain size distribution

A comprehensive review has been made of the currently available data for lunar grain size distributions. It has been concluded that there is little or no statistical difference among the large majority of the soil samples from the Apollo 11, 12, 14, and 15 missions. The grain size distribution for these soils has reached a steady state in which the comminution processes are balanced by the aggregation processes. The median particle size for the steady-state soil is 40 to 130 µm. The predictions of lunar grain size distributions based on the Surveyor television photographs have been found to be quantitatively in error and qualitatively misleading.     

Satellite particle exospheres of planets: Application to Earth

Neutral planetary exospheres are built up by three different kinds of gas particles, namely ballistic, hyperbolic and elliptic particles. Elliptic particles have their origin exclusively in exospheric regions of the planet where they are fed into satellite orbits by different physical processes. It has been suggested that elliptic particles that do not enter the collision-dominated planetary gas regions represent an important fraction of the particles constituting the outer parts of planetary exospheres. Here we develop a theoretical concept for a rigorous calculation of elliptic particle distributions using Boltzmann equation kinetic approaches. Taking into account realistic gain and loss processes a general procedure for the determination of satellite particle densities for the terrestrial case is presented. We give representative height profiles of the satellite particle density in the exosphere for weak and strong solar activity. Our results are compared with those obtained by simplified theoretical approaches; pronounced deviations are obvious. It is shown that satellite particles are more relevant in low temperature exospheres leading to an order-of-magnitude difference above 1500 km between the densities for weak and strong solar activity. There is a general tendency for satellite particles to become increasingly important with increasing height.     

Pitch-angle scattering of energetic particles in the current sheet of the magnetospheric tail and stationary distribution functions

An investigation of pitch-angle scattering of energetic particles in magnetic field configurations with a current sheet similar to that observed in the geomagnetotail has been performed. The magnetic field model is specified by two parameters which are the current sheet thickness in units of particle gyroradius and the angle between the magnetic field lines and the sheet plane. Computations of a considerable number of trajectories (about 20,000 for each model case) has provided the possibility of obtaining the matrix of pitch-angle scattering and the corresponding kernel function of the integral equation for the stationary particle distribution function. Solution of this equation shows that isotropic distributions are formed only in the case of a sufficiently thick current sheet. Particle scattering in a thin field reversal region leads to the formation of an anisotropic stationary distribution. The results can be used for interpretation of the data on the spatial distribution of energetic particle fluxes in the near part of the magnetospheric tail and in the vicinity of the outer boundary of the radiation belt.     

MODELING THE SPORADIC METEOROID BACKGROUND CLOUD

The orbital distributions of dust particles in interplanetary space are revised in the ESA meteoroid model to incorporate more observational data and to comply with the constraints due to the long-term particle dynamics under the planetary gravity and Poynting–Robertson effect. Infrared observations of the zodiacal cloud by the COBE Earth-bound observatory, flux measurements by the dust detectors on board Galileo and Ulysses spacecraft, and the crater size distributions on lunar rock samples retrieved by the Apollo missions are fused into a single model. Within the model, the orbital distributions are expanded into a sum of contributions due to a number of known sources, including the asteroid belt with the emphasis on the prominent families Themis, Koronis, Eos and Veritas, as well as comets on Jupiter-encountering orbits. An attempt to incorporate the meteor orbit database acquired by the Advanced Meteor Orbit Radar at Christchurch is also discussed. Work was done during D. Galligan’s stay at the University of Canterbury.     

宇宙线的超新星遗迹起源

宇宙线的起源是高能天体物理的核心问题之一.一直以来,超新星爆发被认为是能谱膝区以下宇宙线的主要来源.多波段观测表明,超新星遗迹有能力加速带电粒子至亚PeV (10~(15)eV)能量.扩散激波加速被认为是最有效的天体高能粒子加速机制之一,而超新星遗迹的大尺度激波正好为这一机制提供平台.近年来,一系列较高精度的地面和空间实验极大地推动了对宇宙线以及超新星遗迹的研究.新的观测事实挑战着传统的扩散激波加速模型以及其在银河系宇宙线超新星遗迹起源学说上的应用,深化了人们对宇宙高能现象的认识.结合超新星遗迹辐射能谱的时间演化特性,构建的时间依赖的超新星遗迹粒子加速模型,不仅能够解释200 GV附近宇宙线的能谱反常,还自然地形成能谱膝区,甚至可以将超新星遗迹粒子加速对宇宙线能谱的贡献延伸至踝区.该模型预期超新星遗迹中粒子的输运行为表现为湍流扩散,这需要未来的观测以及与粒子输运相关的等离子体数值模拟工作来进一步验证.