On the meaning and inapplicability of the Zeldovich relations of magnetohydrodynamics

Considering a plasma with an initially weak large scale field subject to nonhelical turbulent stirring, Zeldovich (1957), for two‐dimensions, followed by others for three dimensions, have presented formulae of the form 〈b²〉 = f(R_M) . Such “Zeldovich relations” have sometimes been interpreted to provide steady‐state relations between the energy associated with the fluctuating magnetic field and that associated with a large scale or mean field multiplied by a function f that depends on spatial dimension and a magnetic Reynolds number R_M. Here we dissect the origin of these relations and pinpoint pitfalls that show why they are inapplicable to realistic, dynamical MHD turbulence and that they disagree with many numerical simulations. For 2D, we show that when the total magnetic field is determined by a vector potential, the standard Zeldovich relation applies only transiently, characterizing a maximum possible value that the field energy can reach before necessarily decaying. In 3D, we show that the standard Zeldovich relations are derived by balancing subdominant terms. In contrast, balancing the dominant terms shows that the fluctuating field can grow to a value independent of R_M and the initially imposed , as seen in numerical simulations. We also emphasize that these Zeldovich relations of nonhelical turbulence imply nothing about the amount mean field growth in a helical dynamo. In short, by re‐analyzing the origin of the Zeldovich relations, we highlight that they are inapplicable to realistic steady‐states of large R_M MHD turbulence. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The applications of the MHD Alfvén wave oscillation model for kHz quasi‐periodic oscillations

In this paper, we improve the previous work on the MHD Alfvén wave oscillation model for the neutron star (NS) kHz quasi‐periodic oscillations (QPOs), and compare the model with the updated twin kHz QPO data. For the 17 NS X‐ray sources with the simultaneously detected twin kHz QPO frequencies, the stellar mass M and radius R constraints are given by means of the derived parameter A in the model, which is associated with the averaged mass density of the star as 〈ρ 〉 = 3M /(4πR³) ≃ 2.4 × 10¹⁴ (A /0.7)² g/cm³, and we also compare the M ‐R constraints with the stellar equations of state. Moreover, we also discuss the theoretical maximum kHz QPO frequency and maximum twin peak separation, and some expectations on SAX J1808.4–3658 are mentioned, such as its highest kHz QPO frequency ∼ 870 Hz, which is about 1.4–1.5 times less than those of the other known kHz QPO sources. The estimated magnetic fields for both Z sources (about Eddington accretion rate ) and Atoll sources (∼ 1% ) are approximately ∼10⁹ G and ∼10⁸ G, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear simulations of magnetic instabilities in stellar radiation zones: The role of rotation and shear

Using the 3-dimensional ASH code, we have studied numerically the instabilities that occur in stellar radiation zones in presence of large-scale magnetic fields, rotation and large-scale shear. We confirm that some configurations are linearly unstable, as predicted by Tayler and collaborators, and we determine the saturation level of the instability. We find that rotation modifies the peak of the most unstable wave number of the poloidal instability but not its growth rate as much as in the case of the m = 1 toroidal instability for which it is changed to σ = /Ω. Further in the case with rotation and shear, we found no sign of the dynamo mechanism suggested recently by Spruit even though we possess the essential ingredients (Tayler's m = 1 instability and a large scale shear) supposedly at work. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tayler instability with Hall effect in young neutron stars

Collapse calculations indicate that the hot young neutron stars rotate differentially so that strong toroidal magnetic field components should exist in the outer shell where also the Hall effect appears to be important when the Hall parameter = ω_Bτ exceeds unity. The amplitudes of the induced toroidal magnetic fields are limited by the current‐induced Tayler instability. An important characteristics of the Hall effect is its distinct dependence on the sign of the magnetic field. We find for fast rotation that positive (negative) Hall parameters essentially reduce (increase) the stability domain. It is thus concluded that the toroidal field belts in young neutron stars induced by their differential rotation should have different amplitudes in both hemispheres which later are frozen in. Due to the effect of magnetic suppression of the heat conductivity also the brightness of the two hemispheres should be different. As a possible example for our scenario the isolated neutron star RBS 1223 is considered which has been found to exhibit different X‐ray brightness at both hemispheres (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Low‐mass visual binaries in the solar neighbourhood: The case of HD 141272

