Comment on “General relativity resolves galactic rotation without exotic dark matter” by F.I. Cooperstock and S. Tieu

The general relativistic model of Cooperstock and Tieu, which attempts to fit rotation curves of spiral galaxies without invoking dark matter, is tested empirically using observations of the Milky Way. In particular, predictions for the mass density in the solar neighbourhood and the vertical density distribution at the position of the Sun are compared with observations. It is shown that the model of Cooperstock and Tieu, which was so constructed that it gives an excellent fit of the observed rotation curve, singularly fails to reproduce the observed local mass density and the vertical density profile of the Milky Way.     

An Alternative Embedding Method for Thin Section Preparation of Lake Sediments

Embedding soil samples with Vestopal (Chemische Werke Hüls) or Palatal (BASF) polyester resin was described by Altemüller (1974), Altemüller and Vorbach (1987), or Tippkötter (1986). We have modified this method and applied it to lake sediments. The following steps are necessary: dehydration by acetone, replacement of acetone by Palatal, hardening of Palatal, sawing, polishing, and mounting on glass slides. The advantages compared to other methods are very good embedding qualities of different sediments and moderate costs of the embedding resin. The expensive and slow dehydration with acetone and the time consuming embedding are the disadvantages of this method.     

Constraints on Europa’s rotational dynamics from modeling of tidally-driven fractures

Cycloids, arcuate features observed on Europa’s surface, have been interpreted as tensile cracks that form in response to diurnal tidal stress caused by Europa’s orbital eccentricity. Stress from non-synchronous rotation may also contribute to tidal stress, and its influence on cycloid shapes has been investigated as well. Obliquity, fast precession, and physical libration would contribute to tidal stress but have often been neglected because they were expected to be negligibly small. However, more sophisticated analyses that include the influence of Jupiter’s other large satellites and the state of Europa’s interior indicate that perhaps these rotational parameters are large enough to alter the tidal stress field and the formation of tidally-driven fractures. We test tidal models that include obliquity, fast precession, stress due to non-synchronous rotation, and physical libration by comparing how well each model reproduces observed cycloids. To do this, we have designed and implemented an automated parameter-searching algorithm that relies on a quantitative measure of fit quality, which we use to identify the best fits to observed cycloids. We then apply statistical techniques to determine the tidal model best supported by the data. By incorporating obliquity, fits to observed southern hemisphere cycloids improve, and we can reproduce equatorial and equator-crossing cycloids. Furthermore, we find that obliquity plus physical libration is the tidal model best supported by the data. With this model, the obliquities range from 0.32° to 1.35°. The libration amplitudes are 0.72–2.44°, and the libration phases are −6.04° to 17.72° with one outlier at 84.5°. The variability in obliquity is expected if Europa’s ice shell is mechanically decoupled from the interior, and the libration amplitudes are plausible in the presence of a subsurface ocean. Indeed, the presence of a decoupling ocean may result in feedbacks that cause all of these rotational parameters to become time-variable.     

Field-aligned currents above an auroral arc

Simultaneous observations of precipitating electrons and protons in the energy range from 15 eV to 35 keV and magnetic field variations were made onboard a sounding rocket payload launched from the Andoya Rocket Range. The electric current density deduced from the electron precipitation observed during the passage over an auroral arc was comparable to that determined from the magnetic field variations. In addition, a downward current was observed by its magnetic field signature at the northern edge of the arc which was, however, not accompanied by significant particle fluxes in the energy range under consideration. It will be assumed that this current was carried by thermal electrons of ionospheric origin.     

Structural pattern of the western Las Cañadas caldera (Tenerife, Canary Islands) revealed by audiomagnetotellurics

The local and regional structural pattern of volcanic edifices strongly controls the space distribution of electrical resistivity. Here we report on the structural context of the western part of the Las Cañadas caldera of Tenerife (LCC) thought to have initiated the formation of the caldera. Using a new dataset of 11 audiomagnetotelluric tensors we emphasize the resistivity distribution of Ucanca caldera and propose a major revision of its extension. We find that Ucanca caldera has a limited westwards extent and that El Cedro sector is a depression margin of the caldera. According to the extent of hydrothermalized rocks at the base of the LCC wall and the distribution of Pico Teide – Pico Viejo vents, we constrain the location and size of Ucanca caldera. The interpretation of these results also constrains the extension of the Icod Valley and proposes a headwall located below the Pico Teide – Pico Viejo Complex.     

