The tidal stripping of satellites

We present an improved analytic calculation for the tidal radius of satellites and test our results against N -body simulations.
The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and the orbit of the star within the satellite . We demonstrate that this last point is critical and suggest using three tidal radii to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power-law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically.
Over short times (≲1–2 Gyr ∼1 satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic.     

The 550-au Mission: a critical discussion

We have studied the science rationale, goals and requirements for a mission aimed at using the gravitational lensing from the Sun as a way of achieving high angular resolution and high signal amplification. We find that such a mission concept is compromised by several practical problems. Most severe are the effects due to the plasma in the solar atmosphere which cause refraction and scattering of the propagating rays. These effects either limit the frequencies that can be observed to those above ∼1 THz, or they move the optical point outwards beyond the vacuum value of ≥550 au. (Thus for observing frequency of 300 GHz the optical point is moved outwards to ∼ 680 au.) Density fluctuations in the inner solar atmosphere will further cause random pathlength differences for different rays. The corrections for the radiation from the Sun itself will also be a major challenge at any wavelength used, but could be mitigated with coronographic techniques. Given reasonable constraints on the spacecraft (particularly in terms of size and propulsion), source selection as well as severe navigational constraints further add to the difficulties for a potential mission. Nevertheless, unbiased surveys of small-scale structure on the sky at short wavelengths might be the most promising application of such a mission.     

A one-dimensional model for the interaction between continental-scale ice sheets and atmospheric stationary waves

 The great continental ice sheets of the Pleistocene represented a significant topographic obstacle to the westerly winds in northern midlatitudes. This work explores how consequent changes in the atmospheric stationary wave pattern might have affected the shape and growth of the ice sheets themselves. A one dimensional (1-D) model is developed which permits an examination of the types and magnitudes of the feedbacks that might be expected. When plausible temperature perturbations are introduced at the ice-sheet margin which are proportional to the stationary wave amplitude, the equilibrium shape of the ice sheet is significantly altered, and depends on the sign of the perturbation. The proposed feedback also affects the response of the ice sheet to time-varying climate forcing. The results suggest that the evolution of a continental-scale ice sheet with a land-based margin may be significantly determined by the changes it induces in the atmospheric circulation. Received: 1 October 1999 / Accepted: 17 July 2000     

Metamorphism in Archaean greenstone belts: calculated fluid compositions and implications for gold mineralization

An inescapable consequence of the metamorphism of greenstone belt sequences is the release of a large volume of metamorphic fluid of low salinity with chemical characteristics controlled by the mineral assemblages involved in the devolatilization reactions. For mafic and ultramafic sequences, the composition of fluids released at upper greenschist to lower amphibolite facies conditions for the necessary relatively hot geotherm corresponds to those inferred for greenstone gold deposits (X_CO2= 0.2–0.3). This result follows from the calculation of mineral equilibria in the model system CaO–MgO–FeO–Al₂O₃–SiO₂–H₂O–CO₂, using a new, expanded, internally consistent dataset. Greenstone metamorphism cannot have involved much crustal over-thickening, because very shallow levels of greenstone belts are preserved. Such orogeny can be accounted for if compressive deformation of the crust is accompanied by thinning of the mantle lithosphere. In this case, the observed metamorphism, which was contemporaneous with deformation, is of the low-P high-T type. For this type of metamorphism, the metamorphic peak should have occurred earlier at deeper levels in the crust; i.e. the piezothermal array should be of the ‘deeper-earlier’type. However, at shallow crustal levels, the piezothermal array is likely to have been of ‘deeper-later’type, as a consequence of erosion. Thus, while the lower crust reached maximum temperatures, and partially melted to produce the observed granites, mid-crustal levels were releasing fluids prograde into shallow crustal levels that were already retrograde. We propose that these fluids are responsible for the gold mineralization. Thus, the contemporaneity of igneous activity and gold mineralization is a natural consequence of the thermal evolution, and does not mean that the mineralization has to be a consequence of igneous processes. Upward migration of metamorphic fluid, via appropriate structurally controlled pathways, will bring the fluid into contact with mineral assemblages that have equilibrated with a fluid with significantly lower X_CO2. These assemblages are therefore grossly out of equilibrium with the fluid. In the case of infiltrated metabasic rocks, intense carbonation and sulphidation is predicted. If, as seems reasonable, gold is mobilized by the fluid generated by devolatilization, then the combination of processes proposed, most of which are an inevitable consequence of the metamorphism, leads to the formation of greenstone gold deposits predominantly from metamorphic fluids.     

