Nonlinear Interactions Between Kinetic Alfvén and Ion-Sound Waves

The resonant interaction between kinetic Alfvén and ion-acoustic waves is considered using the Hall-MHD theory. The results of previous authors are generalized to cover both finite Larmor radius as well as the ideal MHD results. It is found that the three-wave coupling is strongest when the wavelength is comparable to the ion-sound gyroradius. Applications of our work to weak turbulence theories as well as to the heating of the solar corona are pointed out.     

第二代天体测量卫星及后依巴谷地面天体测量的进展

简述了后依巴谷的天体测量工作。首先给出了第二个天体测量卫星Gaia的最新进展、最近提出的JAMSE和OBSS计划的简介,以及包含天体测量内容的SIM PlanetQuest计划的情况; 叙述了多波段天体参考架的建立和维持,特别是依巴谷星表向暗星方向的扩充和数字巡天,以及其他地面观测计划,如双星和聚星、太阳系天体的观测等;介绍了天体测量与天体物理结合的几个研究课题的进展;最后对我国自然科学基金会“十一五”天体测量优先发展的方向与内容提出建议。     

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker–Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.     

A viable mechanism for the production of energy in active galactic nuclei

It is suggested that a collapsing supermassive object, which acts as an ultra-high energy particle accelerator, is the precursor of an active galactic nucleus and that the gravitational energy released during the collapse of the object is locked in the quark-gluon plasma permeated by leptons into which the entire matter in the core of the object is converted as a result of the collapse. It is also pointed out that the collapse of the object to a space-time singularity is inhibited by Pauli's exclusion principle as well as by Heisenberg's uncertainty principle and that the object explodes, before it could collapse to a singularity, thereby releasing the enormous amount of energy locked in the quark-gluon plasma.     

Equilibrium points and Lyapunov families in the circular restricted three-body problem with an oblate primary and a synchronous rotating dipole secondary: Application to Luhman-16 binary system

We numerically study a version of the synchronous circular restricted three-body problem, where an infinitesimal mass body is moving under the Newtonian gravitational forces of two massive bodies. The primary body is an oblate spheroid while the secondary is an elongated asteroid of a combination of two equal masses forming a rotating dipole which is synchronous to the rotation of the primaries of the classic circular restricted three-body problem. In this paper, we systematically examine the existence, positions, and linear stability of the equilibrium points for various combinations of the model's parameters. We observe that the perturbing forces have significant effects on the positions and stability of the equilibrium points as well as the regions where the motion of the particle is allowed. The allowed regions of motion as determined by the zero-velocity surface and the corresponding isoenergetic curves as well as the positions of the equilibrium points are given. Finally, we numerically study the binary system Luhman-16 by computing the positions of the equilibria and their stability as well as the allowed regions of motion of the particle. The corresponding families of periodic orbits emanating from the collinear equilibrium points are computed along with their stability properties.     

A method solving kepler's equation without transcendental function evaluations

We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series expansion. A combination of these was applied to solving Kepler's equation for the elliptic case. The resulting method requires no evaluation of transcendental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original Newton-Raphson method. Also it is more than 2.5 times as fast as Halley's method, Nijenhuis's method, and others.     

Velocity dispersion in particulate disks with size distribution

Quasi-equilibrium solutions for the pre-planetary disk are studied in terms of Hämeen-Anttila's theory (1984) of collisional, self-gravitating systems. The distribution of particle sizes is assumed to follow simple power-law distributions, with a power index in the range of 1.5–5.0. The treatment includes mutual impacts with a velocity dependent coefficient of restitution, as well as gravitational encounters with dynamical friction. The mean gravitational field of the disk is also taken into account. The results indicate that the energy(equi)-partition depends mainly on the index of size distribution, but is also affected by the optical thickness of the system, as well as on the vertical thickness as compared to the particle size. The vertical component of the gravitational field is found to be important, especially when the mass of the system is concentrated on the large particles.     

