Are there sextuplet and octuplet image systems?

We study gravitational lensing by the family of scale-free galaxies with flat rotation curves. The models are defined by a shape function, which prescribes the radius of the isophote as a function of the position angle from the major axis. The critical curves are analytic, while the caustic network is reducible to a simple quadrature. The cusps are always located at the turning points of the shape function. We show that the models with exactly elliptic isophotes never admit butterfly or swallowtail cusps and so have at most four (or five) images. Higher order imaging is brought about by deviations of the isophotes from pure ellipses, such as pointedness caused by embedded discs or boxiness caused by recent merging. The criteria for the onset of sextuple and octuple imaging can be calculated analytically in terms of the ellipticity ε and the fourth-order Fourier coefficients ( a ₄ and b ₄) used by observers to parametrize the isophote shapes. The six or eight images are arranged roughly in a circle, which appears as an incomplete Einstein ring if inadequately resolved. Using data on the shapes of elliptical galaxies and merger remnants, we estimate that ∼1 per cent of all multiply imaged quasars may be sextuplet systems or higher. Forthcoming satellites such as the Global Astrometric Interferometer for Astrophysics ( GAIA ) will provide data sets of ∼4000 multiply imaged systems, and so ∼40 will show sextuple imaging or higher.     

Hydrology and nitrogen balance of a seasonally inundated Danish floodplain wetland

This paper characterizes a seasonally inundated Danish floodplain wetland in a state close to naturalness and includes an analysis of the major controls on the wetland water and nitrogen balances. The main inputs of water are precipitation and percolation during ponding and unsaturated conditions. Lateral saturated subsurface flow is low. The studied floodplain owes its wetland status to the hydraulic properties of its sediments: the low hydraulic conductivity of a silt–clay deposit on top of the floodplain maintains ponded water during winter, and parts of autumn and spring. A capillary fringe extends to the soil surface, and capillary rise from groundwater during summer maintains near‐saturated conditions in the root zone, and allows a permanently very high evapotranspiration rate. The average for the growing season of 1999 is 3·6 mm day^?1 and peak rate is 5·6 mm day^?1. In summer, the evapotranspiration is to a large degree supplied by subsurface storage in a confined peat layer underlying the silt–clay. The floodplain sediments are in a very reduced state as indicated by low sulphate concentrations. All nitrate transported into the wetland is thus denitrified. However, owing to modest water exchange with surrounding groundwater and surface water, denitrification is low; 71 kg NO₃–N ha^?1 during the study period of 1999. Reduction of nitrate diffusing into the sediments during water ponding accounts for 75% of nitrate removal. Biomass production and nitrogen uptake in above‐ground vegetation is high—8·56 t dry matter ha^?1 year^?1 and 103 kg N ha^?1 year^?1. Subsurface ammonium concentrations are high, and convective upward transport into the root zone driven by evapotranspiration amounted to 12·8 kg N ha^?1year^?1. The floodplain wetland sediments have a high nitrogen content, and conditions are very favourable for mineralization. Mineralization thus constitutes 72% of above‐ground plant uptake. The study demonstrates the necessity of identifying controlling factors, and to combine surface flow with vadose and groundwater flow processes in order to fully comprehend the flow and nitrogen dynamics of this type of wetland. Copyright © 2004 John Wiley & Sons, Ltd.     

Global Energy Transfer from Pick-up Ions to Solar Wind Protons

It has been known for years now that pick-up ions (PUIs) are produced by ionization of interstellar neutral atoms in the heliosphere and are then convected outwards with the solar wind flow as a separate suprathermal ion fluid. Only poorly known is the thermal behaviour of these pick-ups while being convected outwards. On the one hand they drive waves since their distribution function is unstable with respect to wave growth, on the other hand they also experience Fermi-2 energizations by nonlinear wave-particle interactions with convected wave turbulences. Here we will show that this complicated network of interwoven processes can quantitatively be balanced when adequate use is made of transport-kinetic results according to which pick-up ions essentially behave isothermally at their convection to large solar distances. We derive the adequate heat source necessary to maintain this pick-up ion isothermy and use the negative of that source to formulate the enthalpy flow conservation for solar wind protons (SWPs). This takes care of a consistent PUI-induced heat source guaranteeing that the net energy balance in the SWP–PUI two-fluid plasma is satisfied. With this PUI-induced heat input to SWPs we not only obtain the well-observed SWP polytropy, but we can also derive an expression for the percentage of intitial pick-up energy fed into the thermal proton energy. By a first-order evaluation of this expression we then can estimate that, dependent on the actual PUI temperature, about 40 to 50% of the initial pick-up energy is globally passed to solar protons within the inner heliosphere.     