We search for stellar and substellar companions of young nearby stars to investigate stellar multiplicity and formation of stellar and substellar companions. We detect common proper‐motion companions of stars via multi‐epoch imaging. Their companionship is finally confirmed with photometry and spectroscopy. Here we report the discovery of a new co‐moving (13 σ) stellar companion ∼17.8 arcsec (350AU in projected separation) north of the nearby star HD141272 (21 pc).With EMMI/NTT optical spectroscopy we determined the spectral type of the companion to be M3±0.5V. The derived spectral type as well as the near infrared photometry of the companion are both fully consistent with a M_⊙ dwarf located at the distance of HD141272 (21 pc). Furthermore the photometry data rules out the pre‐main sequence status, since the system is consistent with the ZAMS of the Pleiades. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Zur kosmologischen Testung des Machschen Prinzips

The Machian models of isotropic expanding universes according to the “inertia-free” gravo-dynamics imply the equations between the instantan values H₀ and q₀ of the HUBBLE parameter H, the acceleration q, and the matter density o. Therefore, in Machian universes with linear expansion q₀ = 0 the energy integral E = -1/2ϵc² is zero and the matter density becomes (with H₀²R₀² = c²/3) (f₀ the Newtonian gravitational constant). This is the critical density in general relativistic cosmology.     

Synchrotron neutrino-pair radiation in neutron stars

The neutrino-pair radiation by electrons in a non-quantizing magnetic field B is investigated. For a relativistic degenerate electron gas the emissivity of this process is mainly given by \documentclass{article}\pagestyle{empty}\begin{document}$ \varepsilon _r = 5 \times 10^{15} (pF/mc)^{4/3} \,B_{13}^{2/3} T_y^{12/8} \,{\rm erg} \times {\rm cm}^{ - 3} \times {\rm sec}^{- 1} $\end{document} where pF is the electron Fermi momentum. Under typical neutron star conditions at B ∼ 10¹³G neutrino synchrotron radiation appears to be one of the most effective mechanisms of neutrino energy loss in the envelopes of neutron stars; this mechanism may also compete with other known neutrino production mechanisms in the neutron star cores if pion condensate or quark matter is absent.     

New solutions in linearized R+R2 gravity

A general method is proposed to solve in the linear approximation the fourth-order gravitational equations, which stem from Lagrangians $ \text{Q} = 1 ‐ g\left( {R + \frac{1}{2}aR^2 + bR_{av} R^{av} } \right) ‐ x\text{Q}. $ The metric of a static spherically symmetric body and the metric of a straight infinitely thin cosmic string are given.     

Zur Dynamotheorie stellarer und planetarer Magnetfelder I. Berechnung sonnenähnlicher Wechselfeldgeneratoren

Non-reflectionsymmetric turbulent motions in an electrically conducting fluid provide for an average electromotoric force α parallel to the average magnetic field . This effect – furthermore called α-effect – can lead to a self-excited built-up of magnetic fields by dynamo action. Since by actions of Coriolis forces turbulent motions in rotating systems generally are non-reflectionsymmetric, the explanation of stellar and planetary magnetic fields becomes possible. – In this first part spherical alternating field dynamos are calculated on conditions similar to those at the sun; α-effect and differential rotation provide for dynamo action. – The basic equations, which form a system of partial differential equations, are treated by a separation method; in this way our problem is transformed into a two-parametric eigenvalue problem for an infinite system of ordinary differential equations. The two eigenvalues determine the frequency and the amount of the induction actions necessary for the field maintenance. The solution of this problem was made by an electronic computer. – The results give evidence for the possibility of magnetohydrodynamic alternating field dynamos. Furthermore the magnitude of the calculated eigenvalues and the similarities between the calculated field and the observed solar magnetic field are showing that the sun realizes a dynamo of this kind.     

Trägheitsfreie Dynamik und HAMILTONsche Bewegungsgleichung

We formulate the canonical equations of motion for particles with an (post-HEWTON ian) interaction potential and the HAMILTON ian form of our MACH ian dynamics without inertia.     

Do mean‐field dynamos in nonrotating turbulent shear‐flows exist?

