Prediction of plagioclase-melt equilibria in anhydrous silicate melts at 1-atm

Many models for plagioclase-melt equilibria have been proposed over the past 30 years, but the focus is increasingly on the effects of water content and pressure. However, many geological and petrological applications concern low pressure and low water systems, such as the differentiation of large terrestrial basaltic magma chambers, and lunar and asteroidal magmatism. There is, therefore, a justified need to quantify the influence of anhydrous liquid composition on the composition of equilibrium plagioclase at 1-atm. With this in mind, a database of over 500 experimentally determined plagioclase-liquid pairs has been created. The selected low pressure, anhydrous, experiments include both natural and synthetic liquids, whose compositions range from basalt to rhyolite. Four equations are proposed, derived from this data. The first is based on a thermodynamically inspired formalism, explicitly integrating the effect of temperature. This equation uses free energies and activities of crystalline anorthite available from the literature. For the activity of anorthite in the liquid phase, it is found that current models of the activity of individual oxides are insufficient to account for the experimental results. We have therefore derived an empirical expression for the variation of anorthite activity in the liquid as a function of melt composition, based upon inversion of the experimental data. Using this expression allows the calculation of plagioclase composition with a relative error less than 10%. However, in light of the fact that temperature is not necessarily known for many petrological applications, an alternative set of T-independent equations is also proposed. For this entirely empirical approach, the database has been divided into three compositional groups, treated independently for regression purposes: mafic–ultramafic, alkali-rich mafic–ultramafic, and intermediate-felsic. This separation into distinct subgroups was found to be necessary to maintain errors below acceptable limits, but results across group boundaries were found to be comparable. Overall, 50% of plagioclase compositions are predicted to within 2% of the experimentally derived value, and 90% to within 5%, representing a significant improvement over existing models.     

In situ methods for measuring thermal properties and heat flux on planetary bodies

The thermo-mechanical properties of planetary surface and subsurface layers control to a high extent in which way a body interacts with its environment, in particular how it responds to solar irradiation and how it interacts with a potentially existing atmosphere. Furthermore, if the natural temperature profile over a certain depth can be measured in situ, this gives important information about the heat flux from the interior and thus about the thermal evolution of the body. Therefore, in most of the recent and planned planetary lander missions experiment packages for determining thermo-mechanical properties are part of the payload. Examples are the experiment MUPUS on Rosetta's comet lander Philae, the TECP instrument aboard NASA's Mars polar lander Phoenix, and the mole-type instrument HP³ currently developed for use on upcoming lunar and Mars missions. In this review we describe several methods applied for measuring thermal conductivity and heat flux and discuss the particular difficulties faced when these properties have to be measured in a low pressure and low temperature environment. We point out the abilities and disadvantages of the different instruments and outline the evaluation procedures necessary to extract reliable thermal conductivity and heat flux data from in situ measurements.     

The crustal tongue melting model and the origin of massive anorthosites

Recent detailed field studies in several anorthosite complexes have shown that anorthosites are frequently associated with weakness zones in the crust which may have favoured their emplacement at mid-crust levels. Recent experimental data have shown that the parent magma compositions of various anorthosite massifs lie on thermal highs in the relevant phase diagrams at 10–13 kbar, indicating that these magmas cannot be derived by fractionation of peridotitic mantle melts but by melting of gabbronoritic sources in the lower crust at 40–50 km depths. In the Sveconorwegian Province terne boundaries have been traced in deep seismic profiles to Moho offsets or to tongues of lower crustal material underthrust to depths higher than 40 km. In Southern Norway, we suggest that a lithospheric-scale weakness zone (the Feda transition zone?) has channelled the Rogaland anorthosites through linear delamination, asthenospheric uprise and melting of a mafic lower crustal tongue.     

Modelling karst denudation on a synthetic landscape

This contribution presents the results of a numerical study of karst denudation on limestone plateaux. The landscape evolution model used incorporates not only long-range fluvial and short-range hill-slope processes, but also large-scale chemical dissolution of limestone surfaces. The relative efficiencies of fluvial and chemical processes are of equal importance to the landscape evolution of a plateau dropping to sea level along an escarpment. While fluvial processes have an impact confined mostly to river channels, the karst denudation process is more uniform, removing material also from the plateau surface. The combined effect of both processes results in a landscape evolution almost twice as effective as the purely erosional evolution of an insoluble landscape.     

Modeling stalagmite growth by first principles of chemistry and physics of calcite precipitation

Growth rates and morphology of stalagmites are determined by the precipitation kinetics of calcite and the supply rates of water to their apex. Current modeling attempts are based on the assumption that precipitation rates decrease exponentially with distance along the surface. This, however, is an arbitrary assumption, because other functions for decrease could be used as well. Here we give a process-oriented model based on the hydrodynamics of a water sheet in laminar radial flow spreading outwards from the apex, and the well known precipitation rates F = α(c − c_eq); c is the actual calcium concentration at distance R from the growth axis, c_eq the equilibrium concentration of calcium with respect to calcite, and α is a kinetic constant. This enables us to calculate the concentration profile c(R) for any point of an actual surface of a stalagmite and consequently the deposition rates of calcite there. The numerical results show that under conditions constant in time the stalagmite grows into an equilibrium shape, which is established, when all points of its surface are shifting vertically by the same distance during a time interval. We also show this by strict mathematical proof. This new model is based entirely on first principles of physics and chemistry. The results show that the modeled precipitation rates can be approximated by a Gaussian decrease along the equilibrium surface. In general from the mathematical proof one finds a relation between the equilibrium radius of the stalagmite, Q the supply rate of water, and α the kinetic constant. This is also verified by numerical calculations. An interesting scaling law is found. Scaling all stalagmites by 1/R_eq and presenting them with the origin at their apex yields identical shapes of all. The shapes of the modeled stalagmites are compared to natural ones and show satisfactory agreement. Finally we explore the effect of varying water supply Q and kinetic constant α on the shape of a growing stalagmite, and estimate the minimum period of change that can be imprinted into the morphology of the stalagmite.     

