On the stability of equilibria of Hamiltonian systems near the main resonances

The equilibrium point O of an autonomous Hamiltonian system of two degrees of freedom is considered for small-oscillation frequencies related as ₂=2₁+. If under the precise resonance (=0) the equilibrium is unstable, the inner diameter () of the domain of stability containing the point O is estimated. It is shown that for the normalized variables ()/b where b is the corresponding resonance coefficient. The estimates () for other main resonances are reported.     

Variable constant of gravitation and celestial mechanics

In the present paper the celestial mechanics consequences (light deflection, radar ranging of the planet, geodetic precession and secular effects in the orbital elements in the two-body problem) for the class of the theories based on the vacuum Jordan's Lagrangian has been considered. In these theories the gravitational constantG is proportional to ^–, being a scalar field and , some dimensionless parameter and the local law of conservation of the energy-momentum tensor holds. Of all these theories with different the most interesting one is that corresponding to =0. In the postnewtonian approximation this gravitational theory is completely equivalent to the general theory of relativity.     

The blanketing in the rocket ultraviolet from 225.2 to 319.6 nm

The blanketing effect for the solar disc center and its value near the limb (cos = 0.23) are obtained for the rocket ultraviolet region using the Harvard center and limb spectra. The value of for the disc center appears to be 0.67 (on average) relative to the quasicontinuum. The essential decrease of towards the limb is also revealed.     

Noise-Storm Continua: Power Estimates for Electron Acceleration

We use a generic stochastic acceleration formalism to examine the power L_in (erg s^-1) input to non-thermal electrons that cause noise-storm continuum emission. The analytical approach includes the derivation of the Greens function for a general second-order Fermi process, and its application to obtain the particular solution for the non-thermal electron distribution resulting from the acceleration of a Maxwellian source in the corona. We compare L_in with the power L_out observed in noise-storm radiation. Using typical values for the various parameters, we find that L_in 10²³–10²⁶ erg s^-1, yielding an efficiency estimate L_out/L_in in the range 10^-10 10^-6 for this non-thermal acceleration/radiation process. These results reflect the efficiency of the overall process, starting from electron acceleration and culminating in the observed noise-storm emission.     

CASPIR: A cryogenic array spectrometer imager for the MSSSO 2.3 m telescope

CASPIR is a near-infrared spectrometer/imager being built for the Mount Stromlo and Siding Spring Observatories' 2.3 m telescope. The instrument is based on a SBRC 256×256 InSb detector array and uses AR-coated Sapphire, MgO, CaF₂, and BaF₂ optics to produce two imaging focal plane scales with 0.5/pixel and 0.25/pixel. Spectral resolving powers of 500 will be achieved through a 1×128 slit with three grisms designed for the J, H, and K bands. IJ, JH, and HK cross-dispersed échelle grisms will achieve resolving powers of 1100 through a 1×15 slit. Coronograph and imaging polarimetry modes will also be available. The various observing configurations are selected via five remotely controlled wheels. The instrument design and system architecture are discussed, and preliminary detector performance figures reported.     

Morphological properties and origin of the photospheric facular granules

From time series of high resolution photographs, morphological properties of the photospheric facular granules were derived. The facular granules are cells of the common granular pattern, brighter than the normal granules when seen between cos = 0.6 and the limb. Their apparent diameter, which decreases towards the limb, is smaller than that of the normal granules: 0.65 and 1.25 respectively at cos = 0.55; their lifetime is 25 min but their bright stage lifetime is only 15 min; they are visible closer to the limb than the normal granules: 1.2 compared to 2–5; the brightening of the facular granules occurs at a faster rate than their fading. From the great similitude of both morphological properties and temperature models of facular and normal granules, it appears possible that the photospheric facular granules are convective cells modified by the presence of a magnetic field of some hundreds Gauss.     