Potential energy of continuous and discrete distributions of matter from the point of view of the application of the virial theorem

The potential energy of clusters of stars in which the distribution of matter is taken to be continuous is compared with that of static model clusters in which the distribution of matter is discrete, the comparison being made from the point of view of applying the virial theorem to estimate the masses of the clusters. There is good agreement on the average between the two cases as long as the stellar distribution is random. Systematic differences occur whenever there is any departure from randomness. However, reduction of the mass of a cluster as estimated by means of the virial theorem by even as much as a factor of 2 on the average would seem to require even greater departures from randomness in the stellar distribution than are considered here. As might be expected there are sometimes very large fluctuations in the potential energy from one cluster to the next in the discrete case.Contributions of the Louisiana State University Observatory, No. 30.     

Accurate abundance analysis of late-type stars: advances in atomic physics

The measurement of stellar properties such as chemical compositions, masses and ages, through stellar spectra, is a fundamental problem in astrophysics. Progress in the understanding, calculation and measurement of atomic properties and processes relevant to the high-accuracy analysis of F-, G-, and K-type stellar spectra is reviewed, with particular emphasis on abundance analysis. This includes fundamental atomic data such as energy levels, wavelengths, and transition probabilities, as well as processes of photoionisation, collisional broadening and inelastic collisions. A recurring theme throughout the review is the interplay between theoretical atomic physics, laboratory measurements, and astrophysical modelling, all of which contribute to our understanding of atoms and atomic processes, as well as to modelling stellar spectra.     

Gas flow in the solar nebula leading to the formation of Jupiter

Three-dimensional gas flow in the solar nebula, which is subject to the gravity of the Sun and proto-Jupiter, is numerically calculated by using a three-dimensional hydrodynamic code - i.e., the socalled smoothed-particle method. The flow is circulating around the Sun as well as falling into a potential well of proto-Jupiter. The results for various masses of proto-Jupiter show that (1) the e-folding growth time of proto-Jupiter by accretion of the nebular gas is as short as about 300 years in stages where the mass of proto-Jupiter is 0.2 ~ 0.5 times the present Jovian mass, and that (2) proto-Jupiter begins to push away the nebular gas from the orbit of proto-Jupiter and form a gap around the orbit, when its mass is about 0.7 times the present Jovian mass. It is possible that this pushing-away process determined the present Jovian mass.     

Hubble expansion of the universe and structural features of atomic nuclei

An attempt is made to study the concept of “black holes” from the standpoint of the axioms of modern physics. It is found that matter which lies inside a Schwarzschild sphere must disappear, both as a source of electromagnetic waves and as a source of a gravitational field. To resolve this paradox a hypothesis is proposed according to which the accelerated expansion of the universe interacts with atomic nuclei in such a way as to transfer a positive energy to every nucleus in accordance with its volume. The influx of energy into a nucleus gradually neutralizes its binding energy, so that there is an increase in the mass of the nucleus, as well as of its component nucleons. This mechanism suggests that during the inverse process, when matter is compressed, the opposite phenomenon should be observed with a release of binding energy, and the average mass of the nucleons involved in this process should decrease; that is, part of the mass of the material is simply converted into energy.     

On Pfaff's equations of motion in dynamics; Applications to satellite theory

In this article we study a form of equations of motion which is different from Lagrange's and Hamilton's equations: Pfaff's equations of motion. Pfaff's equations of motion were published in 1815 and are remarkably elegant as well as general, but still they are much less well known. Pfaff's equations can also be considered as the Euler-Lagrange equations derived from the linear Lagrangian rather than the usual Lagrangian which is quadratic in the velocity components. The article first treats the theory of changes of variables in Pfaff's equations and the connections with canonical equations as well as canonical transformations. Then the applications to the perturbed two-body problem are treated in detail. Finally, the Pfaffians are given in Hill variables and Scheifele variables. With these two sets of variables, the use of the true anomaly as independent variable is also considered.     

