Families of Periodic Orbits Emanating From Homoclinic Orbits in the Restricted Problem of Three Bodies

We describe and comment the results of a numerical exploration on the evolution of the families of periodic orbits associated with homoclinic orbits emanating from the equilateral equilibria of the restricted three body problem for values of the mass ratio larger than μ ₁. This exploration is, in some sense, a continuation of the work reported in Henrard [Celes. Mech. Dyn. Astr. 2002, 83, 291]. Indeed it shows how, for values of μ. larger than μ ₁, the Trojan web described there is transformed into families of periodic orbits associated with homoclinic orbits. Also we describe how families of periodic orbits associated with homoclinic orbits can attach (or detach) themselves to (or from) the best known families of symmetric periodic orbits. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Cassini Campaign observations of the Jupiter aurora by the Ultraviolet Imaging Spectrograph and the Space Telescope Imaging Spectrograph

We have analyzed the Cassini Ultraviolet Imaging Spectrometer (UVIS) observations of the Jupiter aurora with an auroral atmosphere two-stream electron transport code. The observations of Jupiter by UVIS took place during the Cassini Campaign. The Cassini Campaign included support spectral and imaging observations by the Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS). A major result for the UVIS observations was the identification of a large color variation between the far ultraviolet (FUV: 1100-1700 Å) and extreme ultraviolet (EUV: 800-1100 Å) spectral regions. This change probably occurs because of a large variation in the ratio of the soft electron flux (10-3000 eV) responsible for the EUV aurora to the hard electron flux (∼15-22 keV) responsible for the FUV aurora. On the basis of this result a new color ratio for integrated intensities for EUV and FUV was defined (4πI1550-1620 Å/4πI1030-1150 Å) which varied by approximately a factor of 6. The FUV color ratio (4πI1550-1620 Å/4πI1230-1300 Å) was more stable with a variation of less than 50% for the observations studied. The medium resolution (0.9 Å FWHM, G140M grating) FUV observations (1295-1345 Å and 1495-1540 Å) by STIS on 13 January 2001, on the other hand, were analyzed by a spectral modeling technique using a recently developed high-spectral resolution model for the electron-excited H₂ rotational lines. The STIS FUV data were analyzed with a model that considered the Lyman band spectrum (B ) as composed of an allowed direct excitation component (X ) and an optically forbidden component (X followed by the cascade transition ). The medium-resolution spectral regions for the Jupiter aurora were carefully chosen to emphasize the cascade component. The ratio of the two components is a direct measurement of the mean secondary electron energy of the aurora. The mean secondary electron energy of the aurora varies between 50 and 200 eV for the polar cap, limb and auroral oval observations. We examine a long time base of Galileo Ultraviolet Spectrometer color ratios from the standard mission (1996-1998) and compare them to Cassini UVIS, HST, and International Ultraviolet Explorer (IUE) observations.     

MORPHOLOGIES OF IRON CRYSTALS FROM THE HAVERÖ METEORITE

Studies of unpolished chips of the Haverö meteorite using the scanning electron microscope (SEM) and the electron microprobe (EMP), show two types of metallic iron particles: A, discrete convex globules of 5 to 50 microns made up of lamellae and interlocked grains, evenly interspersed among the matrix; B, flattened contorted crystals, less than one micron, lining the iron globules and cavities in the silicates or forming rounded spiny bodies. This second type of iron is interpreted, according to the current theory, as resulting from the in situ reduction of iron-magnesium silicates     

A Note on a General Algorithm for Two-Body Expansions

This note describes briefly a technique, easily implemented with most computer algebra systems, for the purpose of computing the two-body expansions (in powers of the eccentricity and in Fourier series of the mean-anomaly) of a large class of functions of the distance, the true anomaly and/or the eccentric anomaly. This revised version was published online in July 2006 with corrections to the Cover Date.     

Compressed sensing imaging techniques for radio interferometry

Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals. We propose new generic imaging techniques based on convex optimization for global minimization problems defined in this context. The versatility of the framework notably allows introduction of specific prior information on the signals, which offers the possibility of significant improvements of reconstruction relative to the standard local matching pursuit algorithm CLEAN used in radio astronomy. We illustrate the potential of the approach by studying reconstruction performances on simulations of two different kinds of signals observed with very generic interferometric configurations. The first kind is an intensity field of compact astrophysical objects. The second kind is the imprint of cosmic strings in the temperature field of the cosmic microwave background radiation, of particular interest for cosmology.     

