Kink unstable coronal loops: current sheets,current saturation and magnetic reconnection

The kink instability in a coronal loop is a possible explanation of a compact loop flare as it may cause a current sheet to form allowing reconnection to take place and release the free magnetic energy stored in the loop. However, current sheets do not form in all cases. Ali and Sneyd (2001) investigated three different classes of equilibrium (determined by the form of the twist) using a magneto-frictional code. They searched for the equilibria to which the loop might evolve once it had become unstable to the kink instability. They found indications of current-sheet formation for only one class of equilibrium studied. However, as they pointed out, since their code searched for equilibria they were unable to say for certain that the loop would evolve in this way. In this paper we have considered the same three classes of equilibria but have used a code which follows the non-linear 3D MHD (magnetohydrodynamic) evolution of the loop. We have investigated whether or not there are indications of current-sheet formation. In the cases where there is evidence of this we have found that reconnection does occur and releases sufficient magnetic energy to explain a compact loop flare.     

The effect of magnetic shear on the MHD stability of a prominence model

The Hood-Anzer prominence model (Hood and Anzer, 1990) is modified to include magnetic shear. The stability properties of the model are then assessed to see if significant magnetic shear can stabilize ideal MHD disturbances. It is shown that a strong shear gradient in the magnetic field near the base of the prominence provides a stabilizing effect and realistic prominence heights are indeed possible.     

The stability of 2D current sheet models of prominences

A necessary and sufficient condition for the ideal magnetohydrodynamic stability of 2D current sheet models of prominences suspended in a potential coronal field with line-tying is developed using the energy method. This condition takes the form of two simple coupled second-order differential equations which may be integrated along a field line to find marginal stability. The two conditions (85) and (86) of Anzer (1969) are now only sufficient for stability. Two current sheet models are investigated and it is shown that for a potential coronal field allowing perturbed electric currents to flow, line-tying can completely stabilize the equilibria for realistic heights.     

The MHD stability of a twisted flux tube prominence model

The ideal MHD stability of the 2D twisted magnetic flux tube prominence model of Cartledge and Hood (1993) is investigated. The model includes a temperature profile that varies from realistic prominence values up to typical coronal values. The prominence is considered to be of finite-width and finite height. The stability properties of the prominence models are studied by using a method that generates a separate necessary condition and a sufficient condition. These conditions give bounds on the parameters that define marginal stability. In many cases these bounds are quite close so that further, more detailed, stability calculations are not necessary. A number of parameter regimes are examined, corresponding to different profiles of the prominence temperatures, densities, and magnetic field shear. It is found that the model admits realistic stable and unstable loop lengths for observed prominence parameters when the axial magnetic field component does not vanish.     

Current build-up as a result of the kink instability in a loop

The kink instability may be responsible for compact loop flares since the instability is triggered once the twist in a coronal loop exceeds a critical value. During the non-linear evolution of the instability a large current builds up, reconnection can occur and the magnetic energy released due to reconnection may explain the rapid heating of the flare. However, there has been some debate over the nature of the current concentration and, in particular, whether the current saturates or whether it is a current sheet, and what influences these possible states. In this paper we consider two similar equilibria having a twist function which rises to a peak and then falls off. One is steeper than the other allowing us to investigate whether the steepness of the peak has any effect on the nature of the current. For each profile, we run the code on five different grid resolutions and see how the maximum of the current scales with grid resolution. We also look for behavior in the x-component of the velocity which might be similar to the step-function behavior associated with singularities in the linear kink instability. For both profiles we find that the current scales almost linearly with resolution and that v _x drops steeply at the position of the current concentration. This suggests that, for these particular profiles, there are indications of current sheet formation and that the steepness in the peak of the twist does not affect the nature of the current.     

Studies of multiple stellar systems – IV. The triple-lined spectroscopic system Gliese 644

We present a radial velocity study of the triple-lined system Gliese 644 and derive spectroscopic elements for the inner and outer orbits with periods of 2.965 5 and 627 d. We also utilize old visual data, as well as modern speckle and adaptive optics observations, to derive a new astrometric solution for the outer orbit. These two orbits together allow us to derive masses for each of the three components in the system: M _A=0.410±0.028 (6.9 per cent), M _Ba=0.336±0.016 (4.7 per cent), and M _Bb=0.304±0.014 (4.7 per cent) M_⊙. We suggest that the relative inclination of the two orbits is very small. Our individual masses and spectroscopic light ratios for the three M stars in the Gliese 644 system provide three points for the mass–luminosity relation near the bottom of the main sequence, where the relation is poorly determined. These three points agree well with theoretical models for solar metallicity and an age of 5 Gyr. Our radial velocities for Gliese 643 and vB 8, two common proper motion companions of Gliese 644, support the interpretation that all five M stars are moving together in a physically bound group. We discuss possible scenarios for the formation and evolution of this configuration, such as the formation of all five stars in a sequence of fragmentation events leading directly to the hierarchical configuration now observed, versus formation in a small N cluster with subsequent dynamical evolution into the present hierarchical configuration.