Long-term effects of the Galactic tide on cometary dynamics

We introduce a model for integrating the effects of Galactic tides on Oort cloud comets, which involves two procedures, according to the values of the osculating semi-major axis a and eccentricity e. Ten simulations of the dynamics of 10⁶ comets over 5 Gyr are performed using this model. We thus investigate the long-term effects of the Galactic tide with and without a radial component, the effects of the local density of the Galactic disk, and those of the Oort constants. Most of the results may be understood in terms of the integrability or non-integrability of the system. For an integrable system, which occurs for moderate semi-major axes with or without radial component, the dynamics is explained by periodic variation of the cometary perihelion, inducing the depletion of the outer region of the Oort cloud, a constant flux from the inner region after 500 Myr, and the quick formation of a reservoir of comets with argument of perihelion near 26.6°. When the system is non-integrable, the efficiency of the tide in reducing the cometary perihelion distance is enhanced both by replenishing the Oort cloud domain from which comets are sent toward the planetary system, and by reducing the minimal value that the perihelion distance may reach. No effects of varying the Oort constants were observed, showing that the flat rotation curve is a satisfactory approximation in Oort cloud dynamics.     

Solubility of tin in (Cl, F)-bearing aqueous fluids at 700 °C, 140 MPa: A LA-ICP-MS study on synthetic fluid inclusions

Synthetic fluid inclusions in quartz were grown from cassiterite-saturated fluids in cold-seal pressure vessels at and subsequently analyzed by laser ablation-ICP-MS. Most inclusions were synthesized using a new technique that allows entrapment of fluid that had no immediate contact to the capsule walls, such that potential disequilibrium effects due to alloying could be avoided. Measured Sn solubilities increase with increasing ligand concentration in the fluid, ranging from 100 to 800 ppm in NaCl-bearing fluids (5-35 wt% NaCl), from 70 to 2000 ppm in HF-bearing fluids (0.5-3.2 m HF), and from 0.8 to 11 wt% in HCl-bearing fluids (0.5-4.4 m HCl). Two runs performed with the in-situ cracking method after 1 week of pre-equilibration demonstrate that the speed of hydrogen diffusion through the capsule wall relative to that of fluid inclusion formation is a critical factor in f_O2-dependent solubility studies. Graphical evaluation of the solubility data suggests that Sn may have been dissolved as Sn(OH)Cl in the NaCl-bearing fluids, as Sn(OH)Cl and SnCl₂ in the HCl-bearing fluids, and as SnF₂ in the HF-bearing fluids. Experiments with NaF-bearing fluids produced an additional melt phase with an approximate composition of 53 wt% SiO₂, 25 wt% H₂O, 14 wt% NaF and 8 wt% SnO, which caused the composition of the coexisting fluid to be buffered at 0.5 wt% NaF and 150 ppm Sn. Fluorine-rich, peralkaline melts may therefore serve as important transport media for Sn in the final crystallization stages of tin granites. Based on the available cassiterite-solubility data in fluids and melts, in natural granite systems is estimated to be in the order of 0.1-4 (depending on their aluminosity), suggesting that Sn is not easily mobilized by magmatic-hydrothermal fluids. This interpretation is in accordance with the high degrees of Sn-enrichment commonly observed in highly fractionated melt inclusions. is primarily controlled by the HCl concentration in the fluid, which in turn is a function of the aluminum saturation index of the magma. Compared to HCl, the effect of fluorine on is subordinate.     

Variations in temperature and extent of Atlantic Water in the northern North Atlantic during the Holocene

We compare six high-resolution Holocene, sediment cores along a S–N transect on the Norwegian–Svalbard continental margin from ca 60°N to 77.4°N, northern North Atlantic. Planktonic foraminifera in the cores were investigated to show the changes in upper surface and subsurface water mass distribution and properties, including summer sea-surface temperatures (SST). The cores are located below the axis of the Norwegian Current and the West Spitsbergen Current, which today transport warm Atlantic Water to the Arctic. Sediment accumulation rates are generally high at all the core sites, allowing for a temporal resolution of 10–10² years. SST is reconstructed using different types of transfer functions, resulting in very similar SST trends, with deviations of no more than ±1.0/1.5 °C. A transfer function based on the maximum likelihood statistical approach is found to be most relevant. The reconstruction documents an abrupt change in planktonic foraminiferal faunal composition and an associated warming at the Younger Dryas–Preboreal transition. The earliest part of the Holocene was characterized by large temperature variability, including the Preboreal Oscillations and the 8.2 k event. In general, the early Holocene was characterized by SSTs similar to those of today in the south and warmer than today in the north, and a smaller S–N temperature gradient (0.23 °C/°N) compared to the present temperature gradient (0.46 °C/°N). The southern proxy records (60–69°N) were more strongly influenced by slightly cooler subsurface water probably due to the seasonality of the orbital forcing and increased stratification due to freshening. The northern records (72–77.4°N) display a millennial-scale change associated with reduced insolation and a gradual weakening of the North Atlantic thermohaline circulation (THC). The observed northwards amplification of the early Holocene warming is comparable to the pattern of recent global warming and future climate modelling, which predicts greater warming at higher latitudes. The overall trend during mid and late Holocene was a cooling in the north, stable or weak warming in the south, and a maximum S–N SST gradient of ca 0.7 °C/°N at 5000 cal. years BP. Superimposed on this trend were several abrupt temperature shifts. Four of these shifts, dated to 9000–8000, 5500–3000 and 1000 and 400 cal. years BP, appear to be global, as they correlate with periods of global climate change. In general, there is a good correlation between the northern North Atlantic temperature records and climate records from Norway and Svalbard.