Thin-Shell Magnetohydrodynamic Equations for the Solar Tachocline

We present a new system of equations designed to study global-scale dynamics in the stably-stratified portion of the solar tachocline. This system is derived from the 3D equations of magnetohydrodynamics in a rotating spherical shell under the assumption that the shell is thin and stably-stratified (subadiabatic). The resulting thin-shell model can be regarded as a magnetic generalization of the hydrostatic primitive equations often used in meteorology. It is simpler in form than the more general anelastic or Boussinesq equations, making it more amenable to analysis and interpretation and more computationally efficient. However, the thin-shell system is still three-dimensional and as such represents an important extension to previous 2D and shallow-water approaches. In this paper we derive the governing equations for our thin-shell model and discuss its underlying assumptions, its context relative to other models, and its application to the solar tachocline. We also demonstrate that the dissipationless thin-shell system conserves energy, angular momentum and magnetic helicity.     

Large-scale cosmic homogeneity from a multifractal analysis of the PSCz catalogue

We investigate the behaviour of galaxy clustering on large scales using the PSC z catalogue. In particular, we ask whether there is any evidence of large-scale fractal behaviour in this catalogue. We find the correlation dimension in this survey varies with scale, consistent with other analyses. For example, our results on small and intermediate scales are consistent those obtained from the QDOT sample, but the larger PSC z sample allows us to extend the analysis out to much larger scales. We find firm evidence that the sample becomes homogeneous at large scales; the correlation dimension of the sample is D ₂=2.992±0.003 for r >30  h ⁻¹ Mpc. This provides strong evidence in favour of a universe that obeys the cosmological principle.     

The rotation of Janus and Epimetheus

Epimetheus, a small moon of Saturn, has a rotational libration (an oscillation about synchronous rotation) of 5.9°±1.2°, placing Epimetheus in the company of Earth’s Moon and Mars’ Phobos as the only natural satellites for which forced rotational libration has been detected. The forced libration is caused by the satellite’s slightly eccentric orbit and non-spherical shape.Detection of a moon’s forced libration allows us to probe its interior by comparing the measured amplitude to that predicted by a shape model assuming constant density. A discrepancy between the two would indicate internal density asymmetries. For Epimetheus, the uncertainties in the shape model are large enough to account for the measured libration amplitude. For Janus, on the other hand, although we cannot rule out synchronous rotation, a permanent offset of several degrees between Janus’ minimum moment of inertia (long axis) and the equilibrium sub-Saturn point may indicate that Janus does have modest internal density asymmetries.The rotation states of Janus and Epimetheus experience a perturbation every 4 years, as the two moons “swap” orbits. The sudden change in the orbital periods produces a free libration about synchronous rotation that is subsequently damped by internal friction. We calculate that this free libration is small in amplitude (<0.1°) and decays quickly (a few weeks, at most), and is thus below the current limits for detection using Cassini images.     

The topography of Iapetus' leading side

We have used Cassini stereo images to study the topography of Iapetus' leading side. A terrain model derived at resolutions of 4-8 km reveals that Iapetus has substantial topography with heights in the range of −10 km to +13 km, much more than observed on the other middle-sized satellites of Saturn so far. Most of the topography is older than 4 Ga [Neukum, G., Wagner, R., Denk, T., Porco, C.C., 2005. Lunar Planet. Sci. XXXVI. Abstract 2034] which implies that Iapetus must have had a thick lithosphere early in its history to support this topography. Models of lithospheric deflection by topographic loads provide an estimate of the required elastic thickness in the range of 50-100 km. Iapetus' prominent equatorial ridge [Porco, C.C., and 34 colleagues, 2005. Science 307, 1237-1242] reaches widths of 70 km and heights of up to 13 km from their base within the modeled area. The morphology of the ridge suggests an endogenous origin rather than a formation by collisional accretion of a ring remnant [Ip, W.-H., 2006. Geophys. Res. Lett. 33, doi:10.1029/2005GL025386. L16203]. The transition from simple to complex central peak craters on Iapetus occurs at diameters of 11±3 km. The central peaks have pronounced conical shapes with flanking slopes of typically 11° and heights that can rise above the surrounding plains. Crater depths seem to be systematically lower on Iapetus than on similarly sized Rhea, which if true, may be related to more pronounced crater-wall slumping (which widens the craters) on Iapetus than on Rhea. There are seven large impact basins with complex morphologies including central peak massifs and terraced walls, the largest one reaches 800 km in diameter and has rim topography of up to 10 km. Generally, no rings are observed with the basins consistent with a thick lithosphere but still thin enough to allow for viscous relaxation of the basin floors, which is inferred from crater depth-to-diameter measurements. In particular, a 400-km basin shows up-domed floor topography which is suggestive of viscous relaxation. A model of complex crater formation with a viscoplastic (Bingham) rheology [Melosh, H.J., 1989. Impact Cratering. Oxford Univ. Press, New York] of the impact-shocked icy material provides an estimate of the effective cohesion/viscosity at . The local distribution of bright and dark material on the surface of Iapetus is largely controlled by topography and consistent with the dark material being a sublimation lag deposit originating from a bright icy substrate mixed with the dark components, but frost deposits are possible as well.     