A plane‐shear flow in a fluid with forced turbulence is considered. If the fluid is electrically‐conducting then a mean electromotive force (EMF) results even without basic rotation and the magnetic diffusivity becomes a highly anisotropic tensor. It is checked whether in this case self‐excitation of a large‐scale magnetic field is possible (so‐called W̄ × J̄ ‐dynamo) and the answer is NO. The calculations reveal the cross‐stream components of the EMF perpendicular to the mean current having the wrong signs, at least for small magnetic Prandtl numbers. After our results numerical simulations with magnetic Prandtl number of about unity have only a restricted meaning as the Prandtl number dependence of the diffusivity tensor is rather strong. If, on the other hand, the turbulence field is strati.ed in the vertical direction then a dynamo‐active α ‐effect is produced. The critical magnetic Reynolds number for such a self‐excitation in a simple shear flow is slightly above 10 like for the other – but much more complicated – flow patterns used in existing dynamo experiments with liquid sodium or gallium. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Can turbulent plane‐shear flows support large‐scale dynamos?

Turbulent plane‐shear flow is found to show same basic effects of mean‐fieldMHD as rotating turbulence. In particular, the mean electromotive force (EMF) includes highly anisotropic turbulent diffusion and alpha‐effect. Only magnetic diffusion remains for spatially‐uniform turbulence. The question is addressed whether in this case a self‐excitation of a magnetic field by so‐called sher‐current dynamo is possible and the quasilinear theory provides a negative answer. The streamaligned component of the EMF has the sign opposite to that required for dynamo. If, however, the turbulence is not uniform across the flow direction then a dynamo‐active α ‐effect emerges. The critical magnetic Reynolds number for the alpha‐shear dynamo is estimated to be slightly above ten. Possibilities for cross‐checking theoretical predictions with MHD experiments are discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New exact solutions for power-law inflation Friedmann models

We consider the spatially flat Friedmann model For a ≈ t^p, especially, if p ≥ 1, this is called power-law inflation. For the Lagrangian L = R^m with p = − (m − 1) (2m − 1)/(m − 2) power-law inflation is an exact solution, as it is for Einstein gravity with a minimally coupled scalar field ϕ in an exponential potential V(ϕ) = exp (μϕ) and also for the higher-dimensional Einstein equation with a special Kaluza-Klein ansatz. The synchronized coordinates are not adapted to allow a closed-form solution, so we write The general solutions reads Q(a) = (a^b + C)^f/b with free integration constant C (C = 0 gives exact power-law inflation) and m-dependent values b and f: f = −2 + 1/p, b = (4m − 5)/(m − 1). Finally, special solutions for the closed and open Friedmann model are found.     

Solar dynamo models with α ‐effect and turbulent pumping from local 3D convection calculations

Results from kinematic solar dynamo models employing α ‐effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2–3 m s^–1, having scaled the local quantities with the convective velocity at the bottom of the convection zone from a solar mixing‐length model. Rotation profile of the Sun as obtained from helioseismology is applied in the models; we also investigate the effects of the observed surface shear layer on the dynamo solutions. With these choices of the small‐ and large‐scale velocity fields, we obtain estimate of the ratio of the two induction effects, C _α /C _Ω ≈ 10^–3, which we keep fixed in all models. We also include a one‐cell meridional circulation pattern having a magnitude of 10–20 m s^–1 near the surface and 1–2 m s^–1 at the bottom of the convection zone. The model essentially represents a distributed turbulent dynamo, as the α ‐effect is nonzero throughout the convection zone, although it concentrates near the bottom of the convection zone obtaining a maximum around 30° of latitude. Turbulent pumping of the mean fields is predominantly down‐ and equatorward. The anisotropies in the turbulent diffusivity are neglected apart from the fact that the diffusivity is significantly reduced in the overshoot region. We find that, when all these effects are included in the model, it is possible to correctly reproduce many features of the solar activity cycle, namely the correct equatorward migration at low latitudes and the polar branch at high latitudes, and the observed negative sign of B _r B _ϕ . Although the activity clearly shifts towards the equator in comparison to previous models due to the combined action of the α ‐effect peaking at midlatitudes, meridional circulation and latitudinal pumping, most of the activity still occurs at too high latitudes (between 5° … 60°). Other problems include the relatively narrow parameter space within which the preferred solution is dipolar (A0), and the somewhat too short cycle lengths of the solar‐type solutions. The role of the surface shear layer is found to be important only in the case where the α ‐effect has an appreciable magnitude near the surface. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