The dust grains in the coma of Comet West

The observed variation of reddening as function of the heliocentric distance and the spatial variation of reddening within the coma of Comet West in the visual wavelength range have been considered to infer the properties of the cometary dust grains. The relevant model incorporates the variation in the size distribution function as well as the composition of the spherical grains. The real part of the complex index of refraction (m = m – im) is chosen such thatm = 1.6. The imaginary part is required to vary from m = 0.2 to 0.05 over the wavelength range 0.4 to 0.7 m. This choice of refractive index corresponds to dirty silicate grains. As a by-product, the model also satisfies the observed polarization and albedo for the Comet West.     

Expanding and superdense astrophysical systems in general relativistic hierarchical cosmology

A semi-continuous hierarchy, (i.e., one in which there are galaxies outside clusters, clusters outside superclusters etc.), is examined using an expression of the field equations of general relativity in a form due to Podurets, Misner and Sharp. It is shown (a) that for a sufficiently populous hierarchy, the thinning factor( _i+1/ _i [r _i /r _i+1] is approximately equal to the exponentN in a continuous density law (=aR ^–N) provided (r _i /r _i+1)^3-1; (b) that a hierarchical Universe will not look decidedly asymmetric to an observer like a human being because such salient observers live close to the densest elements of the hierarchy (viz stars), the probability of the Universe looking spherically symmetric (dipole anisotropy0.1 to such an observer being of order unity; (c) the existence of a semi-continuous or continuous hierarchy (Peebles) requires that 2 if galaxies, not presently bound to clusters were once members of such systems; (d) there are now in existence no less than ten arguments for believing 2, though recent number counts by Sandageet al. seem to be in contradiction to such a value; (e) Hubble's law, withH independent of distance, can be proved approximately in a relativistic hierarchy provided (i)N=2, (ii)2GM(R)/c ² R1; (iii)Rc (iv)M0 in a system of massM, sizeR (f) Hubble's law holds also in a hierarchy with density jumps; (g)H100 km s^–1 Mpc^–1; (h) objects forming the stellar level of the hierarchy (in a cosmology of the Wilson type) must once have had 2GM/c ² R1; (i) there is a finite pressurep=2Ga in all astrophysical systems (a=R ^N ,N2); (j) for the Galaxy, theory predictsp _G7×10^–12 dyn cm^–2, observation givesp _G5×10^–12 dyn cm^–2; (k) if the mass-defect (or excess binding energy) hypothesis is taken as a postulate, all non-collapsed astrophysical systems must be non-static, and any non-static, p0 systems must in any case be losing mass; (1) the predicted mass-loss rate from the Sun is 10¹² g s^–1, compared to 10¹¹ g s^–1 in the observed solar wind; (m) the mass-loss rates known by observation imply timescales of 5×10⁹ years for the Sun and 10¹⁰ years for other astrophysical systems; (n) degenerate superdense objects composed of fermions must haveN-2 if they were ever at their Schwarzschild radii and comprised a finite numberN _B of baryons; (o)N _B10⁵⁷N for degenerate fermion and boson systems; (p)285-4; (q) the metric coefficients for superdense bodies give equations of motion that imply equal maximum luminosities for all evolving superdense bodies (L _max10⁵⁹ erg s^–1); (r) larger bodies have longer time-scales of energy radiation atL _max (10^–5 s for stars,1 h for QSO's) (s) expansion velocities are c soon after the initial loss of equilibrium in a superdense object; (t) if the density parametera(t) in aR ^–N isa=a (non-atomic constants of physicsc, G, A), andA, thenN=2; (u) N2 is necessary to giveMM at the stellar level of the hierarchy;(v) systems larger than, and including, galaxies must have formed by clumping of smaller systems and not (as advocated by Wertz and others) in a multiple big bang.     

Exact solutions in Jordan-Brans-Dicke homogeneous universes I

Spatially homogeneous, anisotropic Bianchi types I-II-III-V-VI_o-VI_h and Kantowski-Sachs (KS) are shown to have perfect fluid solutions in Jordan-Brans-Dicke (JDB) cosmological theory. All the solutions obey the relation =a²+b+c, where and are the re-scaled energy density and the re-scaled scalar field, respectively, and is a time parameter. This relation is derived in Bianchi type-I and gives rise to the general solution for this model universe. In the remaining Bianchi types this same relation is shown to hold as well; and new solution, some of which do not possess locally rotational symmetry, are obtained.     

