Orbital dynamics of three-dimensional bars – I. The backbone of three-dimensional bars. A fiducial case

In this series of papers we investigate the orbital structure of three-dimensional (3D) models representing barred galaxies. In the present introductory paper we use a fiducial case to describe all families of periodic orbits that may play a role in the morphology of three-dimensional bars. We show that, in a 3D bar, the backbone of the orbital structure is not just the x1 family, as in two-dimensional (2D) models, but a tree of 2D and 3D families bifurcating from x1. Besides the main tree we have also found another group of families of lesser importance around the radial 3:1 resonance. The families of this group bifurcate from x1 and influence the dynamics of the system only locally. We also find that 3D orbits elongated along the bar minor axis can be formed by bifurcations of the planar x2 family. They can support 3D bar-like structures along the minor axis of the main bar. Banana-like orbits around the stable Lagrangian points build a forest of 2D and 3D families as well. The importance of the 3D x1-tree families at the outer parts of the bar depends critically on whether they are introduced in the system as bifurcations in z or in   z˙   .     

Precision timing measurements of PSR J1012+5307

We present results and applications of high-precision timing measurements of the binary millisecond pulsar J1012+5307. Combining our radio timing measurements with results based on optical observations, we derive complete 3D velocity information for this system. Correcting for Doppler effects, we derive the intrinsic spin parameters of this pulsar and a characteristic age of 8.6±1.9 Gyr . Our upper limit for the orbital eccentricity of only 8×10⁻⁷ (68 per cent confidence level) is the smallest ever measured for a binary system. We demonstrate that this makes the pulsar an ideal laboratory in which to test certain aspects of alternative theories of gravitation. Our precision measurements suggest deviations from a simple pulsar spin-down timing model, which are consistent with timing noise and the extrapolation of the known behaviour of slowly rotating pulsars.     

Second National Workshop on Solar Physics,Indian Institute of Astrophysics,Kodaikanal, India

This paper presents a brief report about the topics discussed at the second Indian National Workshop on Solar Physics held in September 1987.     

Evaluation of the accuracy of the EIGEN-1S and -2 CHAMP-derived gravity field models by satellite crossover altimetry

Since the advent of CHAMP, the first in a series of low-altitude satellites being almost continuously and precisely tracked by GPS, a new generation of long-wavelength gravitational geopotential models can be derived. The accuracy evaluation of these models depends to a large extent on the comparison with external data of comparable quality. Here, two CHAMP-derived models, EIGEN-1S and EIGEN-2, are tested with independent long-term-averaged single satellite crossover (SSC) sea heights from three altimetric satellites (ERS-1, ERS-2 and Geosat). The analyses show that long-term averages of crossover residuals still are powerful data to test CHAMP gravity field models. The new models are tested in the spatial domain with the aid of ERS-1/-2 and Geosat SSCs, and in the spectral domain with latitude-lumped coefficient (LLC) corrections derived from the SSCs. The LLC corrections allow a representation of the satellite-orbit-specific error spectra per order of the models spherical harmonic coefficients. These observed LLC corrections are compared to the LLC projections from the models variance–covariance matrix. The excessively large LLC errors at order 2 found in the case of EIGEN-2 with the ERS data are discussed. The degree-dependent scaling factors for the variance-covariance matrices of EIGEN-1S and –2, applied to obtain more realistic error estimates of the solved-for coefficients, are compatible with the results found here.     

On the efficiency of Runge-Kutta-Nystrom methods with interpolants for solving equations of the form Y″ = F(T,Y, Y′) over short timespans

Runge-Kutta-Nystrom (RKN) codes for the solution of the initial value problem for the general second order differential system have been developed recently, although the methodology on which they are based was known many years ago. In this paper we try to examine the efficiency of several known general Runge-Kutta-Nystrom (GRKN) methods by posing some criteria of cost and accuracy. These methods supplied with the corresponding interpolants, have been applied to some problems of Celestial Dynamics. The results obtained show that these codes have a good response in the approximation of the solution of these problems.Department of Mechanics     

The low-frequency radio spectrum of the continuum emission from the undisturbed sun

The low-frequency radio spectrum of the continuum emission from the undisturbed Sun is determined for 24 days during the period 1985 May-September. It is found that the spectral index varied from + 1.6 to +3.6 during this period. It is suggested that the large positive spectral indices are due to the existence of temperature gradients in the outer corona.     

Collective resonant phenomena on small bodies in the solar system

For both asteroids and meteor streams, and also for comets, resonances play a major role for their orbital evolutions but on different time scales. For asteroids both mean motion resonances and secular resonances not only structure the phase space of regular orbits but are mainly at the origin for the inherent chaos of planet crosser objects.For comets and their chaotic routes temporary trapping into orbital resonances is a well known phenomenon. In addition for slow diffusion through the Kuiper belt resonances are the only candidates for originating a slow chaos.Like for asteroids, resonances with Jupiter play a major role for the orbital evolution of meteor streams. Crossing of separatrix like zones appears to be crucial for the formation of arcs and for the dissolution of streams. In particular the orbital inclination of a meteor stream appears to be a critical parameter for arc formation. Numerical results obtained in an other context show that the competition between the Poynting-Robertson drag and the gravitational interaction of grains near the 2/1 resonance might be very important in the long run for the structure of meteor streams.     

A Hierarchical Hybrid SVM Method for Classification of Remotely Sensed Data

The focus of this work is on developing a new hierarchical hybrid Support Vector Machine (SVM) method to address the problems of classification of multi or hyper spectral remotely sensed images and provide a working technique that increases the classification accuracy while lowering the computational cost and complexity of the process. The paper presents issues in analyzing large multi/hyper spectral image data sets for dimensionality reduction, coping with intra pixel spectral variations, and selection of a flexible classifier with robust learning process. Experiments conducted revealed that a computationally cheap algorithm that uses Hamming distance between the pixel vectors of different bands to eliminate redundant bands was quite effective in helping reduce the dimensionality. The paper also presents the concept of extended mathematical morphological profiles for segregating the input pixel vectors into pure or mixed categories which will enable further computational cost reductions. The proposed method’s overall classification accuracy is tested with IRS data sets and the Airborne Visible Infrared Imaging Spectroradiometer Indian Pines hyperspectral benchmark data set and presented.