The stability parameters of three-dimensional periodic three-body orbits

Formulae containing the elements of the variational matrix are obtained which determine the linear isoenergetic stability parameters of three-dimensional periodic orbits of the general three-boy problem. This requires the numerical integration of the variational equations but produces the stability parameters with the effective accuracy of the numerical integration. The conditions for stability, criticality, and bifurcations are briefly examined and the stability determination procedure is tested in the determination of some three-dimensional periodic orbits of low inclination bifurcating from vertical-critical coplanar orbits.     

The lunar geochemistry of chromium and vanadium

Crystal/liquid partition coefficients for Cr, V, Mn, and Fe have been determined experimentally between olivine, orthopyroxene, clinopyroxene and silicate melt possesing the composition of a primitive lunar green glass, at oxygen fugacities appropriate to the lunar interior. These species all behave essentially as compatible elements and possess crystal/liquid partition coefficients mostly between 0.3 and 0.9. Partition coefficients for Cr, V, and Mn are generally similar to those of Fe. This implies that crystal/liquid fractionation processes in the lunar interior which do not involve the participation of spinels would not have been effective in fractionating MnO, CrO, and VO from FeO. The well-known constancy of FeO/MnO ratios in nearly all lunar rocks is a reflection of this behaviour. It is shown that comparably strong correlations between CrO-;FeO and VO-;FeO exist for lunar highland breccias and soils from all sites and that these correlations extend to primitive lunar volcanic glasses associated with mare volcanism, strongly suggesting that the CrO/FeO and VO/FeO ratios so derived are of global importance. The observed ratios characterizing differentiated regions of the Moon can be combined with the corresponding ratios for residual refractory portions of the Moon, using measured partition coefficients for Fe, Mg, Cr, V, and Mn between olivine, orthopyroxene and liquid. Bulk Moon abundances for Cr and V have been calculated for a range of reasonable assumptions concerning the petrogenetic relationships between differentiated portions of the Moon and complementary refractory residua consisting of olivine and orthopyroxene mineralogies. Because of the small differences in crystal liquid partition coefficients between FeO, CrO, and VO, these estimates are insensitive to large variations in the models. The bulk Moon is accordingly estimated to contain 2190–2463 ppm Cr and 79–95 ppm V. These values are very similar to the Cr and V contents of the Earth's mantle, estimated as 3010 ppm Cr and 81 ppm V by Sun (1982). The geochemical implications of these similarities are discussed.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

Observations of interstellar HOCO+: abundance enhancements toward the galactic center

A survey of the 4(04)-3(03) and 1(01)-0(00) transitions of HOCO+ has been made toward several molecular clouds. The HOCO+ molecule was not observed in any sources except Sgr B2 and Sgr A. The 5(05)-4(04) and 4(14)-3(13) transitions were also detected toward Sgr B2. The results indicate that gas phase CO2 is not a major carbon reservoir in typical molecular clouds. In Sgr B2, the HOCO+ antenna temperature exhibits a peak approximately 2' north of the Sgr B2 central position (Sgr B2[M]) and the 4(04)-3(03) line emission is extended over a approximately 10' x 10' region. The column density of HOCO+ at the northern peak in Sgr B2 is approximately 3 x 10(14) cm-2, and the fractional abundance relative to H2 > or = 3 x 10(-10), which is about 2 orders of magnitude greater than recent predictions of quiescent cloud ion-molecule chemistry.     

Identification of the interstellar cyanomethyl radical (CH2CN) in the molecular clouds TMC-1 and Sagittarius B2

We report the astronomical identification of the cyanomethyl radical, CH2CN, the heaviest nonlinear molecular radical to be identified in interstellar clouds. The complex fine and hyperfine structures of the lowest rotational transitions at about 20.12 and 40.24 GHz are resolved in TMC-1, where the abundance appears to be about 5 x 10(-9) relative to that of H2. This is significantly greater than the observed abundance of CH3CN (methyl cyanide) in TMC-1. In Sgr B2 the hyperfine structure is blended in the higher frequency transitions at 40, 80, and 100 GHz, although the spin-rotation doubling is clearly evident. Preliminary searches in other sources indicate that the distribution of CH2CN is similar to that for such carbon chain species as HC3N or C4H.     

Heterodyne spectroscopy of the 158 micron C II line in M42

We have obtained velocity-resolved spectra of the 12C II 157.8 microns 2P3/2-2P1/2 fine structure line in the M42 region of Orion. Observations at 0.8 km s-1 resolution with a laser heterodyne spectrometer show multiple velocity components in some locations, with typical linewidths of 3-5 km s-1. Spectra of theta 1C and BN-KL also show weak emission from the F = 2-1 hyperfine component of the equivalent 13C II line. From the observed 12C II/13C II line intensity ratios, we deduce that the 12C II emission is optically thick with tau approximately 5 at both positions. Excitation temperatures of 128 K and 90 K, together with column densities of approximately 1 x 10(19) cm-2 and approximately 4 x 10(18) cm-2, are derived for theta 1C and BN-KL, respectively.     

