A multiresolution model for small-body gravity estimation

A new model, dubbed the MRQSphere, provides a multiresolution representation of the gravity field designed for its estimation. The multiresolution representation uses an approximation via Gaussians of the solution of the Laplace’s equation in the exterior of a sphere. Also, instead of the spherical harmonics, variations in the angular variables are modeled by a set of functions constructed using quadratures for the sphere invariant under the icosahedral group. When combined, these tools specify the spatial resolution of the gravity field as a function of altitude and required accuracy. We define this model, and apply it to representing and estimating the gravity field of the asteroid 433 Eros. We verified that a MRQSphere model derived directly from the true spherical harmonics gravity model satisfies the user defined precision. We also use the MRQSphere model to estimate the gravity field of Eros for a simulated satellite mission, yielding a solution with accuracy only limited by measurement errors and their spatial distribution.     

Production spectrum of gamma rays in interstellar space through neutral pion decay

We have obtained a simple representation to the observed invariant cross-section for the production of neutral pions in proton-proton collisions. Making use of this representation, we have calculated the differential and integral production spectra of gamma rays in the Galaxy from interactions of cosmic ray nuclei with interstellar gas. It is shown that the uncertainties in deducing interstellar proton spectrum by demodulating the observed spectrum do not affect very much the gamma ray spectrum. We have also determined the gamma ray production spectrum through bremsstrahlung process for a typical interstellar electron spectrum derived from the radio spectrum in the Galaxy. From these, the total gamma ray production spectrum resulting from the interaction of cosmic rays with interstellar matter is compared with the observed gamma ray spectrum in the Galaxy and some inferences have been obtained. We also point out the possible uncertainty in the present calculation and suggest the improvements needed.     

Multidimensional cosmological models in effective string gravitation. II

We carry out an analysis of the exact solution obtained in the first part of this work for a homogeneous and anisotropic flat cosmological model in the general conformal representation of multidimensional low-energy string theory. We show that the singular solutions with power law of variation of the scale factors of maximally symmetric subspaces and scalar field are asymptotes of the general solution in early and late stages of evolution. We study the conditions under which models of exponential, extended, and violent inflation are realized. As an illustration of the general regularities we consider the specific example of an antisymmetric Kalb-Ramond field as a gravitational source. We demonstrate the possibility of dynamic compactification of the extra dimensions.Translated fromAstrofizika, Vol. 38, No. 3, 1995.     

Fast compression and reconstruction of astronomical images based on compressed sensing

With the fast increase in the resolution of astronomical images, the question of how to process and transfer such large images has become a key issue in astronomy. We propose a new real-time compression and fast reconstruction algorithm for astronomical images based on compressive sensing techniques. We first reconstruct the original signal with fewer measurements, according to its compressibility. Then,based on the characteristics of astronomical images, we apply Daubechies orthogonal wavelets to obtain a sparse representation. A matrix representing a random Fourier ensemble is used to obtain a sparse representation in a lower dimensional space. For reconstructing the image, we propose a novel minimum total variation with block adaptive sensing to balance the accuracy and computation time. Our experimental results show that the proposed algorithm can efficiently reconstruct colorful astronomical images with high resolution and improve the applicability of compressed sensing.     

A new numerical scheme for structures of rotating magnetic stars

We have developed a new numerical scheme for obtaining structures of rapidly rotating stars with strong magnetic fields. In our scheme, both poloidal and toroidal magnetic fields can be treated for stars with compressibility and infinite conductivity. By introducing the vector potential and its integral representation, we can treat the boundary condition for the magnetic fields across the surface properly. We show structures and distributions of magnetic fields as well as the distributions of the currents of rotating magnetic polytropic stars with polytropic index   N = 1.5  . The shapes of magnetic stars are oblate as long as the magnetic vector potential decreases as 1/ r when   r →∞  . For extremely strong magnetic fields, equilibrium configurations can be of toroidal shapes.     

The Minispiral in the Galactic Center revisited

We present the results of a re-examination of a [Ne II] line emission data cube (λ 12.8μm) and discuss the kinematic structure of the inner 3×4 pc of the Galaxy. The quality of [Ne II] as a tracer of ionized gas is examined by comparing it to radio data. A three-dimensional representation of the data cube allows us to disentangle features which are projected onto the same location on the sky. A model of gas streams in different planes is fitted to the data. We find that most of the material is located in a main plane which itself is defined by the inner edge of the Circum-Nuclear Disk in the Galactic Center. Finally, we present a possible three-dimensional model of the gas streams.     

