C. D. C. Steele

The eruption of a prominence and coronal mass ejection which drive reconnection

Two possible limiting scenarios are proposed for the production of a coronal mass ejection. In the first the magnetic field around a prominence evolves until it loses equilibrium and erupts, which drives reconnection below the prominence and an eruption of the overlying magnetic arcade. In the second a large-scale magnetic arcade evolves until it loses equilibrium and erupts, thereby causing a prominence to erupt. In general it is likely to be the non-equilibrium of the coupled system which creates the eruption. Furthermore, large quiescent prominences are expected to be centred within the magnetic bubble of a coronal mass ejection whereas when active-region prominences erupt they are likely to be located initially to one side of the bubble.A model is set up for the eruption of a magnetically coupled prominence and coronal mass ejection. This represents a development of the Anzer and Pneuman (1982) model by overcoming two limitations of it, namely that: it is not globally stable initially and so one wonders how it can be set up in a stable way before the eruption; it has reconnection driving the CME whereas recent observations suggest that the reverse may be happening. In our model we assume that magnetic reconnection below the prominence is driven by the eruption and the driver is magnetic non-equilibrium in the coupled prominence-mass ejection system. The prominence is modelled as a twisted flux tube and the mass ejection as an overlying void and magnetic bubble. Two different models of the prominence are considered. In one a globally stable equilibrium becomes unstable when a threshold magnetic flux below the prominence is exceeded and, in the other, equilibrium ceases to exist. In both cases, the prominence and mass-ejection accelerate upwards before reaching constant velocities in a manner that is consistent with observations. It is found that the greater the reconnection that is driven by the eruption, the higher is the final speed.

Thermal equilibria of coronal magnetic loops

Equations of thermal equilibrium along coronal loops with footpoint temperatures of 2 × 104 K are solved. Three fundamentally different categories of solution are found, namely hot loops with summit temperatures above about 4 × 105 K, cool loops which are cooler than 8 × 104 K along their whole length and hot-cool loops which have summit temperatures around 2 × 104 K but much hotter parts at intermediate points between the summit and the footpoints. Hot loops correspond to the hot corona of the Sun. The cool loops are of relevance for fibrils, for the cool cores observed by Foukal and also for active-region prominences where the magnetic field is directed mainly along the prominence. Quiescent prominences consist of many cool threads inclined to the prominence axis, and each thread may be modelled as a hot-cool loop. In addition, it is possible for warm loops at intermediate summit temperatures (8 × 104K to 4 × 105 K) to exist, but the observed differential emission measure suggests that most of the plasma in the solar atmosphere is in either the hot phase or the cool phase. Thermal catastrophe may occur when the length or pressure of a loop is so small that the hot solution ceases to exist and there are only cool loop solutions. Many loops can be superimposed to form a coronal arcade which contains loops of several different types.

Magnetic reconnection and energy release in the solar corona by Taylor relaxation

The heating of the solar corona by resistive turbulence of coronal magnetic fields is considered. The theory of this process, based on the Taylor-Heyvaerts-Priest hypothesis and a magnetic relaxation equation, is developed. Such an approach allows one to obtain the successive magnetic reconnection configurations and energy balance of the coronal magnetic field in response to prescribed motions of the photospheric footpoints. Two specific models of the coronal magnetic configuration are investigated, namely an array of closely packed flux tubes and a two-dimensional magnetic arcade.

On the nonlinear theory of the long‐wavelength radiative condensation instability

Nonlinear evolution of the radiative condensation instability (RCI) of an optically thin plasma is investigated in the framework of a one‐dimensional model. The model is applicable for motions either along a sufficiently strong magnetic field, when the transverse heat conduction is suppressed, or perpendicular to a straight, shear‐free magnetic field. The long‐wavelength limit of the RCI is considered when the characteristic radiative cooling time is much shorter than the acoustic (or magnetoacoustic) time. The case when the isochoric thermal mode is damped, while one of the two ‘‘acoustic’’ (or ‘‘magnetoacoustic’’) modes is unstable, is studied. Two different problems of the instability are considered. In the first, the heat conduction is negligible and the instability is described by a reduced set of equations, which formally coincide with those of a gas whose effective compressibility as a function of the density is of alternating sign. The study starts with small perturbations and follows them numeric...