Combustion as the cause of comet P/Halley's activity

The totality of the results obtained in the VEGA, GIOTTO and SUISEI projects does not lend itself to interpretation within the old sublimation models of comet activity considering solar radiation as the sole source of energy. Among them are the systematic excess of the velocity and temperature of the gas escaping from the nucleus over the theoretical values, the outflow being concentrated in several ( ~ 12–15) narrow ( ~ 300 m in size at the nucleus) hypersonic jets carrying very large amounts of remarkably fine CHON dust and located along continuous lines on the nuclear surface, intense release from the nucleus or very close to it (2 × 10³km) of CO (Q _Co/Q _{H2 O} = 0.05–0.2) with a smaller amount of CO₂ (Q _{CO 2}/ Q _{H2 O} 0.015), large near-nucleus abundances of C, C⁺ (Q _C/Q _CO 0.29), etc.The new observations, together with some earlier data still poorly understood (e.g. the appearance in the coma of large amounts of C₃) can be accounted for by assuming the cometary ices to contain, apart from hydrocarbons, nitrogen-containing compounds, etc. also of free oxygen ( ~ 15 wt.%). Under these conditions, burning should occur in the products of sublimation under deficiency of oxidizer accompanied by the production of soot, smoke, etc. The burning should propagate under the surface crust and localize primarily at a few sites.The presence of oxygen in cometary ices follows from a new eruption theory assuming the minor bodies of the Solar System to have formed in explosions of the massive ice envelopes saturated by electrolysis products on distant moonlike bodies of the type of Ganymede and Callisto.     

Dynamical effects of dark matter in systems of galaxies

SeveralN-body experiments were performed in order to simulate the dynamical behaviour of systems of galaxies gravitationally dominated by a massive dark background.We discuss mass estimates from the dynamics of the luminous component (M _VT) under the influence of such a background, assuming a constant dark/luminous mass ratio (M _D/M _L) and plausible physical conditions. We extend in this way previous studies (Smith, 1980, 1984) about the dependence ofM _VT on the relative distributions of dark and luminous matter (Limber, 1959). We found that the observed ratio of the virial theorem mass to luminosity (M _VT/L) in systems of galaxies of different sizes could be the result of different stages of their post-virialisation evolution as was previously suggested by White and Rees (1978) and Barnes (1983). This evolution is mainly the result of the dynamical friction that dark matter exerts on the luminous component. Thus our results give support to the idea that compact groups of galaxies are dynamically more evolved than large clusters, which is expected from the hierarchical clustering picture for the formation of such structures.     

Evolution of galaxies: One-zone model with a birth-rate stellar function depending on gas density and temperature

In this paper closed one-zone models with a birth-rate stellar function depending on gas density and temperature are built up, in order to make a zeroth order approximation of thermo-chemical evolution of galaxies. To get a more realistic picture, the models are allowed first to expand with the universe and then to contract according to three successive time-scales, in order to simulate violent relaxation, rapid contraction, and slow contraction processes.Star formation occurs according to a birth-rate (m, t) _g ⁿ T ^r m ^p ( _g , gas density;T, gas temperature; andm, star mass), which reproduces the usual Schmidt-type law in the limitr0. Further we suppose that synthesized metals and helium are instantaneously mixed when returned to gas component at star death, and that relative metal abundances are time-independent: ( any element heavier than He, ). An energy fraction of each typical supernova event is assumed to heat interstellar medium, which is also though always to maintain a steady state.Under these hypotheses it becomes possible to use the interstellar cooling function of Dalgarno and McCray (1972), which is related to a special cosmic abundance of elements, to express analytically an interstellar cooling function related to any abundance. At this stage, numerical computations are performed up to about 12 Gy and the results analyzed in order to reproduce some morphological features observed in the galaxy, namely: (i) the extreme scarcity of stars with nearly zero metal content; (ii) the metal content and mass fraction of halo stars; (iii) the metal content and mass fraction of disk stars; and (iv) the ratio of the present-day birth-rate to the past birth-rate averaged over the age of the disk. It is found that a whole class of theoretical models exist, with slope of the mass spectrum between –2.5 and –2.6, which range from a Schmidt's law limitn=1.3 andr=0 to the opposite limitn=0 andr=–1.2, and are able to fit more or less at the same extent the observations mentioned above. On the analysis of further computations, it is also shown that an universal birth-rate stellar function is in contradiction with neither a dynamical hystory starting from the initial expansion of proto-galaxies, nor a morphological sequence where the amount of angular momentum is the only free parameter for any given mass, at least for what concerns spiral types. Finally, possible refinements for future work are briefly outlined.     

Discrete Alfvén waves in planar flux tubes

Properties of discrete Alfvén wave modes are derived, at frequencies up to the ion-cyclotron frequency, for current-carrying plasma slabs with non-uniform densities. It is shown that the essential features of the dispersion relations can be derived by examining the dominant terms in the potential function, when the wave equation is cast in the Schrödinger equation form. Analytical predictions for a class of mass and current density profiles are compared with numerically calculated dispersion relations and wavefields for particular profiles.