On model predictions of the power spectral density of radial solar p modes

We investigate the frequency dependence of the power spectral density of low-degree solar p modes by comparing measurements with the results of a stochastic-excitation model. In the past it was common practice to use the total power in such investigations. Using the maximum of the power spectral density instead provides a direct comparison with the measured mode heights in the observed power spectrum. This method permits a more careful calibration of the adjustable parameters in the excitation model, a model which we present here, for the first time, in a format that precisely and unambiguously relates the amplitudes of the modes of oscillation to the Reynolds stress in the equilibrium model. We find that errors in the theory of the linear mode damping rates, particularly at low frequency, have a dramatic impact on the predictions of the mode heights in the spectral density, whereas parameter changes in the stochastic excitation model, within a plausible domain of parameter space, have a comparatively small effect.     

Search For Correlations Between Batse Gamma-Ray Bursts and Supernovae

We report on our statistical research of space–time correlated supernovae and CGRO-BATSE gamma-ray bursts (GRBs). There exists a significantly higher abundance of core-collapse supernovae among the correlated supernovae, but the subset of all correlated objects does not seem to be physically different from the whole set.     

Radar observations of Itokawa in 2004 and improved shape estimation

Abstract— We present June 2004 radar images of asteroid 25143 Itokawa (1998 SF36) that improve upon the longitude‐latitude coverage of images obtained in 2001 by Ostro et al. (2004) and use the 2001–2004 data to refine that paper's constraints on Itokawa's shape. The 2004 images, the first of the asteroid's southern side, look distinctly different from the 2001 images, revealing leading edges that are much more curved and rugged than the nearly convex leading edges seen at northern latitudes in 2001. Itokawa is shaped like a slightly asymmetrical, bent, lumpy ellipsoid with dimensions along the principal axes within 10% of 594 times 320 times 288 m. To illustrate the uncertainty space associated with shape reconstruction from images with suboptimal orientational coverage, we present two alternative three‐dimensional models of the object.     

A note on Le Verrier's expansion of the disturbing function

An examination of Le Verrier's seventh-order expansion of the disturbing function has revealed only one non-trivial error in Le Verrier's work. The error occurs in a sixth order term in the eccentricities.     

Average velocity components in a rotating infinitely flattened self-gravitating system near an equilibrium state

The average radial and angular velocity components are obtained for a rotating two-dimensional self-gravitating system near an equilibrium state. First-order perturbation configurations of flaring straight bars emanating from the center provide examples of such systems. In these systems the average velocity field to first order is incompressible and irrotational. The second-order effects on the product of the average velocity components with the spatial density are essentially independent of the angular coordinate.     

Profiles of spectral lines of an accretion ring around a Kerr black hole

Profiles of spectral lines emitted from an accretion ring around an object with strong gravitational field should be affected by Doppler shift, gravitational redshift, and deflection of light. Taking these effects into account, precise line profile of a Keplerian ring around a Kerr black hole for a distant observer is obtained by solving the kinetic equation of photons.     

The formal integrals of the restricted planar problem of the three bodies

The first integrals of motion of the restricted planar circular problem of three bodies are constructed as the formal power series in r^1/2, r being the distance of a moving particle from the primary. It is shown that the coefficients of these series are trigonometric polynomials of an angular variable. Some particular solutions have been found in a closed form. The proposed method for constructing the formal integrals can be generalized to a spatial problem of three bodies.     

Roughness of the lunar soil

In situ measurements at the lunar surface at millimeter resolution by the Apollo astronauts have been analyzed. Several statistical parameters have been determined for the landing site. The surface roughness has been found to be very nearly gaussian. The root-mean-square slopes have been obtained over scales between 0.5 mm and 5 cm. They steadily decrease with increasing scale length from 58° to 2° and are in reasonable agreement with radar-measured values. The autocorrelation coefficient of the height distribution has also been obtained. It has a scale-length of 0.7 mm.Adjunct Professor at the University of Massachusetts.Visiting Scholar at the University of Massachusetts.     

A new class of periodic solutions in the Kovalevskaya case of a rigid body in rotation about a fixed point

The equation of motion of a rigid body in Kovaleveskaya case is reduced to a plane motion. By using the method of small parameters introduced by Poincaré, the existence of a periodic solution is established.