Effects of a deformation of a star on the gravitational lensing

We study analytically a gravitational lens due to a deformed star, which is modelled by using a monopole and a quadrupole moment. Positions of the images are discussed for a source on the principal axis. We present explicit expressions for the lens equation for this gravitational lens as a single real 10th-order algebraic equation. Furthermore, we compute an expression for the caustics as a discriminant for the polynomial. Another simple parametric representation of the caustics is also presented in a more tractable form. A simple expression for the critical curves is obtained to clarify a topological feature of the critical curves; the curves are simply connected if and only if the distortion is sufficiently large.     

The 27-Day Signal in Sunspot Number Series and the Solar Dynamo

We analyze the Wolf number daily series WN (1849 to present) as well as two other related series characterizing solar activity. Our analysis consists in computing the amplitude of a given Fourier component in a sliding time window and examining its long-term evolution. We start with the well-known 27.03- and 27.6-day periods and observe strong decadal variations of this amplitude as well as a sharp increase of the average value starting around 1905. We then consider a packet of 31 lines with periods from 25.743 to 28.453 days, which is shown to be a better representation of the synodic solar rotation. We first examine the temporal evolution of individual lines, then the energy of the packet. The energy of the packet increases sharply at the beginning of the 20th century, leading by more than two decades the well-known increase of the Wolf number. The nonaxisymmetry of sunspots increases before the total increase of activity and may be considered as a precursor. We discuss briefly and tentatively this observation in terms of solar dynamo theory.     

Multi-dimensional cosmological models in effective string gravitation. I

We consider multi-dimensional cosmological models in the low-energy field theory of strings with a boson gravitational sector containing a metric, dilaton field, and antisymmetric Kalb-Ramon field. We study the conformal properties of the action and show that in the general conformal representation the theory is equivalent to a generalized scalar-tensor theory with a Lagrangian of nongravitating matter dependent on the dilaton. We find exact solutions of the flat homogeneous anisotropic model with structure R×M¹×...×Mⁿ and with equation of state p_i=a_i in the space Mⁱ. We discuss the picture of cosmological evolution in different conformal representations.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

On Motions Near the Lagrange Equilibrium Point L 4 in the Case of Routh's Critical Mass Ratio

We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L ₄ when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L ₄. We also show that in the case of instability of L ₄ the trajectories starting in a vicinity of L ₄ remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date.     

On the evaluation of an integral connected with the thermonuclear reaction rate in closed form

The standard expression of the reaction rate for low-energy, nonresonant nuclear reactions in nondegenerate plasma contains a parameter-dependent integral which in all previous calculations with physical or astrophysical background is considered as not capable of being evaluated in a closed form. So one usually resorts to approximation methods concerning large values of the parameter. At first we point out that CONSUL (1964) has given a series representation of the integral which was identified with a MEIJER 's G-function by MATHAI (1971). Next, in view of a physically more exact determination of the reaction rate formula, especially in connection with calculations concerning stellar energy generation, we consider a more general integral containing the mentioned one as special case and give an approximation-free representation by means of MEIJER 's G-function. The G-function so obtained may be conceived as complex-valued continuation of CONSUL 's series representation of a certain class of integrals contained in the considered one. From the series we extract a small parameter approximation of the special integral.     

Geometrical considerations in imaging the solar corona

X-ray observations of the solar corona show that it is comprised of three-dimensional magnetic structures which appear to be primarily in the form of fluxtubes or loops. Imaging the X-ray corona has led to a greater understanding of the dynamical behaviour of and the energy distribution in these magnetic structures. However, imaging observations, by their very nature, integrate along the line of sight resulting in a two-dimensional representation of the actual three-dimensional distribution. The optically thin nature of the solar corona to X-ray radiation makes the integrated images particularly difficult to interpret. The analysis of the two-dimensional observations must, therefore, inlcude the effect of the orientation of the coronal structure to the line-of-sight direction; a fact which is almost always ignored. In this paper we discuss the effect of loop orientation on the two-dimensional representation and argue that these effects may lead to a misinterpretation of the physics occurring in the structures observed. In particular, we discuss observations taken by the Soft X-ray Telescope (SXT) on board the Yohkoh satellite, taking account of the instrumental thermal response, spatial resolution, and point-spread-function.We test the effect of geometry on the determination of the loop pressure by considering equatorial loops at various longitudes and discuss the implications of this for studies of coronal soft X-ray loops.     