Free-convection flow in the stokes problem for a vertical plate with variable surface temperature

The free-convection flow of an incompressible viscous fluid past an infinite, vertical plate for impulsive as well as uniformly accelerated motion of the plate is discussed when the plate temperatuve varies as the square root of time. The Laplace transform technique is used to obtain the expressions for velocity and skin-friction. The influence of the various parameters, entering into problem, on the velocity field and skin-friction is extensively discussed.     

A new way to conserve total energy for Eulerian hydrodynamic simulations with self-gravity

We propose a new method to conserve the total energy to round-off error in grid-based codes for hydrodynamic simulations with self-gravity. A formula for the energy flux due to the work done by the self-gravitational force is given, so the change in total energy can be written in conservative form. Numerical experiments with the code Athena show that the total energy is indeed conserved with our new algorithm and the new algorithm is second order accurate. We have performed a set of tests that show the numerical errors in the traditional, non-conservative algorithm can affect the dynamics of the system. The new algorithm only requires one extra solution of the Poisson equation, as compared to the traditional algorithm which includes self-gravity as a source term. If the Poisson solver takes a negligible fraction of the total simulation time, such as when FFTs are used, the new algorithm is almost as efficient as the original method. This new algorithm is useful in Eulerian hydrodynamic simulations with self-gravity, especially when results are sensitive to small energy errors, as for radiation pressure dominated flow.     

Kernel regression for determining photometric redshifts from Sloan broad-band photometry

We present a new approach, namely kernel regression, to determine photometric redshifts for 399 929 galaxies in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS). Kernel regression is a weighted average of spectral redshifts of the neighbours for a query point, and higher weights are associated with points that are closer to the query point. One important design decision when using kernel regression is the choice of bandwidth. We apply 10-fold cross-validation to choose the optimal bandwidth, which is obtained as the cross-validation error approaches its minimum. The results show that the optimal bandwidth is different for different input patterns: the lowest rms error of photometric redshift estimation arrives at 0.019 using colour+eClass as the inputs, the lowest rms errors comes to 0.020 using ugriz +eClass as the inputs. Where eClass is a galaxy spectral type, and 0.021 using colour+ r as the inputs. Thus, in addition to parameters such as magnitude and colour, eClass is a valid parameter with which to predict photometric redshifts. Moreover, the results suggest that the accuracy of estimating photometric redshifts is improved when the sample is divided into early-type and late-type galaxies; in particular, for early-type galaxies, the rms scatter is 0.016 with colour+eClass as the inputs. In addition, kernel regression achieves high accuracy when predicting the photometric eClass  (σ_rms= 0.034)  using colour+ r as the input pattern. For kernel regression, the accuracy of the photometric redshifts does not always increase with the number of parameters considered, but is satisfactory only when appropriate parameters are chosen. Kernel regression is a comprehensible and accurate regression method. Experiments reveal the superiority of kernel regression over other empirical training approaches.     

Beware λ-truncation! Sample truncation and bias in luminosity calibration using trigonometric parallaxes

The common practice in luminosity calibration of sample truncation according to relative parallax error λ can lead to bias with indirect methods such as reduced parallaxes as well as with direct methods. This bias is not cancelled by the Lutz–Kelker corrections and in fact can be either negative or positive. Making the selection stricter can actually lead to a larger absolute amount of bias and lower accuracy in certain cases.
The degree to which this bias is present depends upon whether the sample is more nearly specified by the relative parallax error or by the limiting apparent magnitude when both limits formally apply; when the latter limit dominates it is absent. The difference between the means for the two extreme cases is what is customarily termed the Malmquist bias. However, it is not truly bias, but rather what we call here an offset .
For a sample to be effectively magnitude-limited, there is a lower bound imposed on the mean absolute magnitude which depends on the limiting magnitude. If a wide-ranging luminosity relation such as the Wilson–Bappu relation is to be calibrated, some portion of the relation may be magnitude-limited and the rest not. In that case there will be offsets between the different parts of the relation, including the transition region between the two extremes, as well as bias outside the magnitude-limited part.
Another, less common, practice is truncation according to weight, specifically with the reduced parallax method. Such truncation can also bias the calibration with one variant of the method. Indeed, the weighting scheme used with that variant introduces bias even without truncation.
For calibration it is probably best to use a general maximum likelihood method such as the grid method with a magnitude-limited sample and no limit on relative parallax error. The Malmquist shift could then be applied to obtain an estimate of the volume-limited mean.     