The solar O i λ 7773 triplet

The reduction of observations of the O i 7773 triplet obtained at high spatial resolution (0.5) at two disk positions is described. Two sets of triplet profile data are presented at each disk position. One set represents data taken from 0.5 regions centered on the brightest granules, while the other set represents data taken from 0.5 regions centered on the cooler infalling intergranular material.     

Gravothermal catastrophe in rotating galaxies

Violent relaxation in a rotating galaxy can lead to a core-halo, system. In order to understand this, a very, crude model is studied in which all details are ignored, and only the dimensions of physical quantities are retained. The behaviour depends on the ratio of the potential in the core to the potential in the halo. When >5/2, the core contracts; when >5, the contraction is a runaway process, or gravothermal catastrophe.     

The geometrical height-scale and the pressure equilibrium in the sunspot umbra

Spectra of spots very near to the solar limb (limb distance 8) are used to determine the height difference between the levels of formation of the continuum and the line cores of 60 medium-strong Fraunhofer lines. For all lines (with Rowland Intensity < 10), this difference is < 1 (= 725 km) and well correlated with the Rowland intensity. The line absorption coefficient is calculated for some lines with known oscillator strength. This gives a possibility to deduce a value for the scale height of the umbra, which is found to be about 100 km, thus being equal to the photospheric scale height. Pure hydrostatic equilibrium exists, therefore, in the umbra, and vertical magnetic forces are negligible. Other methods for determining the scale height are discussed for comparison.The horizontal pressure equilibrium is discussed by taking into account the Wilson effect, and by neglecting dynamic terms (flow of matter). The magnetic field is confirmed to be force-free in higher layers (chromosphere). The pressure difference umbra-photosphere increases towards deeper layers, having a maximum at ^* - 1 which corresponds to about two times the magnetic pressure H ²/8. If rotational symmetry of the field is assumed, this can be explained by a minimum radius of curvature of the field lines of 1/4 spot radius.Mitteilungen aus dem Fraunhofer Institut Nr. 90.     

The nature of η carinae

We give an overview of the Car phenomenon on the basis of ground and space observations. We discuss in particular the IRAS images. We conclude that Car, initially with a mass > 100M , is presently an intermediate-type hypergiant withL=5×10⁶ L , in a rapid evolutionary stage. This phase started with a large increase of mass loss in mid-1800 followed by dust condensation and a large visual fading, at constant bolometric luminosity.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

In situ acceleration and gradients of charged particles in the outer solar system observed by the voyager spacecraft

The probable connection between cosmic rays and the electromagnetic state of the interplanetary medium was recognized by Hannes Alfvén as early as 1949 (Alfvén, 1949, 1950); he pointed out that the properties of cosmic rays necessitate a mechanism, external to Earth but within the solar system, capable of accelerating particles to extremely high energies. In advocating the view of local origin for part of the cosmic-ray spectrum, Alfvén and his colleagues developed a very general type of acceleration mechanism called magnetic pumping. The unique data set of the two Voyagers extends over an entire decade (1977–1987) and is most suitable to explore the problem of acceleration of charged particles in the heliosphere. The energy coverage of the Low Energy Charged Particle (LECP) experiment covers the range 30 keV to several hundred MeV for ions and 22 keV to several MeV for electrons. Selected observations of interplanetary acceleration events from 1 to 25 AU are presented and reviewed. These show frequent acceleration of ions to several tens of MeV in association with shocks; highest energies (220 MeV oxygen) were measured in the near-perpendicular ( _Bn 87.5°) shock of January 5, 1978 at 1.9 AU, where electron acceleration was also observed. Examples of ion acceleration in association with corotating interaction regions are presented and discussed. It is shown that shock structures have profound effects on high-energy (70 MeV) cosmic rays, especially during solar minimum, when a negative latitudinal gradient was observed after early 1985 at all energies from 70 MeV down to 30 keV. By early 1987, most shock acceleration activity in the outer heliosphere (25 to 30 AU) had ceased both in the ecliptic (Voyager-2) and at higher (30°) ecliptic latitudes (Voyager-1). The totality of observations demonstrate that local acceleration to a few hundred MeV, and as high as a few GeV is continually present throughout the heliosphere. It should be noted that in 1954 when Alfvén suggested local acceleration and containment of cosmic rays within the solar system, no one treated his suggestion seriously, at any energy. The observations reviewed in this paper illustrate once more Alfvén's remarkable prescience and demonstrate how unwise it is to dismiss his ideas.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Observations of helium and hydrogen emission in quiescent prominences