Shock metamorphism and shock barometry at a complex impact structure: Slate Islands, Canada

The Slate Islands archipelago is believed to represent the central uplifted portion of a complex impact structure. Planar microstructures in quartz and feldspars and shock vitrification of rocks are the most common shock metamorphic features encountered. No diaplectic quartz was identified in the exposed rocks, but minor maskelynite is present. Shatter cones occur on all islands of the archipelago suggesting minimum pressures of 4 ± 2 GPa. The relative frequency of low index planar microstructures of specific, optically determined crystallographic orientations in quartz are correlated with results from shock barometric experiments to estimate peak shock pressures experienced by the exposed target rocks. In general, there is a decrease in shock pressure recorded in the target rocks from about 20–25 GPa in east-central Patterson Island to about 5–10 GPa at the western shore of this island and on Mortimer Island. The shock attenuation gradient is ∼4.5 GPa/km across this section of the island group. However, the shock attenuation has a roughly concentric plan only over the western part of the archipelago. There is no distinct shock center and there are other deviations from circularity. This is probably the result of: (1) the shock wave not having expanded from a point or spherical source because of the ∼1. 0 to 1.5 km size of the impactor; (2) differential movement of large target rock blocks during the central uplift and crater modification phases of the impact process. The orientation of planar deformation features in quartz appears to be independent of the shock wave direction suggesting that crystal structure exerts the primary control on microstructure development. Based on the results of XRD analyses, residual, post-impact temperatures were high enough to cause annealing of submicroscopic damage in shocked quartz. Received: 15 July 1997 / Accepted: 6 October 1997     

Brittle–ductile deformation in the Glarus thrust Lochseiten (LK) calc-mylonite

The Glarus thrust accommodated at least 30 km of northward displacement strongly localized within a 1-m layer of 'Lochseiten' (LK) calc-mylonite. This layer displays veins in various states of plastic deformation and a wildly refolded foliated gouge texture. Lattice- and shape-preferred orientations are observed within the fine-grained, recrystallized matrix. These features indicate the alternate activity of brittle and ductile deformation mechanisms. In contrast to the classical view that grain boundary sliding (superplasticity) is the dominant deformation mechanism, it is advocated that fluids, derived from the footwall and expelled along the thrust, are responsible for hydrofracturing and cataclastic deformation. In periods between fracture events, deformation was ductile. In this new interpretation, a substantial amount of the total thrust displacement was accommodated by numerous short-lived and strongly localized fracture events at the base of the Verrucano thrust sheet, rather than a permanently weak décollement lithology.     

Minimum mean squared error (MSE) adjustment and the optimal Tykhonov–Phillips regularization parameter via reproducing best invariant quadratic uniformly unbiased estimates (repro-BIQUUE)

In a linear Gauss–Markov model, the parameter estimates from BLUUE (Best Linear Uniformly Unbiased Estimate) are not robust against possible outliers in the observations. Moreover, by giving up the unbiasedness constraint, the mean squared error (MSE) risk may be further reduced, in particular when the problem is ill-posed. In this paper, the α-weighted S-homBLE (Best homogeneously Linear Estimate) is derived via formulas originally used for variance component estimation on the basis of the repro-BIQUUE (reproducing Best Invariant Quadratic Uniformly Unbiased Estimate) principle in a model with stochastic prior information. In the present model, however, such prior information is not included, which allows the comparison of the stochastic approach (α-weighted S-homBLE) with the well-established algebraic approach of Tykhonov–Phillips regularization, also known as R-HAPS (Hybrid APproximation Solution), whenever the inverse of the “substitute matrix” S exists and is chosen as the R matrix that defines the relative impact of the regularizing term on the final result. The delay in publishing this paper is due to a number of unfortunate complications. It was first submitted as a multi-author paper in two parts. Due to some miscommunication among the original authors, it was reassigned to one of the J Geod special issues, but later reassigned at this author’s request to a standard issue of J Geod. This compounded with a difficulty to find willing reviewers to slow the process. We apologize to the author.