The High-Resolution Solar Reference Spectrum between 250 and 550 nm and its Application to Measurements with the Ozone Monitoring Instrument

We have constructed a new high resolution solar reference spectrum in the spectral range between 250 and 550 nm. The primary use of this spectrum is for the calibration of the Dutch – Finnish Ozone Monitoring Instrument (OMI), but other applications are mentioned. The incentive for deriving a new high resolution solar reference spectrum is that available spectra do not meet our requirements on radiometric accuracy or spectral resolution. In this paper we explain the steps involved in constructing the new spectrum, based on available low and high resolution spectra and discuss the main sources of uncertainty. We compare the result with solar measurements obtained with the OMI as well as with other UV-VIS space-borne spectrometers with a similar spectral resolution. We obtain excellent agreement with the OMI measurements, which indicates that both the newly derived solar reference spectrum and our characterization of the OMI instrument are well understood. We also find good agreement with previously published low resolution spectra. The absolute intensity scale, wavelength calibration and representation of the strength of the Fraunhofer lines have been investigated and optimized to obtain the resulting high resolution solar reference spectrum.     

The Cosmological Scalar in the Jordan-Brans-Dicke Theory. II.

Cosmological solutions are examined in the proper representation of the JBD theory with a dominant nonminimally coupled scalar field. It is shown that only the introduction of a cosmological scalar that transforms to the ordinary cosmological constant in the Einstein representation enables a phase of evolution with a uniform and then an accelerated expansion of the universe over cosmological time scales. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 633–640 (November 2005).     

Local pulsars: A note on the birth-velocity distribution

We explore a simple model for the representation of the observed distributions of the motions, and the characteristic ages of the local population of pulsars. The principal difference from earlier models is the introduction of a unique value,S, for the kick velocity with which pulsars are born. We consider separately the proper motion components in galactic longitude and latitude, and find that the distributions of the velocity components parallel and perpendicular to the galactic plane are represented satisfactorily byS = 200 km/sec, and leave no room for a significant fraction of much higher velocities. The successful proposition of a unique value for the kick velocity may provide an interesting tool in attempts to understand the physical process leading to the expulsion of the neutron star. This paper is an extended analysis of the talk presented by A. Blaauw at the Raman Research Institute on 20th February, 1996.     

Coupling equations for a flow-wave field used to faculae heating

In a binary system of a background fluid-wave field, the wave effect may be important in some cases. From general properties of thermodynamics of the medium, we derive the coupling equations for the mean flow-wave field. For six wave modes (Langmuir wave, ion-acoustic oscillations, whistlers, Alfvén waves, magneto-acoustic oscillations, and transverse plasma wave) the corresponding representation of the wave stress tensor is found. Finally, the representation for the Alfvén waves is applied to the faculae heating and a result consistent with observations is obtained.     

Dust motions in quasi-statically charged binary asteroid systems

In this paper, we discuss dust motion and investigate possible mass transfer of charged particles in a binary asteroid system, in which the asteroids are electrically charged due to solar radiation. The surface potential of the asteroids is assumed to be a piecewise function, with positive potential on the sunlit half and negative potential on the shadow half. We derive the nonautonomous equations of motion for charged particles and an analytic representation for their lofting conditions. Particle trajectories and temporary relative equilibria are examined in relation to their moving forbidden regions, a concept we define and discuss. Finally, we use a Monte Carlo simulation for a case study on mass transfer and loss rates between the asteroids.     

Theoretische Betrachtungen zum Verhalten des Magnetfeldes in einem sphärischen Erdmodell

The theoreticl treatment of several geophysical problems presupposes the solution of field equations of the magnetic field in the Earth's mantle. The field equations are given in a scalar form for a spherical model of the Earth. It will be shown that analytical solutions are possible in all cases. The boundary conditions are discussed with regard to the dynamo process in the Earth's core and the existence of a field representation, which is investigated on the Earth's surface. The question is discussed, to what extend the mantle's field is given by this field representation, when some special assumptions about the Earth's model are made.