A sapphirine–phlogopite–cordierite paragenesis in a low-P amphibolite facies terrain, Arunta Inlier, Australia

Summary Silica-undersaturated phlogopite schists from the Cackleberry Metamorphics, Arunta Inlier, central Australia, preserve relatively low-temperature sapphirine-bearing parageneses that developed during low-pressure upper amphibolite facies metamorphism. Peak metamorphic phlogopite–cordierite–sapphirine assemblages are interpreted to have formed during the same event recorded in nearby metapelites, at c.3 kbar and 650–700 °C. Initial cooling of the terrain resulted in the breakdown of sapphirine to corundum–chlorite–phlogopite and corundum–spinel–chlorite assemblages. Further retrogression at greenschist facies conditions resulted in the replacement of sapphirine by diaspore–chlorite intergrowths. The reaction textures are consistent with a near-isobaric heating-cooling path at low-pressure, and provide evidence for the stability of sapphirine at c.700 °C at low pressures in rocks of an appropriate Mg- and Fe³⁺-rich bulk composition. Received August 15, 2001 accepted December 27, 2001     

Comparison of results from several AOGCMs for global and regional sea-level change 1900–2100

 Sea-level rise is an important aspect of climate change because of its impact on society and ecosystems. Here we present an intercomparison of results from ten coupled atmosphere-ocean general circulation models (AOGCMs) for sea-level changes simulated for the twentieth century and projected to occur during the twenty first century in experiments following scenario IS92a for greenhouse gases and sulphate aerosols. The model results suggest that the rate of sea-level rise due to thermal expansion of sea water has increased during the twentieth century, but the small set of tide gauges with long records might not be adequate to detect this acceleration. The rate of sea-level rise due to thermal expansion continues to increase throughout the twenty first century, and the projected total is consequently larger than in the twentieth century; for 1990–2090 it amounts to 0.20–0.37 m. This wide range results from systematic uncertainty in modelling of climate change and of heat uptake by the ocean. The AOGCMs agree that sea-level rise is expected to be geographically non-uniform, with some regions experiencing as much as twice the global average, and others practically zero, but they do not agree about the geographical pattern. The lack of agreement indicates that we cannot currently have confidence in projections of local sea-level changes, and reveals a need for detailed analysis and intercomparison in order to understand and reduce the disagreements. Received: 1 September 2000 / Accepted: 20 April 2001     

Why Mt Etna?

The Etna volcano is located in an apparently anomalous position on the hinge zone of the Apennines subduction and its Na-alkaline geochemistry does not favour a magma source from the deep slab as indicated for the Aeolian K-alkaline magmatism. The steeper dip of the regional foreland monocline at the front of the Apennines in the Ionian Sea than in Sicily, implies a larger rollback of the subduction hinge in the Ionian Sea. Moreover, the lengthening of the Apennines arc needs extension parallel to the arc. Therefore, the larger southeastward subduction rollback of the Ionian lithosphere with respect to the Hyblean plateau in Sicily, should kinematically produce right-lateral transtension and a sort of vertical 'slab window' which might explain (i) the Plio-Pleistocene alkaline magmatism of eastern Sicily (e.g. the Etna volcano) and (ii) the late Pliocene to present right lateral transtensional tectonics and seismicity of eastern Sicily. The area of transfer of different dip and rollback occurs along the inherited Mesozoic passive continental margin between Sicily and the oceanic Ionian Sea, i.e. the Malta escarpment.     

A techno-economic comparison of power systems for autonomousunderwater vehicles

This paper compares lead-acid batteries, sodium-sulfur batteries, solid polymer fuel cells and closed-cycle diesel engines for autonomous underwater vehicle (AUV) applications. The service is described in terms of a parametric mission and life cycle. A generic AUV is used as a basis for comparison. Power systems are evaluated by two criteria: (1) submerged endurance capability and (2) life cycle cost. This study determines categories of service for which each power system is preferred. The solid polymer fuel cell can provide greater submerged endurance than other power systems examined. For extremely long duration AUV missions, the fuel cell is the required system, indicating a possible market niche for today's fuel cell technology. Considering cost projections for each power system, the results also show that the SPFC can become cost-competitive with conventional technologies, particularly for services characterized by high levels of utilization     

Trace-element contents and cathodoluminescence of “trapiche” rubies from Mong Hsu, Myanmar (Burma): geological significance

Summary ?Mong Hsu rubies of the “trapiche” type are sporadically seen in the gem market. However, they have never been described in the field. The study of the nature of solid inclusions, the variation of trace-element contents, as well as the cathodoluminescence behaviour of six “trapiche” rubies permit the conclusion that these rubies crystallised in the same geological environment (marble-type deposit) as the normal rubies from Mong Hsu: (1) Cr and V are the main chromophorous elements in both ruby types; they act, together with Ti, as activators or quenchers for cathodoluminescence; (2) calcite, dolomite, rutile, mica, diaspore, apatite, chlorite, and feldspar are solid inclusions found in both ruby types; (3) the presence of bastn?site in trapiche ruby and fluorite in non-trapiche ruby indicates the circulation of F-bearing fluids during ruby deposition; (4) the distribution of trace-element contents in the crystal is similar for both ruby types. In the Cr₂O₃ vs. Fe₂O₃ and Cr₂O₃ vs. Fe₂O₃/TiO₂ diagrams, the population fields of Mong Hsu “trapiche” and non-“trapiche” rubies overlap. They are distinct from those of rubies and sapphires hosted in basalts from South-east Asia. Received October 30, 2001; revised version accepted March 25, 2002