Coordinate gauge conditions in theN-body equations of motion in the first-order post-Newtonian approximation of general relativity

The explicit forms of the metric as well as the equations of motion in the first-order post-Newtonian approximation are worked out under several gauge conditions. It is noted that the so-called EIH (Einstein, Infeld, and Hoffman) equation of motion for an assembly ofN finite mass points mutually interacting via gravitation is identically obtained under three different gauge conditions, namely the harmonic gauge, Chandrasekhar gauge and a composite Chandrasekhar gauge used by Misneret al. (1970), even though the solutions for the metric are found to be all different. In one case the metric has a component apparently diverging, but finally generates regular affine connections so that the equations of motions become free from any singularity. By use of the Chandrasekhar gauge and his formulation, the second-order contribution to the acceleration of planets in the limit of test particle motion around the Sun has been calculated, the inclusion of which in the EIH set of the equations of motion would extend the relative accuracy of computing the total acceleration of any planet to better than one part in 10¹⁷.     

Non‐equilibrium concepts lead to a unified explanation of the formation of chondrules and chondrites

Abstract— Calculations of the formation of seven types of chondrules in Semarkona from a gas of solar composition were performed with the FACT computer program to predict the chemistries of oxides (including silicates), developed by the authors and their colleagues. The constrained equilibrium theory was used in the calculations with two nucleation constraints suggested by nucleation theory. The first constraint was the blocking of Fe and other metal gaseous atoms from condensing to form solids or liquids because of very high surface free energies and high surface tensions of the solid and liquid metals, respectively. The second constraint was the blocking of the condensation of solids and the formation of metastable liquid oxides (including silicates) well below their liquidus temperatures. Our laboratory experiments suggested subcooling of type IIA chondrule compositions of 400 degrees or more below the liquidus temperature. The blocking of iron leads to a supersaturation of Fe atoms, so that the partial pressure of Fe (p_Fe) is larger than the partial pressure at equilibrium (p_Fe(eq)). The supersaturation ratio S = p_Fe/p_Fe(eq) becomes larger than 1 and increases rapidly with a decrease in temperature. This drives the reaction Fe + H₂O ? H₂ + FeO to the right. With S = 100, the activity of FeO in the liquid droplet is 100 times as large as the value at equilibrium. The FeO activities are a function of temperature and provide relative average temperatures of the crystallization of chondrules. Our calculations for the LL3.0 chondrite Semarkona and our study of some non‐equilibrium effects lead to accurate representations of the compositions of chondrules of types IA, IAB, IB, IIA, IIAB, IIB, and CC. Our concepts readily explain both the variety of FeO concentrations in the different chondrule types and the entire process of chondrule formation. Our theory is unified and could possibly explain the formation of chondrules in all chondritic meteorites as well as provide a simple explanation for the complex chemistries of chondrites, and especially for type 3 chondrites.     

Wavelet Spectrum Analysis Of Eit/Soho Images

The extreme ultraviolet imaging telescope (EIT) of SOHO offers a unique record of the solar atmosphere for its sampling in temperature, field of view, resolution, duration, and cadence. To investigate globally and locally its topology and evolution during the solar cycle, we consider a multi-scale approach, and more precisely we use the wavelet spectrum. We present three results among the applications of such a procedure. First, we estimate the typical dimension of the supergranules as seen in the 30.4 nm passband, and we show that the evolution of the characteristic network scale is almost in phase with the solar cycle. Second, we build pertinent time series that give the evolution of the signal energy present in the corona at different scales. We propose a method that detects eruptions and post-flaring activity in EUV image sequences. Third, we introduce a new way to extract active regions in EIT images, with perspectives in, e.g., long-term irradiance analysis.     

Evolutionary Processes in Low-Mass Binary Systems

We consider the evolution of certain low-mass binaries, incorporating models of (a) internal evolution, (b) tidal friction, (c) dynamo activity driven by an elementary α,Ω dynamo, (d) stellar wind driven by the activity, and (e) magnetic braking as a consequence of wind and poloidal dynamo-generated magnetic field. In some circumstances the stellar wind is found to remove mass on a nuclear timescale, as is necessary to explain some observed systems. We can hope that various uncertainties in the model may be clarified by a careful comparison of the models with such observed quantities as rotation periods. These are modified by processes (a), (b) and (e). Assuming that stellar evolution is slow, rotation rate should in some circumstances represent a balance between magnetic braking trying to slow the star down and tidal friction trying to spin it up. Preliminary attempts are promising, but indicate that some fine tuning is necessary. When there is a third body present, in an orbit which is inclined but not necessarily of short period, the eccentricity of a close binary can be strongly modified by ‘Kozai cycles’. We show that this may complicate attempts to account for spin rates of stars in close binaries.     

2060 Chiron back to a minimum of brightness

The results of photometric observations of comet/asteroid 2060 Chiron at the Observatório do Pico dos Dias (Brazil-OPD) and the Observatoire de Haute-Provence (France-OHP) during 1994 and 1995 are presented. The analysis of the data shows a decrease of 2060 Chiron brightness from its peak values of 1988–1991. The absolute magnitude, H_v, varies from a maximum of 6.6 in February 1994 up to a minimum of 6.8 in June 1995. Therefore 2060 Chiron is back to a minimum of activity close to that of 1983–1985. The slope parameter G is found to be G = 0.71 ± 0.15. It is suggested that the H-G magnitude system, generally adopted to present 2060 Chiron brightness, is not the most appropriate due to the cometary activity of this object.     

Cygnus A

Cygnus A was the first hyper-active galaxy discovered, and it remains by far the closest of the ultra-luminous radio galaxies. As such, Cygnus A has played a fundamental role in the study of virtually all aspects of extreme activity in galaxies. We present a review of jet theory for powering the double-lobed radio emitting structures in powerful radio galaxies, followed by a review of observations of Cygnus A in the radio, optical, and X-ray relevant to testing various aspects of jet theory. Issues addressed include: jet structure from pc- to kpc-scales, jet stability, confinement, composition, and velocity, the double shock structure for the jet terminus and the origin of multiple radio hotspots, the nature of the filamentary structure in the radio lobes, and the hydrodynamic evolution of the radio lobes within a dense cluster atmosphere, including an analysis of pressure balance between the various gaseous components. Also discussed are relativistic particle acceleration and loss mechanisms in Cygnus A, as well as magnetic field strengths and geometries both within the radio source, and in the intracluster medium. We subsequently review the classification, cluster membership, and the emission components of the Cygnus A galaxy. The origin of the activity is discussed. Concentrating on the nuclear regions of the galaxy, we review the evidence for an obscured QSO, also given the constraints on the orientation of the radio source axis with respect to the sky plane. We present an overview of models of central engines in AGN and observations of Cygnus A which may be relevant to testing such models. We conclude with a brief section concerning the question of whether Cygnus A is representative of powerful high redshift radio galaxies. Received October 10, 1995