A new tool for the study of periodic orbits

We present the generalization of the method of rational Fourier-series approximations for nonlinear ordinary differential equations in galactic dynamics. In previous papers we presented the formulae which describe simple families of periodic orbits with very good accuracy. In this Letter we generalize our formulae to describe periodic orbits of any resonancem:n.     

Accretion disc–stellar magnetosphere interaction: field line inflation and the effect on the spin-down torque

We calculate the structure of a force-free magnetosphere which is assumed to corotate with a central star and which interacts with an embedded differentially rotating accretion disc. The magnetic and rotation axes are aligned, and the stellar field is assumed to be a dipole. We concentrate on the case when the amount of field line twisting through the disc–magnetosphere interaction is large , and consider different outer boundary conditions. In general the field line twisting produces field line inflation (e.g. Bardou & Heyvaerts), and in some cases with large twisting many field lines can become open. We calculate the spin-down torque acting between the star and the disc, and we find that it decreases significantly for cases with large field line twisting. This suggests that the oscillating torques observed for some accreting neutron stars could be caused by the magnetosphere varying between states with low and high field line inflation. Calculations of the spin evolution of T Tauri stars may also have to be revised in the light of the significant effect that field line twisting has on the magnetic torque resulting from star–disc interactions.     

The depletion of carbon by extra mixing in metal-poor giants

There is an apparent dichotomy between the metal-poor  ([Fe/H]≤−2)  yet carbon-normal giants and their carbon-rich counterparts. The former undergo significant depletion of carbon on the red giant branch after they have undergone first dredge-up, whereas the latter do not appear to experience significant depletion. We investigate this in the context that the extra mixing occurs via the thermohaline instability that arises due to the burning of  ³He  . We present the evolution of [C/Fe], [N/Fe] and  ¹²C/¹³C  for three models: a carbon-normal metal-poor star, and two stars that have accreted material from a  1.5 M_⊙  AGB companion, one having received  0.01 M_⊙  of material and the other having received  0.1 M_⊙  . We find the behaviour of the carbon-normal metal-poor stars is well reproduced by this mechanism. In addition, our models also show that the efficiency of carbon-depletion is significantly reduced in carbon-rich stars. This extra-mixing mechanism is able to reproduce the observed properties of both carbon-normal and carbon-rich stars.     

Glacier change in Garibaldi Provincial Park, southern Coast Mountains, British Columbia, since the Little Ice Age

Fluctuations of glaciers during the 20th century in Garibaldi Provincial Park, in the southern Coast Mountains of British Columbia, were reconstructed from historical documents, aerial photographs, and fieldwork. Over 505 km², or 26%, of the park, was covered by glacier ice at the beginning of the 18th century. Ice cover decreased to 297 km² by 1987–1988 and to 245 km² (49% of the early 18th century value) by 2005. Glacier recession was greatest between the 1920s and 1950s, with typical frontal retreat rates of 30 m/a. Many glaciers advanced between the 1960s and 1970s, but all glaciers retreated over the last 20 years. Times of glacier recession coincide with warm and relatively dry periods, whereas advances occurred during relatively cold periods. Rapid recession between 1925 and 1946, and since 1977, coincided with the positive phase of the Pacific Decadal Oscillation (PDO), whereas glaciers advanced during its negative phase (1890–1924 and 1947–1976). The record of 20th century glacier fluctuations in Garibaldi Park is similar to that in southern Europe, South America, and New Zealand, suggesting a common, global climatic cause. We conclude that global temperature change in the 20th century explains much of the behaviour of glaciers in Garibaldi Park and elsewhere.     