UNUSUAL WEATHERING PRODUCTS OF OLDHAMITE PARENTAGE IN THE NORTON COUNTY ENSTATITE ACHONDRITE

White, pale-yellow and brown deposits occur on surfaces of fragments of the Norton County enstatite achondrite. X-ray powder analysis of these materials indicates that they consist of several calcium-bearing minerals: portlandite [Ca(OH)₂], vaterite (CaCO₃, hexagonal), calcite (CaCO₃, trigonal) and bassanite (CaSO₄-1/2 H₂O). We suggest that these minerals formed by weathering of oldhamite (CaS), which we found to occur in Norton County. The occurrence of portlandite suggests that at low temperatures and in the terrestrial environment, hydrolysis of oldhamite is the most important first step in the weathering sequence. Subsequent carbonation of portlandite is thought to produce vaterite, and vaterite in turn might transform into calcite. Thus, we suggest a weathering sequence in the terrestrial environment of oldhamite portlandite vaterite calcite. The mineral bassanite is clearly also a terrestrial weathering product but its precise mode of origïn is somewhat uncertain: in the system CaSO₄-H₂O, bassanite forms from gypsum at about 100 °C (an unlikely high T for the weathering environment of Norton County).     

Planar deformation features in quartz grains from the resurge deposit of the Lockne structure,Sweden

Abstract— Microscopic planar deformation features (PDFs) in quartz grains are diagnostic of shock meta-morphism during hypervelocity impact cratering. Measurements of the poles of sets of PDFs and the optic axis of 25 quartz grains were carried out for a sample of the Loftarsten deposit from the Lockne area, Sweden. The most abundant PDFs observed in the sample from the Lockne area correspond to those found at known impact craters (i.e., ω (1013} and π (1012). This study confirms the previous suggestion that the Lockne structure is an impact crater. The Loftarsten is, therefore, interpreted as the final stage of resurge deposition after a marine impact at Lockne in the Middle Ordovician.     

An experimental study of silver and palladium partitioning between solid and liquid metal,with applications to iron meteorites

Abstract— Solid metal/liquid metal partition coefficients for Ag and Pd were determined experimentally as a function of the S concentration of the metallic liquid. Silver is incompatible in solid metal and strongly sensitive to the S content of the metallic liquid; partition coefficients for Ag decrease more than an order of magnitude with increasing S content of the metallic liquid and can be expressed as: where k(Ag) is the molar solid metal/liquid metal partition coefficient and X_S is the molar S content of the metallic liquid. The partition coefficient of Pd is less variable but changes from modestly incompatible to modestly compatible in solid metal with increasing S content of the metallic liquid: With these new partition coefficients for Pd and a fractional crystallization model, Pd abundance trends recorded in iron meteorite groups are modeled successfully. Measured Ag distribution between troilite-rich nodules and adjacent metal in iron meteorites also agree well with experimental solid metal/liquid metal equilibrium values. However, observed Pd metal/nodule distributions do not agree with experimentally determined partition coefficients, which suggests a more complex history than simple solid metal/liquid metal equilibrium.     

Gravitation und weitreichende schwache Wechselwirkungen bei Neutrino-Feldern Gedanken zu einer Theorie der solaren Neutrinos

