George B. Field

The topological properties of magnetic helicity

The relation of magnetic helicity to the topological structure of field lines is discussed. If space is divided into a collection of flux tubes, magnetic helicity arises from internal structure within a flux tube, such as twist and kinking, and external relations between flux tubes, i.e. linking and knotting. The concepts of twist number and writhing number are introduced from the mathematical-biology literature to describe the contributions to helicity from twist about the axis of a flux tube, and from the structure of the axes themselves. There exists no absolute measure of the helicity within a subvolume of space if that subvolume is not bounded by a magnetic surface. However, a topologically meaningful and gauge-invariant relative measure of helicity for such volumes is presented here. The time derivative of this relative measure is calculated, which leads to an expression for the flow of topological structure across boundaries.

Spectroscopic Constraints on Models of Ion Cyclotron Resonance Heating in the Polar Solar Corona and High-Speed Solar Wind

Using empirical ion velocity distributions derived from Ultraviolet Coronagraph Spectrometer (UVCS) and Solar Ultraviolet Measurements of Emitted Radiation (SUMER) ultraviolet spectroscopy, we construct theoretical models of the nonequilibrium plasma state of the polar solar corona. The primary energy deposition mechanism we investigate is the dissipation of high-frequency (10-10,000 Hz) ion cyclotron resonant Alfven waves which can heat and accelerate ions differently depending on their charge and mass. We solve the internal energy conservation equations for the ion temperature components parallel and perpendicular to the superradially expanding magnetic field lines and use empirical constraints for the remaining parameters. We find that it is possible to explain many of the kinetic properties of the plasma (such as high perpendicular ion temperatures and strong temperature anisotropies) with relatively small amplitudes for the resonant waves. There is suggestive evidence for steepening of the Alfven wave spectrum between the coronal base and the largest heights observed spectroscopically, and it is important to take Coulomb collisions into account to understand observations at the lowest heights. Because the ion cyclotron wave dissipation is rapid, the extended heating seems to demand a constantly replenished population of waves over several solar radii. This indicates that the waves are generated gradually throughout the wind rather than propagated up from the base of the corona.

Excitation of the Hydrogen 21-CM Line

The importance of spin temperature for 21-cm line studies is reviewed, and four mechanisms which affect it are studied. Two of the mechanisms, collisions with free electrons and interactions with light, are studied here in detail for the first time. The results are summarized in Table II of Section VI, in the form of certain efficiencies which can be used with (15) to calculate the spin temperature. In Section VI the results are applied to a variety of astronomical situations, and it is shown that in the usual situation collisions with H atoms are very effective in establishing the spin temperature equal to the kinetic temperature. Under conditions of low-density and/or high-radiation intensity, however, important deviations from the usual are noted. The significance of such deviations for absorption studies of radio sources and the galactic halo is discussed. In Section VII the deuterium line at 91.6 cm is considered in like fashion. It is shown that for deuterium also, the spin temperature probably is close to the kinetic temperature.

Constraints on the magnitude of α in dynamo theory

We consider the back-reaction of the magnetic field on the magnetic dynamo coefficients and the role of boundary conditions in interpreting whether numerical evidence for suppression is dynamical. If a uniform field in a periodic box serves as the initial condition for modeling the back-reaction on the turbulent EMF, then the magnitude of the turbulent EMF, and thus the dynamo coefficient α, have a stringent upper limit that depends on the magnetic Reynolds number RM to a power of order -1. This is not a dynamic suppression but results just because of the imposed boundary conditions. In contrast, when mean field gradients are allowed within the simulation region, or nonperiodic boundary conditions are used, the upper limit is independent of RM and takes its kinematic value. Thus only for simulations of the latter types could a measured suppression be the result of a dynamic back-reaction. This is fundamental for understanding a long-standing controversy surrounding α suppression. Numerical simulations that do not allow any field gradients and invoke periodic boundary conditions appear to show a strong α suppression (e.g., Cattaneo & Hughes). Simulations of accretion disks that allow field gradients and allow free boundary conditions (Brandenburg & Donner) suggest a dynamo α that is not suppressed by a power of RM. Our results are consistent with both types of simulations.

New dynamical mean-field dynamo theory and closure approach.

We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.

A STATISTICAL MODEL OF THE FORMATION OF STARS AND INTERSTELLAR CLOUDS

Oort model of stars and interstellar cloud formation and destruction mathematically formulated, obtaining time-dependent cloud-mass spectrum equations

Primordial magnetic fields from pseudo Goldstone bosons

Harvard-Smithsonian Center for Astrophysics60 Garden Street, Cambridge, Massachussetts 02138 USA(Received 21 July 1992)The existence of large-scale magnetic fields in galaxies is well established, butthere is no accepted mechanism for generating a primordial field which could growinto what is observed today. We discuss a model which attempts to account for thenecessary primordial field by invoking a pseudo-Goldstone boson coupled to electro-magnetism. The evolution of this boson during inflation generates a magnetic field;however, it seems difficult on rather general grounds to obtain fields of sufficientstrength on astrophysically interesting scales.98.80.Cq, 98.60.Jk, 95.30.Cq, 14.80.Gt

Is there evidence for cosmic anisotropy in the polarization of distant radio sources

Measurements of the polarization angle and orientation of cosmological radio sources may be used to search for unusual effects in the propagation of light through the Universe. Recently, Nodland and Ralston [Phys.Rev.Lett.{bold 78}, 3043 (1997)] have claimed to find evidence for a redshift- and direction-dependent rotation effect in existing data. We reexamine these data and argue that there is no statistically significant signal present. We are able to place stringent limits on hypothetical chiral interactions of photons propagating through spacetime. {copyright} {ital 1997} {ital The American Physical Society}

Nonlinear α-Effect in Dynamo Theory

The standard two-scale theory of the dynamo coefficient α in incompressible isotropic helical MHD turbulence is extended to include nonlinear effects of , the large-scale magnetic field. We express α in terms of statistical quantities that can be calculated from numerical simulations of the case =0. For large magnetic Reynolds numbers, our formula agrees approximately with that of Kraichnan but disagrees with that of Cattaneo & Hughes.

Coronal activity from dynamos in astrophysical rotators

We show that a steady mean-field dynamo in astrophysical rotators leads to an outflow of relative magnetic helicity and thus magnetic energy available for particle and wind acceleration in a corona. The connection between energy and magnetic helicity arises because mean-field generation is linked to an inverse cascade of magnetic helicity. To maintain a steady state in large magnetic Reynolds number rotators, there must then be an escape of relative magnetic helicity associated with the mean field, accompanied by an equal and opposite contribution from the fluctuating field. From the helicity flow, a lower limit on the magnetic energy deposited in the corona can be estimated. Steady coronal activity including the dissipation of magnetic energy, and formation of multi-scale helical structures therefore necessarily accompanies an internal dynamo. This highlights the importance of boundary conditions which allow this to occur for non-linear astrophysical dynamo simulations. Our theoretical estimate of the power delivered by a mean-field dynamo is consistent with that inferred from observations to be delivered to the solar corona, the Galactic corona, and Seyfert 1 AGN coronae.