Radio observations of Jupiter-family comets

Radio observations from decimetric to submillimetric wavelengths are now a basic tool for the investigation of comets. Spectroscopic observations allow us: (i) to monitor the gas production rate of the comets, by directly observing the water molecule, or by observing secondary products (e.g., the OH radical) or minor species (e.g., HCN); (ii) to investigate the chemical composition of comets; (iii) to probe the physical conditions of cometary atmospheres: kinetic temperature and expansion velocity. Continuum observations probe large-size dust particles and (for the largest objects) cometary nuclei.Comets are classified from their orbital characteristics into two separate classes: (i) nearly isotropic, mainly long-period comets and (ii) ecliptic, short-period comets, the so-called Jupiter-family comets (JFCs). These two classes apparently come from two different reservoirs, respectively, the Oort cloud and the trans-Neptunian scattered disc. Due to their different history and—possibly—their different origin, they may have different chemical and physical properties that are worth being investigated.The present article reviews the contribution of radio observations to our knowledge of the JFCs. The difficulty of such a study is the commonly low gas and dust productions of these comets. Long-period, nearly isotropic comets from the Oort cloud are better known from Earth-based observations. On the other hand, JFCs are more easily accessed by space missions. However, unique opportunities to observe JFCs are offered when these objects come by chance close to the Earth (like 73P/Schwassmann-Wachmann 3 in 2006), or when they exhibit unexpected outbursts (as did 17P/Holmes in 2007).About a dozen JFCs were successfully observed by radio techniques up to now. Four to ten molecules were detected in five of them. No obvious evidence for different properties between JFCs and other families of comets is found, as far as radio observations are concerned.     

Equivalence for lie transforms

The Lie transform method used in Perturbation Theory is based upon an intrinsic algorithm for transforming functions or vector fields by a transformation close to the identity. It can thus be viewed as a specialization of methods and results of differential geometry as is shown in the first part of this paper. In a second part we answer some of the questions left open in connection with the equivalence of the algorithms proposed by Hori and Deprit. From a formal point of view, the methods are shown to be equivalent for non-canonical as well as canonical transformations and a formula relating directly the two generating functions (or vector fields) is presented (formula (5.17)). On the other hand, the equivalence is shown to hold also in the ring ofp-differentiable functions.     

Spectral observations of spicules at two heights in the solar chromosphere

An observational program at the Sacramento Peak Observatory in 1965 provided high-dispersion spectra of the solar chromosphere in several spectral regions simultaneously. These regions included various combinations of the spectral lines Hα, Hβ and H?, the D₃-line of Hei, the infrared triplet of Oi, and the H- and K-lines and the infrared triplet of Caii. With the use of an image slicer the observations were made simultaneously at two heights in the solar chromosphere separated by several thousand kilometers. From these data we draw the following conclusions:

1. Emission of different lines arises in the same chromospheric features. The intensity ratio of lines of different elements varies significantly from spicule to spicule. For the H- and K-lines of ionized calcium, this ratio remains constant, independent of wavelength throughout the line, overall intensity, and height in the chromosphere. Two rare-earth lines in the wing of the H-line show no spicular structure at all.
2. The line-of-sight velocities of many features reverse as a function of time, although most spicules show velocities in only one direction. The simultaneous spectra at two heights show most spicules to have the same line-of-sight velocity at both. There may be an additional class of features, mostly rapidly moving, whose members have line-of-sight velocities that increase with height. These features comprise perhaps 10% of the total. Velocity changes occur simultaneously, to within 20 sec, at two heights separated by 1800 km, indicating velocities of propagation of hundreds of km/sec. The velocity field of individual features is often quite complicated; many spectral features are inclined to the direction of dispersion, implying that differential mass motions are present.
3. The existence of anomalously broad H and K profiles is real. Even with high dispersion and the best seeing, such profiles are not resolved into smaller features. The central reversal in K, H and Hα appears to remain unshifted when the wings are displaced in wavelength, indicating that the reversal is non-spicular.