A submillimetre survey of the kinematics of the Perseus molecular cloud – I. Data

We present submillimetre observations of the   J = 3 → 2  rotational transition of ¹²CO, ¹³CO and C¹⁸O across over 600 arcmin² of the Perseus molecular cloud, undertaken with the Heterodyne Array Receiver Programme (HARP), a new array spectrograph on the James Clerk Maxwell Telescope. The data encompass four regions of the cloud, containing the largest clusters of dust continuum condensations: NGC 1333, IC348, L1448 and L1455. A new procedure to remove striping artefacts from the raw HARP data is introduced. We compare the maps to those of the dust continuum emission mapped with the Submillimetre Common-User Bolometer Array (SCUBA; Hatchell et al.) and the positions of starless and protostellar cores (Hatchell et al.). No straightforward correlation is found between the masses of each region derived from the HARP CO and SCUBA data, underlining the care that must be exercised when comparing masses of the same object derived from different tracers. From the ¹³CO/C¹⁸O line ratio the relative abundance of the two species  ([¹³CO]/[C¹⁸O]∼ 7)  and their opacities (typically τ is 0.02–0.22 and 0.15–1.52 for the C¹⁸O and ¹³CO gas, respectively) are calculated. C¹⁸O is optically thin nearly everywhere, increasing in opacity towards star-forming cores but not beyond  τ₁₈∼ 0.9  . Assuming the ¹²CO gas is optically thick, we compute its excitation temperature, T _ex (around 8–30 K), which has little correlation with estimates of the dust temperature.     

Assimilation of thermal emission spectrometer atmospheric data during the Mars Global Surveyor aerobraking period

The Thermal Emission Spectrometer aboard the Mars Global Surveyor spacecraft has produced an extensive atmospheric data set, beginning during aerobraking and continuing throughout the extended scientific mapping phase. Temperature profiles for the atmosphere below about 40 km, surface temperatures and total dust and water ice opacities, can be retrieved from infrared spectra in nadir viewing mode. This paper describes assimilation of nadir retrievals from the spacecraft aerobraking period, L_S=190°–260°, northern hemisphere autumn to winter, into a Mars general circulation model. The assimilation scheme is able to combine information from temperature and dust optical depth retrievals, making use of a model forecast containing information from the assimilation of earlier observations, to obtain a global, time-dependent analysis. Given sufficient temperature retrievals, the assimilation procedure indicates errors in the a priori dust distribution assumptions even when lacking dust observations; in this case there are relatively cold regions above the poles compared to a model which assumes a horizontally-uniform dust distribution. One major reason for using assimilation techniques is in order to investigate the transient wave behavior on Mars. Whilst the data from the 2-h spacecraft mapping orbit phase is much more suitable for assimilation, even the longer (45–24 h) period aerobraking orbit data contain useful information about the three-dimensional synoptic-scale martian circulation which the assimilation procedure can reconstruct in a consistent way. Assimilations from the period of the Noachis regional dust storm demonstrate that the combined assimilation of temperature and dust retrievals has a beneficial impact on the atmospheric analysis.     

Enceladus: Present internal structure and differentiation by early and long-term radiogenic heating