Observations of a number of helium triplet ( 10830, 4713, 4471, 3889, 4026) and hydrogen (H, , , ) emission line intensities in six quiescent prominences are presented. The regions of prominence and neighboring corona were raster-scanned by the telescope, and all lines were measured concurrently at each point. The instrumental field of view was 5 × 20. The results are compared with previous observations and theory. In particular, the intensity of the 10830 emission relative to the other triplets is found to differ strongly from the predictions of the recent detailed calculations of Heasley et al. (1974) for model quiescent prominences.     

Dynamics of Blinkers

The relative Doppler and non-thermal velocities of quiet-Sun and active-region blinkers identified in Ov with CDS are calculated. Relative velocities for the corresponding chromospheric plasma below are also determined using the Hei line. Ov blinkers and the chromosphere directly below, have a preference to be more red-shifted than the normal transition region and chromospheric plasma. The ranges of these enhanced velocities, however, are no larger than the typical spread of Doppler velocities in these regions. The anticipated ranges of Doppler velocities of blinkers are 10–15 km s^–1 in the quiet Sun (10–20 km s^–1 in active regions) for Hei and 25–30 km s^–1 in the quiet Sun (20–40 km s^–1 in active regions) for Ov. Blinkers and the chromosphere below also have preferentially larger non-thermal velocities than the typical background chromosphere and transition region. Again the increase in magnitude of these non-thermal velocities is no greater than the typical ranges of non-thermal velocities. The ranges of non-thermal velocities of blinkers in both the quiet Sun and active regions are estimated to be 15–25 km s^–1 in Hei and 30–45 km s^–1 in Ov. There are more blinkers with larger Doppler and non-thermal velocities than would be expected in the whole of the chromosphere and transition region. The recently suggested mechanisms for blinkers are revisited and discussed further in light of the new results.     

A novel methodology for radiative transfer in a planetary atmosphere

A novel methodology for evaluating the field of anisotropically scattered radiation within a homogeneous slab atmosphere of arbitrary optical thickness is provided. It departs from the traditional radiative transfer approach in first considering that the atmosphere is illuminated by an isotropic light source. From the solution of this problem, it subsequently proceeds to that for the more conventional case of monodirectional illumination. The azimuthal dependence of the field is separated in the usual manner by an harmonic expansion, leaving a problem in four dimensions (=optical depth, ₀=thickness, , =directions of incidence and scattering) which, as is well known, is numerically extremely inconvenient. Two auxiliary radiative transfer formulations of increasing dimensionality are considered: (i) a transfer equation for the newly introduced functionb ^m(,,₀) with Sobolev's function ^m(,₀) playing the role of a source-function. Because the incident direction does not intervene, ^m is simply expressed as a single integral term involvingb ^m. For bottom illumination, an analogous equation holds for the other new functionh ^m(,,₀). However, simple reciprocity relations link the two functions so that it is only necessary to considerb ^m; (ii) a transfer equation for the other new functiona ^m(,,,₀) with a source-function provided by Sobolev's functionD ^m(,,₀). For bottom illumination, another functionf ^m(,,,₀) is introduced; by a similar argument using reciprocity relations,f ^m is reduced toa ^m rendering necessary only the consideration ofa ^m. However, a fundamental decomposition formula is obtained which shows thata ^m is expressible algebraically in terms of functions of a single angular variable. The functions ^m andD ^m are shown to be the values in the horizontal plane ofb ^m anda ^m, respectively. The other auxiliary functionsX ^m andY ^m are also expressed algebraically in terms ofb ^m. These results enable one to proceed to the final step of evaluating the radiation field for monodirectional illumination. The above reductions toalgebraic relations involving only the functionb ^m appear to be more advantageous than Sobolev's (1972) recent approach; they also circumvent some basic numerical difficulties in it. We believe the present approach may likewise prove to be superior to most (if not all) other methods of solution known heretofore.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory under Contract No. NAS-7-100 sponsored by the National Aeronautics and Space Administration.     