Spatial Characterization of a Flare Using Radio Observations and Magnetic Field Topology

Using magnetograms, EUV and Hα images, Owens Valley Solar Array microwave observations, and 212-GHz flux density derived from the Solar Submillimeter Telescope data, we determine the spatial characteristics of the 1B/M6.9 flare that occurred on November 28, 2001, starting at 16:26 UT in active region (AR) NOAA 9715. This flare is associated with a chromospheric mass ejection or surge observed at 16:42 UT in the Hα images. We compute the coronal magnetic field under the linear force-free field assumption, constrained by the photospheric data of the Michelson Doppler Imager and loops observed by the Extreme Ultraviolet Imaging Telescope. The analysis of the magnetic field connectivity allows us to conclude that magnetic field reconnection between two different coronal/chromospheric sets of arches was at the origin of the flare and surge, respectively. The optically thick microwave spectrum at peak time shows a shape compatible with the emission from two different sites. Fitting gyrosynchrotron emission to the observed spectrum, we derive parameters for each source. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Evidence that Synchrotron Emission from Nonthermal Electrons Produces the Increasing Submillimeter Spectral Component in Solar Flares

We investigate the origin of the increasing spectra observed at submillimeter wavelengths detected in the flare on 2 November 2003 starting at 17:17 UT. This flare, classified as an X8.3 and 2B event, was simultaneously detected by RHESSI and the Solar Submillimeter Telescope (SST) at 212 and 405 GHz. Comparison of the time profiles at various wavelengths shows that the submillimeter emission resembles that of the high-energy X rays observed by RHESSI whereas the microwaves observed by the Owens Valley Solar Array (OVSA) resemble that of ∼50 keV X rays. Moreover, the centroid position of the submillimeter radiation is seen to originate within the same flaring loops of the ultraviolet and X-ray sources. Nevertheless, the submillimeter spectra are distinct from the usual microwave spectra, appearing to be a distinct spectral component with peak frequency in the THz range. Three possibilities to explain this increasing radio spectra are discussed: (1) gyrosynchrotron radiation from accelerated electrons, (2) bremsstrahlung from thermal electrons, and (3) gyrosynchrotron emission from the positrons produced by pion or radioactive decay after nuclear interactions. The latter possibility is ruled out on the grounds that to explain the submillimeter observations requires 3000 to 2×10⁵ more positrons than what is inferred from X-ray and γ-ray observations. It is possible to model the emission as thermal; however, such sources would produce too much flux in the ultraviolet and soft X-ray wavelengths. Nevertheless we are able to explain both spectral components at microwave and submillimeter wavelengths by gyrosynchrotron emission from the same population of accelerated electrons that emit hard X rays and γ rays. We find that the same 5×10³⁵ electrons inferred from RHESSI observations are responsible for the compact submillimeter source (0.5 arcsec in radius) in a region of 4500 G low in the atmosphere, and for the traditional microwave spectral component by a more extended source (50 arcsec) in a 480 G magnetic field located higher up in the loops. The extreme values in magnetic field and source size required to account for the submillimeter emission can be relaxed if anisotropy and transport of the electrons are taken into account.     

δC profiles along growth layers of stalagmites: Comparing theoretical and experimental results

The isotopic carbon ratio of a calcite-precipitating solution flowing as a water film on the surface of a stalagmite is determined by Rayleigh distillation. It can be calculated, when the -concentration of the solution at each surface point of the stalagmite and the fractionation factors are known. A stalagmite growth model based entirely on the physics of laminar flow and the well-known precipitation rates of a supersaturated solution of calcite, without any further assumptions, is employed to obtain the spatial distribution of the -concentration, which contributes more than 95% to the dissolved inorganic carbon (DIC). The δ¹³C profiles are calculated along the growth surface of a stalagmite for three cases: (A) isotopic equilibrium of both CO₂ outgassing and calcite precipitation; (B) outgassing of CO₂ is irreversible but calcite precipitation is in isotopic equilibrium. (C) Both CO₂ outgassing and calcite precipitation are irreversible. In all cases the isotopic shift δ¹³C increases from the apex along the distance on a growth surface. In cases A and B, calcite deposited at the apex is in isotopic equilibrium with the solution of the drip water. The difference between δ¹³C at the apex and the end of the growth layer is independent of the stalagmite’s radius, but depends on temperature. For case A, it is about half the value obtained for cases B and C. In case C, the isotopic composition of calcite at the apex equals that of the drip water, but further out it becomes practically identical with that of case B. The growth model has been applied to field data of stalagmite growth, where the thickness and the δ¹³C of calcite precipitated to a glass plate located on the top of a stalagmite have been measured as function of the distance from the drip point. The calculated data are in good agreement to the observed ones and indicate that deposition occurred most likely under conditions B, eventually also C. A sensitivity analysis has been performed, which shows that within the limits of observed external parameters, such as drip rates and partial pressure of carbon dioxide P_CO2 in the cave, the results remain valid.