Dynamics of nonlinear ion-waves in Fermi-Dirac electron-positron-ion magnetoplasmas

Oblique propagation and head-on collisions of solitary structures is studied in a dense magnetized plasma comprised of relativistic ultra-cold electrons and positrons and positive dynamic ions using conventional extended multi-scales technique, in the ground of quantum hydrodynamics model. The variations of head-on collision phase-shift as well as the characteristic soliton amplitude and width is evaluated numerically in terms of other plasma parameters such as mass-density, normalized magnetic field strength, its angle with respect to the soliton propagation and the relative positron number-density. The relevance of current investigations, with appropriate plasma parameters for the astrophysical dense magnetized objects such as white-dwarfs, is addressed.     

A High-accuracy, Small Field of View Star Guider with Application to SNAP

To accomplish its mission, the spaceborne observatory SNAP (SuperNova Acceleration Probe) requires a pointing stability of <0.03 arcseconds during exposures lasting up to 500 sec. A Monte Carlo simulation of the photoelectron statistics from the guiding star investigates geometrical (such as the pixel size of the detector or the plate scale) and physical parameters (such as the magnitude of the star). It is shown that simple centroiding calculations can lead to the desired accuracy with guide stars as faint as magnitude 16. Availability of these stars is verified thanks to the HST Guide Star Catalog complemented with a statistical model of the distribution of stars. Thus a through-the-lens sensor that uses stars as faint as magnitude 16 to provide the necessary guiding signals is feasible. This revised version was published online in July 2006 with corrections to the Cover Date.     

Critique of fluid theory of magnetospheric phenomena

It is pointed out that the fluid theory has been successful in magnetospheric problems (such as the shape of the magnetopause) which involve basic considerations such as the conservation of particles, of momentum, and of energy, but that it is inadequate for other problems (such as the energization of auroral particles). Difficulties arise from the fact that it is not always possible to specify a volume of plasma because particles do not remain as neighbours. Misuse of the fluid theory has led to a number of fallacies, such as the idea that the causal order of physical events in cosmic electrodynamics is the reverse of that in the familiar laboratory electrodynamics. This mistaken idea comes from a confusion of a mathematical sequence of calculations with the causal order. Also, the importance of the magnetic field as an active element is over-emphasized. Appreciation of the fact that kinetic theory is the more fundamental seems to be widely lacking. A plea is made for a common sense approach to magnetospheric and auroral problems wherein the fluid theory is used whenever it can, but where it is not expected to be adequate for all purposes.     

Shear-induced folding in Arsia Mons aureole: Evidence for low-latitude martian glaciations

Folds up to 50 km across have been identified on Arsia Mons aureole. Tharsis Province, Mars. The structures, located on Mars for the first time, are close to Aganippe Fossa and other huge faults which have behaved as left-lateral shear zones and then as extensional features. A tectonic scheme is proposed to explain the folds as shear-induced structures. Folding reveals a layered sequence in the aureole, and that is taken as a definitive evidence for its deposition by ice.If at least some of the Tharsis volcanoes aureoles are basal moraines, their study is critical, as they could contain a record of Mars paleoclimatic fluctuations. Martian past frozen lakes or oceans have been proposed, and some sediments found on the northern plains could have been deposited on the bottom of those basins. If this is so, those formations should be layered sequences and could also bear the traces of tectonic stresses, detectable as folds on Viking imagery. Correlation of these two kinds of evidence seems a promising line to tackle the Martian paleoclimatic problem.