Ambient Changes in Tracer Concentrations from a Multilevel Monitoring System in Basalt

Starting in 2008, a 4‐year tracer study was conducted to evaluate ambient changes in groundwater concentrations of a 1,3,6‐naphthalene trisulfonate tracer that was added to drill water. Samples were collected under open borehole conditions and after installing a multilevel groundwater monitoring system completed with 11 discrete monitoring zones within dense and fractured basalt and sediment layers in the eastern Snake River aquifer. The study was done in cooperation with the U.S. Department of Energy to test whether ambient fracture flow conditions were sufficient to remove the effects of injected drill water prior to sample collection. Results from thief samples indicated that the tracer was present in minor concentrations 28 days after coring, but was not present 6 months after coring or 7 days after reaming the borehole. Results from sampling the multilevel monitoring system indicated that small concentrations of the tracer remained in 5 of 10 zones during some period after installation. All concentrations were several orders of magnitude lower than the initial concentrations in the drill water. The ports that had remnant concentrations of the tracer were either located near sediment layers or were located in dense basalt, which suggests limited groundwater flow near these ports. The ports completed in well‐fractured and vesicular basalt had no detectable concentrations.     

A mineral magnetic and scaled-chrysophyte paleolimnological study of two northeastern Pennsylvania lakes: records of fly ash deposition, land-use change, and paleorainfall variation

A combined mineral magnetic and scaled chrysophyte study of lake sediments from Lake Lacawac and Lake Giles in northeastern Pennsylvania was conducted to determine the effects of land-use and sediment source changes on the variation of pH, conductivity, and alkalinity inferred from biotic changes. Ten 30–40 cm long gravity cores were collected from Lake Lacawac and three from Lake Giles. Isothermal remanent magnetizations (IRMs) were given to the lake sediments in a 1.3 T magnetic field to measure magnetic mineral concentration variations. IRM acquisition experiments were conducted to identify magnetic mineralogy. The bedrock, soils and a peat bog on the shores of Lake Lacawac were also sampled for magnetic analysis to determine possible lake sediment sources. The top 10 cm of sediment collected from Lakes Lacawac and Giles was two to four times more magnetic than deeper sediment. ²¹⁰Pb dating suggests that this intensity increase commenced circa 1900. SEM images of magnetic extracts from the highly magnetic sediments indicates the presence of magnetic fly ash microspheres from fossil fuel burning electric power generation plants. The similarity in magnetic coercivity in the top 8 cm lake sediments and in the peat bog supports an atmospheric source for some of the magnetic minerals in the youngest lake sediments. The highly magnetic sediments also contain an antiferromagnetic mineral in two cores closest to Lake Lacawacs southeastern shore. This magnetic mineral is only present deep in the soil profile and would suggest erosion and significant land-use changes in the Lacawac watershed as another cause for the high magnetic intensities (concentrations) in the top 10 cm of the lake sediments. The most significant changes in the scaled chrysophyte flora occurred immediately above the 10 cm level and were used to infer a doubling of the specific conductivity between circa 1910 and 1929. These variations also support land-use changes in the Lacawac catchment at this time. A similar shift in the scaled chrysophte flora was not observed in the top of Lake Giles, however, distinct changes were found in the deeper sections of the core coupled with a smaller peak in magnetic concentration. Fourier analysis of the ²¹⁰Pb-dated lake sediment magnetics indicates the presence of a 50 year period, low amplitude variation in the Lake Lacawac, Lake Giles, and Lake Waynewood (Lott et al., 1994) magnetic concentration records. After removal of the land-use/fly ash magnetic concentration peak by Gaussian filtering, the 50 year variation correlates strongly from lake to lake even though the lakes are in different watersheds separated by up to 30 km. When this magnetic variation is compared with Gaussian-filtered rainfall variations observed in New York City and Philadelphia over the past 120–250 years there is a strong correlation suggesting that magnetic concentration variations can record regional rainfall variations with an approximately 50 year period. This result indicates that magnetics could be used to document regional variations in climatic change.