Effect of pressure gradients and line-tying on the magnetic stability of coronal loops

Abstract

In this paper we study the stability of an idealised magnetostatic coronal loop, incorporating both the effect of line-tying, due to the dense photosphere, and of pressure gradients. The stability equations may be solved analytically for our particular equilibrium. From the marginally stable case, the critical conditions separating instability from stability are derived. It is found that stretching or twisting a loop eventually makes it kink unstable.     

Tidal channel meander formation by depositional rather than erosional processes: examples from the prograding Skagit River Delta (Washington,USA)

Channel meander dynamics in fluvial systems and many tidal systems result from erosion of concave banks coupled with sediment deposition on convex bars. However, geographic information system (GIS) analysis of historical aerial photographs of the Skagit Delta marshes provides examples of an alternative meander forming process in a rapidly prograding river delta: deposition‐dominated tidal channel meander formation through a developmental sequence beginning with sandbar formation at the confluence of a blind tidal channel and delta distributary, proceeding to sandbar colonization and stabilization by marsh vegetation to form a marsh island opposite the blind tidal channel outlet, followed by narrowing of the gap between the island and mainland marsh, closure of one half of the gap to join the marsh island to the mainland, and formation of an approximately right‐angle blind tidal channel meander bend in the remaining half of the gap. Topographic signatures analogous to fluvial meander scroll bars accompany these planform changes. Parallel sequences of marsh ridges and swales indicate locations of historical distributary shoreline levees adjacent to filled former island/mainland gaps. Additionally, the location of marsh islands within delta distributaries is not random; islands are disproportionately associated with blind tidal channel/distributary confluences. Furthermore, blind tidal channel outlet width is positively correlated with the size of the marsh island that forms at the outlet, and the time until island fusion with mainland marsh. These observations suggest confluence hydrodynamics favor sandbar/marsh island development. The transition from confluence sandbar to tidal channel meander can take as little as 10 years, but more typically occurs over several decades. This depositional blind tidal channel meander formation process is part of a larger scale systemic depositional process of delta progradation that includes distributary elongation, gradient reduction, flow‐switching, shoaling, and narrowing. Copyright © 2010 John Wiley & Sons, Ltd.     

Current sheet models for inverse polarity prominences in twisted flux tubes

This paper treats the prominence model of Low (1993) to examine more complicated sheet currents than those used in the original model. Nonlinear force-free field solutions, in Cartesian coordinates, invariant in a given direction, are presented to show the possibility of an inverse-polarity prominence embedded in a large twisted flux tube. The force-free solution is matched to an external, unsheared, potential coronal magnetic field. These new solutions are mathematically interesting and allow an investigation of different profiles of the current intensity, magnetic field vector and mass density in the sheet. These prominence models show a general increase in magnetic field strength with height in agreement with observations. Other prominence properties are shown to match the observed values.     

The fibril structure of prominences

We suggest that the fibril structure of prominences may be caused by filamentation during its formation by radiative instability. We also discuss the effects of other types of instability and give a mechanism for the formation of vertical threads. The models indicate that highly inhomogeneous density structures can exist in the presence of smooth profiles for the plasma pressure and magnetic field. In our particular models the plasma pressure of a fibril prominence is higher and the vertical magnetical field is weaker than in a uniform prominence model, while the mass is substantially smaller.     

The effect of shear on numerical models of quiescent normal-polarity prominences

The equilibrium structure of normal-polarity, quiescent prominences is investigated and the influence of magnetic shear in response to a slow, shearing, photospheric velocity discussed. The results show that the overall field structure predicted by Fiedler and Hood (1992) is largely unaffected but that magnetic shear reduces the plasma beta and lengthens and flattens the magnetic field when viewed from the side. The flatness of the field suggests that the initial condensation can form and, when the mass is sufficient, deform the field slightly into the equilibrium structure calculated here. Thus, it is postulated that the field must be highly sheared for the radiation (or condensation) time to be less than the free-fall time along the field. A simple estimate predicts that the field must lie close to the polarity inversion line with an angle in agreement with observations. Hence, it is apparent that normal polarity prominences will always be observed with a highly sheared field.It is shown that the line-of-sight field component depends on the imposed shear profile and the viewing angle and in certain cases it is possible for this field component to appear to increase with height. Any observed increase of the line-of-sight magnetic field with height may then be due to the angle of the prominence to the line of sight.     

