Methods of analyzing radio polarization data

Abstract

Methods of estimating the strength and direction of galactic magnetic fields from radio polarization measurements are reviewed. Particular attention is paid to the analysis of the Faraday rotation in order to derive the large scale magnetic field structure. Ways in which an axisymmetric spiral field structure can be observationally distinguished from a bisymmetric spiral structure are described, as are the ways in which field symmetric with respect to the galactic plane can be distinguished from those that are antisymmetric.     

月球磁学观测与研究进展

月球磁场观测一直是月球研究的重要内容。20世纪六七十年代,通过绕月小卫星、Apollo登月及返回样品等观测实验,月球磁学研究已取得一系列重要进展,九十年代末期Lunar Prospector（LP）获得了月球的全球磁异常分布图。本文主要评述前人已取得的重要进展,重点讨论月球样品的剩磁来源、月球磁场古强度和发电机争论及其月球演化意义。     

Convective plan-form of two-scale dynamos in a plane layer

We study generation of magnetic fields, involving large spatial scales, by convective plan-forms in a horizontal layer. Magnetic modes and their growth rates are expanded in power series in the scale ratio, and the magnetic eddy diffusivity (MED) tensor is derived for flows, symmetric about the vertical axis in a layer. For convective rolls we demonstrate that MED is never below molecular magnetic diffusivity. For cell patterns possessing the symmetries of a rectangle, critical values of molecular magnetic diffusivity for the onset of small- and large-scale magnetic field generation are the same. No instances of negative MED in hexagonal cells have been detected. A family of plan-forms has been found numerically, where MED is negative for molecular magnetic diffusivity over the threshold for the onset of small-scale magnetic field generation. However, the region in the parameter space, where large-scale dynamo action is observed, is small.     

On the inverse dynamo problem in a simplified mean-field model

Inverse dynamo theory seeks to gain information about the motion of a liquid conductor from measurements of the magnetic field in the surrounding vacuum. We consider here a highly simplified model problem, namely a steady α²-dynamo in plane geometry with an α-field varying only in the z-direction normal to the conductor–vacuum interface. Based on perturbation theory about constant-α solutions, we find as many integral conditions on α(z) as modes are present in the vacuum field. This result is corroborated by the complete solution of a special case.     

On the onset of thermal convection in slowly rotating fluid shells

Abstract

The problem of the removal of the degeneracy of the patterns of convective motion in a spherically symmetric fluid shell by the effects of rotation is considered. It is shown that the axisymmetric solution is preferred in sufficiently thick shells where the minimum Rayleigh number corresponds to degree l = 1 of the spherical harmonics. In all cases with l > 1 the solution described by sectional spherical harmonics Y^l _l (θ,φ) is preferred.     

Inverse dynamo problem in a cylinder

An inverse dynamo problem is presented in which we search for either kinematic dynamos which produce the same external magnetic fields or an invisible dynamo. The existence of flows which produce the same external magnetic fields is proved. However, we have not found general conditions necessary for such kind of dynamos. An “invisible dynamo” operates in an electrically conducting region surrounded by vacuum and generates a magnetic field trapped in the electrically conducting region so that no magnetic field exists in the vacuum. Invisible magnetic decay modes exist in cylinders, but no invisible growing field supported by the dynamo mechanism has been found.     

Kinematic dynamo action in spherical Couette flow

We investigate numerically kinematic dynamos driven by flow of electrically conducting fluid in the shell between two concentric differentially rotating spheres, a configuration normally referred to as spherical Couette flow. We compare between axisymmetric (2D) and fully 3D flows, between low and high global rotation rates, between prograde and retrograde differential rotations, between weak and strong nonlinear inertial forces, between insulating and conducting boundaries and between two aspect ratios. The main results are as follows. Azimuthally drifting Rossby waves arising from the destabilisation of the Stewartson shear layer are crucial to dynamo action. Differential rotation and helical Rossby waves combine to contribute to the spherical Couette dynamo. At a slow global rotation rate, the direction of differential rotation plays an important role in the dynamo because of different patterns of Rossby waves in prograde and retrograde flows. At a rapid global rotation rate, stronger flow supercriticality (namely the difference between the differential rotation rate of the flow and its critical value for the onset of nonaxisymmetric instability) facilitates the onset of dynamo action. A conducting magnetic boundary condition and a larger aspect ratio both favour dynamo action.     

Stable and unstable barotropic shelf waves in a coastal current

Abstract

We consider the linearized stability of a barotropic coastal current flowing parallel to a straight coastline over a continental shelf and slope whose depth varies monotonically with distance from the coast. Some necessary conditions for stability and various semi-circle theorems are reviewed for general current profiles and bottom topography. A criterion for topography to be a destabilizing influence is derived. Some general results for stable waves are also described. Analytic solutions are obtained for a piece-wise linear current profile and the exponential depth profile (Buchwald and Adams, 1968). Dispersion diagrams are obtained for a monotonic current profile, where it is shown that the effect of topography is destabilizing, and for a triangular current profile. The dispersion diagrams generally contain a finite number (usually one or two) of unstable waves, and a set of stable waves, which may be infinite in number. The results are applied to some specific coastal regimes.     

Dynamo model with a small number of modes and magnetic activity of T Tauri stars

We suggest a model based on the representation of the stellar magnetic field as a superposition of a finite number of poloidal and toroidal free decay modes to describe the dynamo action in fully convective stars. For the adopted law of stellar differential rotation, we determined the dynamo number in exceeding which the generation of a cyclically varying magnetic field is possible in stars without a radiative core and derived an expression for the period of the cycle. The dynamo cycles in fully convective stars and in stars with thin convective envelopes are shown to differ qualitatively: first, the distributions of spots in latitude during the cycle are different for these two types of stars and, second, the model predicts a great weakening of the spot formation in fully convective stars at certain phases of the cycle. To compare the theory with observations, we have analyzed the historical light curve for the weak-line T Tauri star V410 Tau and found that its long-term activity is not a well-defined cycle with a definite period—its activity is more likely quasi-cyclic with a characteristic time of ～4 yr and with a chaotic component superimposed. we have also concluded that a redistribution of spots in longitude is responsible for the secular brightness variations in the star. This does not allow the results of photometric observations to be directly compared with predictions of ourmodel, in which, for simplicity, we assumed a symmetry in longitude and investigated the temporal evolution of the spot distribution in latitude. Therefore, we discuss the questions of what and how observations can be compared with predictions of the dynamo theory.