A model for the fibril structure of normal-polarity solar prominences

A normal-polarity prominence is modelled as a series of cool fibrils set in the hotter corona. Equations of magnetostatic equilibrium are solved and each fibril corresponds to a dip in the mgnetic field. The ratio of fibril width to interfibril spacing is dependent on the prominence-coronal temperature ratio and the ratio of plasma to magnetic pressure. The prominence mass is found to depend on the square of the magnetic field strength. When variations along the prominence are allowed in addition to those across the prominence, an apparently random pattern of fibrils results.

On the nonlinear theory of the radiation-driven thermal instability of a magnetized plasma

Abstract The nonlinear evolution of perturbations in a magnetized plasma subject to the radiation-driven thermal instability (RDTI) is investigated analytically in a simplified model. The perturbed plasma motions are assumed to be one-dimensional and perpendicular to the magnetic field. The intermediate- and long-wavelength limits of the RDTI are considered. In the former limit, the force balance sets in rapidly, on the magneto-acoustic time scale and we assume the total (thermal-magnetic) pressure remains constant. By transforming to Lagrangian variables, the problem is reduced to a single generalized reaction-diffusion equation, which is employed to analyze the two following stages of the RDTI. The first develops on the radiative time scale, when the heat conduction is insignificant, while the second usually occurs on a much longer, heat conduction-related time scale. For the first stage, a simple analytical solution is found, which describes the development of a strong plasma stratification (coexisting...

Non-equilibrium of a cylindrical magnetic arcade

A cylindrically-symmetric magnetic arcade with its axis on the photosphere is perturbed by means of an alteration in the pressure along the base. The perturbation is examined with a view to finding equilibrium configurations close to the original equilibrium. It is found that equilibria can only be found when the integral of the excess pressure along the base is zero. In other cases no equilibria can be found and the arcade is likely either to collapse or, in the case of a coronal mass ejection, to erupt. For an initial arcade whose field increases linearly with radial distance from the axis, the neighbouring equilibria have been found.

Magnetic field lines for a flux tube

Equations for the magnetic field components in a two dimensional cylindrically symmetric flux tube equilibrium have been derived and, in a simple case, solved. The resulting magnetic configuration possesses a strong magnetic field in a thin tube below a reference level (solar photosphere). Above this reference level the field lines spread out in all directions.

Thermal equilibria of coronal magnetic loops with non-constant cross-sectional area

Equations of thermal equilibrium along coronal loops are solved in the absence of gravity but where the cross-sectional area changes along the loop. The footpoint temperature is assumed to be 2 × 104 K. Several fundamental types of solution are found, namely hot loops, cool loops, hot-cool loops (where the footpoints and summits are cool but the intermediate parts are hotter) and warm loops (cool along most of their lengths except the summits). On increasing the cross-sectional area the summit temperature generally increases slightly except for warm loops where no increase in temperature is recorded and hot-cool loops where a dramatic increase in summit temperature may occur. The cool and hot-cool loops may model elementary fibril structures within prominences.

Thermal equilibria of isobaric coronal magnetic arcades

A coronal magnetic arcade can be thought of as consisting of an assembly of coronal loops. By solving equations of isobaric thermal equilibrium along each loop and assuming a base temperature of 2 × 104 K, the thermal structure of the arcade can be found. The possible thermal equilibria can be shown to depend on two parameters L*p* and h*/p* representing the ratios of cooling (radiation) to condu and heating to cooling, respectively. Arcades can contain four types of loops: hot loops with summits hotter than 400000 K; cool loops at temperatures less than 80000 K along their lengths; hot-cool loops with cool summits and cool footpoints but hotter intermediate portions; and warm loops, cooler than 80000 K along most of their lengths but with summits as hot as 400000 K. Two possibilities for coronal heating are considered, namely a heating that is independent of magnetic field and a heating that is proportional to the square of the local magnetic field. When the arcade is sheared the thermal structure of the arcade may change, leading in some cases to non-equilibrium or in other cases to the formation of a cool core.