Pre-Cassini images of Saturn's small icy moon Enceladus provided the first indication that this satellite has undergone extensive resurfacing and tectonism. Data returned by the Cassini spacecraft have proven Enceladus to be one of the most geologically dynamic bodies in the Solar System. Given that the diameter of Enceladus is only about 500 km, this is a surprising discovery and has made Enceladus an object of much interest. Determining Enceladus' interior structure is key to understanding its current activity. Here we use the mean density of Enceladus (as determined by the Cassini mission to Saturn), Cassini observations of endogenic activity on Enceladus, and numerical simulations of Enceladus' thermal evolution to infer that this satellite is most likely a differentiated body with a large rock-metal core of radius about 150 to 170 km surrounded by a liquid water-ice shell. With a silicate mass fraction of 50% or more, long-term radiogenic heating alone might melt most of the ice in a homogeneous Enceladus after about 500 Myr assuming an initial accretion temperature of about 200 K, no subsolidus convection of the ice, and either a surface temperature higher than at present or a porous, insulating surface. Short-lived radioactivity, e.g., the decay of ²⁶Al, would melt all of the ice and differentiate Enceladus within a few million years of accretion assuming formation of Enceladus at a propitious time prior to the decay of ²⁶Al. Long-lived radioactivity facilitates tidal heating as a source of energy for differentiation by warming the ice in Enceladus so that tidal deformation can become effective. This could explain the difference between Enceladus and Mimas. Mimas, with only a small rock fraction, has experienced relatively little long-term radiogenic heating; it has remained cold and stiff and less susceptible to tidal heating despite its proximity to Saturn and larger eccentricity than Enceladus. It is shown that the shape of Enceladus is not that of a body in hydrostatic equilibrium at its present orbital location and rotation rate. The present shape could be an equilibrium shape corresponding to a time when Enceladus was closer to Saturn and spinning more rapidly, or more likely, to a time when Enceladus was spinning more rapidly at its present orbital location. A liquid water layer on Enceladus is a possible source for the plume in the south polar region assuming the survivability of such a layer to the present. These results could place Enceladus in a category similar to the large satellites of Jupiter, with the core having a rock-metal composition similar to Io, and with a deep overlying ice shell similar to Europa and Ganymede. Indeed, the moment of inertia factor of a differentiated Enceladus, C/MR², could be as small as that of Ganymede, about 0.31.     

Hyperspectral mapping of alteration assemblages within a hydrothermal vug at the Haughton impact structure,Canada

Meteorite impacts on Earth and Mars can generate hydrothermal systems that alter the primary mineralogies of rocks and provide suitable environments for microbial colonization. We investigate a calcite–marcasite‐bearing vug at the ~23 km diameter Haughton impact structure, Devon Island, Nunavut, Canada, using imaging spectroscopy of the outcrop in the field (0.65–1.1 μm) and samples in the laboratory (0.4–2.5 μm), point spectroscopy (0.35–2.5 μm), major element chemistry, and X‐ray diffraction analyses. The mineral assemblages mapped at the outcrop include marcasite; marcasite with minor gypsum and jarosite; fibroferrite and copiapite with minor gypsum and melanterite; gypsum, Fe³⁺ oxides, and jarosite; and calcite, gypsum, clay, microcline, and quartz. Hyperspectral mapping of alteration phases shows spatial patterns that illuminate changes in alteration conditions and formation of specific mineral phases. Marcasite formed from the postimpact hydrothermal system under reducing conditions, while subsequent weathering oxidized the marcasite at low temperatures and water/rock ratios. The acidic fluids resulting from the oxidation collected on flat‐lying portions of the outcrop, precipitating fibroferrite + copiapite. That assemblage then likely dissolved, and the changing chemistry and pH resulting from interaction with the calcite‐rich host rock formed gypsum‐bearing red coatings. These results have implications for understanding water–rock interactions and habitabilities at this site and on Mars.     

Book Review

The aim of this book is to present techniques for the study of motion of solar system objects in highly eccentric orbits. Instead of using the usual anomalies (mean, true, eccentric), the authors define and use a new kind of anomaly, the elliptic anomaly.In this way, it is possible, in a theory using perturbation series expansions, to make the ratio: (accuracy)/(number of needed terms), higher than in the classical techniques. The book consists of six chapters. The first chapter deals with the elliptic anomaly in the two-body problem and the second chapter presents the general technique to construct first-order perturbation theory in elliptic function expansions. The next three chapters deal with applications of the new technique to artificial satellites and asteroids, in highly eccentric orbits. The last chapter describes the basic algorithms of the theory.The tools developed in the book demand the use of computer algebra, which is implemented by means of Mathematica 3.0.The book is well written and the new technique is clearly presented and related to the existing techniques, making it useful to all those who use analytical or semi-analytical methods for the study of highly eccentric motion. Celestial Mechanics at High Eccentricities, Gordon and Breach Publishers, US$95, GBP 59, EUR 79, ISBN 90-5699-212-0