The strange non-evidence of the solar-neutrino current by the experiments of DAVIS et al. postulates a fundamental revision of the theory of weak interactions and of its relations to gravitation theory. (We assume that the astrophysical stellar models are not completely wrong.) – Our paper is based on PAULI 's grand hypothesis about the connection between weak and gravitational interactions. According to PAULI and BLACKETT the (dimensionless) gravitation constant is the square of the (dimensionless) FERMI -interaction constant and according to the hypotheses of PAULI, DE BROGLIE , and JORDAN the RIEMANN -EINSTEIN gravitational metric g_ik is fusioned by the four independent WEYL ian neutrino fields (β-neutrinos and β-antineutrinos, μ-neutrinos and μ-antineutrinos). This fusion gives four reference tetrads h_i^A(x^l) as neutrino-current vectors, firstly. Then, the metric g_ik is defined by the equation g_ik = η_AB h_i^Ah_η^B according to EINSTEIN 's theory of tele-parallelism in RIEMANN ian space-times. The relation of the gravitation field theory to FERMI 's theory of weak interactions becomes evident in our reference-tetrads theory of gravitation (TREDER 1967, 1971). – According to this theory the coupling of the gravitation potential h_i^A with the matter T_ιⁱ is given by a potential-like (FERMI -like) interaction term. In this interaction term two WEYL spinor-fields are operating on the matter-tensor, simultanously. Therefore, the gravitation coupling constant is PAULI 's square of the FERMI -constant. Besides of the fusion of the RIEMANN -EINSTEIN metric g_ik by four WEYL spinors we are able to construct a conformal flat metric ĝ_ik = ϕ²η_ik by fusion from each two WEYL spinors. (This hypothesis is in connection with our interpretation of EINSTEIN 's hermitian field theory as a unified field-theory of the gravitational metric g_ik and a WEYL spinor field [TREDER 1972].) Moreover, from the reference-tetrads theory is resulting that the WEYL spinors in the “new metric” ĝ_ik are interacting with the DIRAC matter current by a FERMI -like interaction term and that these WEYL spinors fulfil a wave equation in the vacuum. Therefore, we have a long-range interaction with the radiced gravitational constant \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {\frac{{tm^2 }}{{hc}}} $\end{document} as a coupling constant. That means, we have a long-range interaction which is 10¹⁸ times stronger than the gravitation interaction. – However, according to the algebraic structure of the conform-flat this long-range interaction is effective for the neutrino currents, only. And for these neutrinos the interaction is giving an EINSTEIN -like redshift of its frequences. The characteristic quantity of this “EINSTEIN shift” is a second gravitation radius â of each body: N = number of baryons, m = mass of a baryon.) This radius â is 10¹⁸ times larger than the EINSTEIN -SCHWARZSCHILD gravitation radius a = fM/c²: But, this big “weak radius” â has a meaning for the neutrinos, only.–The determination of the exterior and of the interior “metrics” ĝ_ik is given by an “ansatz” which is analogous to the ansatz for determination of strong gravitational fields in our tetrads theory. That is by an ansatz which includes the “self-absorption” of the field by the matter. For all celestial bodies the “weak radius” â is much greater than its geometrical dimension. Therefore, a total EINSTEIN redshift of the neutrino frequences v is resulting according to the geometrical meaning of our long-range weak interaction potential ĝ_ik = ϕ²η_ik. That means, the cosmic neutrino radiation becomes very weak and unable for nuclear reactions. Theoretically, our hypothesis means an ansatz for unitary theory of gravitation and of weak interaction. This unitary field theory is firstly based on EINSTEIN 's hermitian field theory and secondly based on our reference-tetrads theory of gravitation.     

Depositional processes of impactites from the YAX-1 drill core in the Chicxulub impact structure inferred from vertical profiles of PDF orientations and grain size distributions of shocked quartz

Core samples from the Chicxulub impact structure provide insights into the formation processes of a shallow-marine-target, complex crater. Although previous studies investigated the impactites (generally suevitic and polymict breccias) of the Yaxcopoil-1 (YAX-1) drill core in the Chicxulub impact structure, the interpretation of its deposition remains controversial. Here, we analyze planar deformation features (PDFs), grain size, and abundance of shocked quartz throughout the YAX-1 impactite sequence (794–895 m in depth). PDF orientations of most quartz grains in YAX-1 impactites show a distribution of both low angles ({104}, {103}, {102}) and high angles (orientations higher than 55° to c-axis), while the lower part of the impactite sequence contains quartz showing only PDF orientations of low angles. High-abundance, coarse-grained shocked quartz is found from the lower to middle parts of the impactites, whereas it abruptly changes to low-abundance, fine-grained shocked quartz within the upper part. In the uppermost part of the impactites, repeated oscillations in contents of these two components are observed. PDF orientation pattern suggests most of the shocked quartz grains experienced a range of shock pressure, except two samples in the lower part of impactites, which experienced only a high level of shock. We suggest that the base and lower part of the impactite sequence were formed by ejecta curtain and melt surge deposits, respectively. Our results are also consistent with the interpretation that the middle part of the impactite sequence is fallback ejecta from the impact plume. Additionally, we support the contention that massive seawater resurges into the crater occurred during the deposition of the upper and uppermost part of the impactites.