External and internal solutions for the twisted,flux-tube,prominence model

In this paper the twisted flux-tube model for the support of a prominence sheet with constant axial current density, given by Ridgway, Priest, and Amari (1991), is considered.The model is extended in Section 2 to incorporate a current sheet of finite height. The sheet is supported in a constant current density force-free field in the configuration of a twisted flux tube. The mass of the prominence sheet, using a typical height and field strength, is computed. Outside the flux tube the background magnetic field is assumed to be potential but the matching of the flux tube onto this background field is not considered here.Instead our attention is focussed, in Section 3, on the interior of the prominence. An expanded scale is used to stretch the prominence sheet to a finite width. We analytically select solutions for the internal magnetic field in this region which match smoothly onto the external force-free solutions at the prominence edge.The force balance equation applied inside the prominence then yields expressions for the pressure and density and a corresponding temperature may be computed.     

Twisted magnetic flux tubes: Effect of small twist

The shape of a magnetic flux tube is investigated when photospheric motion causes small twist at the magnetic footpoints. Using a Fourier-Bessel series expansion, the previous results of Zweibel and Boozer (1985) and Steinolfson and Tajima (1987), when the twist is small, are substantiated. A twisting motion that is restricted to a finite region is investigated. Inside the twisted region, the tube contracts, but in the outer region the field remains straight, except for a slight expansion at the outside of the loop near the footpoints. The amount of twist depends on the radial position and can in fact be larger in the contracted region with the twist decreasing as the tube expands. An axial boundary-layer region is present, as noted by the above authors, through which the field adjusts to the line-tied magnetic footpoint positions. An analysis of the boundary layer shows that the thickness remains constant as the loop-length is increased with the result that the main part of the loop has constant cross-sectional area and can be described by cylindrically-symmetric fields. This new 1-D model predicts the main behaviour of the loop without the need to solve the more complicated 2-D problem directly. It is speculated that the boundary layers will remain even when the twist becomes large and a simple example is presented. A detailed parametric study of different twist profiles shows how the central part of the loop responds.Using the result that the majority of the loop can be described by a constant cross-sectional area, a model for a toroidal loop is presented that models coronal loops in a more realistic manner. The main result from this section is that the coronal loops can only remain in equilibrium if they are confined by an external magnetic field (possibly potential in nature) and not by a gas pressure unless additional physical effects are included.     

A model for quiescent solar prominences with normal polarity

A class of 2-D models of solar quiescent prominences, with normal polarity, is presented. These represent an extension to the Kippenhahn-Schlüter model for which the prominence configuration matches smoothly onto an external non-potential coronal solution of a constant field. Using typical prominence values a model is constructed which also matches the coronal conditions. It is found that the magnetic field component along the prominence influences the internal structure of the prominence. A simple extension to the basic models is indicated as a means of taking a lower boundary of the prominence and eliminating parasitic polarities in the photosphere.     

Geochemical study of the Uinta Basin: formation of petroleum from the Green River formation

Kerogen from the Green River formation is rich in lipid material and contains predominantly aliphatic chains, with subordinate saturated cyclic material. Compositional differences due to the environment of deposition are observed in the extractable hydrocarbons. The influence of microbial degradation during deposition of organic matter is intense in the stratigraphically lowest zone and decreases toward younger beds, where fossil molecules derived from higher plants, algae and other planktonic organisms and bacteria are abundant.The great depth of the oil generation stage may be explained by a combination of (a) a relatively low geothermal gradient, and (b) a high oil generation threshold. The lower part of the formation has reached the principal stage of oil generation and is responsible for most of the crude oils produced in the Uinta Basin.     

Magnetohydrostatic structures in the solar atmosphere

Separable two-dimensional solutions to the isothermal magnetohydrostatic equations are presented which include the effect of gravity. Examples of three types of linear solution are given in which photospheric magnetic fields are prescribed and the field topologies are discussed. In addition, a new nonlinear solution is discussed. The functional form of the pressure distribution is restricted by the separable assumption. An analysis suggests that these are the only separable analytical solutions.