The application of a non-static spherically-symmetric metric to clusters of galaxies

An approximate metric is found which represents a sphere of matter embedded in a background of dust. The use of this metric in conjunction with the Friedmann equations gives values of for the three possible values ofk as +6×10^–36 (k=+1), +3×10^–35 (k=0), +10^–36 (k=–1). These values depend on data regarding clusters of galaxies, and are probably accurate to within an order of magnitude given the correctness of the assumptions on which their derivation rests.     

Birth of the presolar nebula: The sequence of condensation revealed in the Allende meteorite

This work applies the well-known supernova-trigger hypothesis for solar system formation to explain in detail many properties of the Allende meteorite. The Allende carbonaceous chondrite meteorite is an assemblage of millimetre- to centimetre-sized Ca-Al-rich inclusions (CAI's), fine-grained alkali-rich spinel aggregates, amoeboid olivine aggregates, olivine chondrules and sulfide chondrules set in an extremely fine-grained black matrix. Detailed isotopic, chemical and textural properties show that these components formed in the above order as independent cosmic grains. Some CAI's containmicron-sized metal nuggets in which the normally incompatible refractory (Mo, Re, W) and platinum group (Pt, Os, Ir, Ru) metals are alloyed together in approximately cosmic proportions, suggesting that these nuggets also condensed as cosmic grains.From the consistent pattern of enclosure of earlier components on the above list within later ones, it appears that in the environment where these materials formed, condensation moved inexorably in the direction of increasing olivine and decreasing refractory element and¹⁶O content (from 4% excess¹⁶O to normal terrestrial oxygen isotopic composition). Condensation sequences are all short and incomplete, from which it is concluded that condensing materials were soon separated from the condensing environment and isolated until all were brought together in a final snowstorm of fine-grained, olivine crystals constituting the meteorite matrix.These major properties can be accounted for in a model in which a supernova remnant (SNR) in the snowplow phase, whose oxygen was initially pure¹⁶O, pushes into a dark interstellar cloud. In the model, condensation of CAI's begins in the SNR shell when it has been diluted with 2500 times its mass of matter from the cloud, which also in part explains the rarity of observed isotopic anomalies in CAI's. The retardation of the SNR by the cloud propels condensed grains ahead toward the cloud under their own momentum. Continuing dilution by the cloud and continuing removal of the most refractory elements in grains can explain the evolving patterns of fractionation and depletion of refractory elements, including REE's, in successive condensates. Features such as rims on CAI's and concentric zonation of fine-grained aggregates can also be satisfied in the model. A presolar origin and a short ( 10 000 years) formation time for inclusions in carbonaceous chondrites are major implications of the model.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6–8 September, 1978.     

The visco-resistive stability of arcades in the corona of the Sun

The stability of ballooning modes in coronal arcades is studied using linear visco-resistive MHD. Rigid wall conditions are adopted for modelling the photospheric line-tying of the magnetic field. The full Braginskii viscosity stress tensor is used and particular attention is given to the effect of the viscosity coefficient ₃ which was left out of an earlier investigation by Van der Linden, Goossens, and Hood (1987, 1988). The numerical results for shearless arcades show that the coefficient ₃ has a stabilizing effect. However, for realistic values of the equilibrium quantities the stabilizing effect by ₃ can be neglected in comparison with the strong stabilizing effect of the perpendicular viscosity. The effect of magnetic field strength and mode number on stability are determined. In particular it is found that there exists a critical field strength for every mode number such that the mode is stable for weaker fields and unstable for stronger fields.