Quantifying extreme behaviour in geomagnetic activity

Understanding the extremes in geomagnetic activity is an important component in understanding just how severe conditions can become in the terrestrial space environment. Extreme activity also has consequences for technological systems. On the ground, extreme geomagnetic behavior has an impact on navigation and position accuracy and the operation of power grids and pipeline networks. We therefore use a number of decades of one-minute mean magnetic data from magnetic observatories in Europe, together with the technique of extreme value statistics, to provide a preliminary exploration of the extremes in magnetic field variations and their one-minute rates of change. These extremes are expressed in terms of the variations that might be observed every 100 and 200 years in the horizontal strength and in the declination of the field. We find that both measured and extrapolated extreme values generally increase with geomagnetic latitude (as might be expected), though there is a marked maximum in estimated extreme levels between about 53 and 62 degrees north. At typical midlatitude European observatories (55–60 degrees geomagnetic latitude), compass variations may reach approximately 3–8 degrees/minute, and horizontal field changes may reach 1000–4000 nT/minute, in one magnetic storm once every 100 years. For storm return periods of 200 years the equivalent figures are 4–11 degrees/minute and 1000–6000 nT/minute

'Stable' QPOs and Black Hole Properties from Diskoseismology

We compare our calculations of the frequencies of the fundamental g, c, and p--modes of relativistic thin accretion disks with recent observations of high frequency QPOs in X-ray binaries with black hole candidates. These classes of modes encompass all adiabatic perturbations of such disks. The frequencies of these modes depend mainly on only the mass and angular momentum of the black hole; their weak dependence on disk luminosity is also explicitly indicated. Identifying the recently discovered relatively stable QPO pairs with the fundamental g and c modes provides a determination of the mass and angular momentum of the black hole. For GRO J1655-40, M=5.9\pm 1.0 M_\sun, $J=(0.917\pm 0.024)GM^2/c$, in agreement with spectroscopic mass determinations. For GRS 1915+105, M=42.4\pm 7.0 M_\sun, $J=(0.926\pm 0.020)GM^2/c$ or (less favored) M=18.2\pm 3.1 M_\sun, $J=(0.701\pm 0.043)GM^2/c$. We briefly address the issues of the amplitude, frequency width, and energy dependence of these QPOs.Comment: 10 pages, 1 figure. Accepted for publication in Astrophysical Journal Letter

Electrostatic Patch Effect in Cylindrical Geometry. III. Torques

We continue to study the effect of uneven voltage distribution on two close cylindrical conductors with parallel axes started in our papers [1] and [2], now to find the electrostatic torques. We calculate the electrostatic potential and energy to lowest order in the gap to cylinder radius ratio for an arbitrary relative rotation of the cylinders about their symmetry axis. By energy conservation, the axial torque, independent of the uniform voltage difference, is found as a derivative of the energy in the rotation angle. We also derive both the axial and slanting torques by the surface integration method: the torque vector is the integral over the cylinder surface of the cross product of the electrostatic force on a surface element and its position vector. The slanting torque consists of two parts: one coming from the interaction between the patch and the uniform voltages, and the other due to the patch interaction. General properties of the torques are described. A convenient model of a localized patch suggested in [2] is used to calculate the torques explicitly in terms of elementary functions. Based on this, we analyze in detail patch interaction for one pair of patches, namely, the torque dependence on the patch parameters (width and strength) and their mutual positions. The effect of the axial torque is then studied for the experimental conditions of the STEP mission.Comment: 28 pages, 6 Figures. Submitted to Classical Quantum Gravit

On the Energy-Momentum Tensor of the Scalar Field in Scalar--Tensor Theories of Gravity

We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively identify as the energy-momentum tensor of the scalar field is not appropriate because it is spoiled by a part of the dynamical description of gravity. A new connection can be defined in terms of which the full dynamical description of gravity is explicit, and the correct scalar field energy-momentum tensor can be immediately identified. Certain inequalities must be imposed on the two free functions (the coupling function and the potential) that define a particular scalar-tensor theory, to ensure that the scalar field energy density never becomes negative. The correct dynamical description leads naturally to the Einstein frame formulation of scalar-tensor gravity which is also studied in detail.Comment: Submitted to Phys. Rev D15, 10 pages. Uses ReVTeX macro

The Covariant Entropy Bound, Brane Cosmology, and the Null Energy Condition

In discussions of Bousso's Covariant Entropy Bound, the Null Energy Condition is always assumed, as a sufficient {\em but not necessary} condition which helps to ensure that the entropy on any lightsheet shall necessarily be finite. The spectacular failure of the Strong Energy Condition in cosmology has, however, led many astrophysicists and cosmologists to consider models of dark energy which violate {\em all} of the energy conditions, and indeed the current data do not completely rule out such models. The NEC also has a questionable status in brane cosmology: it is probably necessary to violate the NEC in the bulk in order to obtain a "self-tuning" theory of the cosmological constant. In order to investigate these proposals, we modify the Karch-Randall model by introducing NEC-violating matter into $AdS_5$ in such a way that the brane cosmological constant relaxes to zero. The entropy on lightsheets remains finite. However, we still find that the spacetime is fundamentally incompatible with the Covariant Entropy Bound machinery, in the sense that it fails the Bousso-Randall consistency condition. We argue that holography probably forbids all {\em cosmological} violations of the NEC, and that holography is in fact the fundamental physical principle underlying the cosmological version of the NEC.Comment: 21 pages, 3 figures, version 2:corrected and greatly improved discussion of the Bousso-Randall consistency check, references added; version3: more references added, JHEP versio

Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory

The ``Newtonian'' theory of spatially unbounded, self--gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space $\R^3$ from closed models based (without loss of generality) on a flat torus \T^3. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form a spatially homogeneous ``background'' model and that the averages of open models, if they exist at all, in general do not obey the dynamical laws of homogeneous models. We then specialize to those inhomogeneous toroidal models whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution equations which govern the (conformally rescaled) displacement of the inhomogeneous flow with respect to its homogeneous background. Finally, we set up an iteration scheme and prove that the resulting equations have unique solutions at any order for given initial data, while for open models there exist infinitely many different solutions for given data.Comment: submitted to G.R.G., TeX 30 pages; AEI preprint 01