The stability and uniqueness of coronal loops

Abstract

A hydrodynamic model of high resolution is used to examine the stability of coronal loops to finite amplitude perturbations. The loop is heated by means of a low-amplitude energy input and its subsequent dynamic relaxation is followed.Firstly, the initial atmosphere is generated by solving the time independent form of the hydrodynamic equations. It is shown that the loop structure depends critically on the balance between the radiative losses and the quiescent heating at the base of the transition zone, i.e. on the concavity of the temperature profile in this region. This result already anticipates the need for high spatial resolution across the model transition zone.The dynamic evolution of the loop is then investigated for two classes of lower boundary conditions. In one case the chromospheric temperature is fixed throughout the simulation; in the other the low chromosphere is represented by a rigid insulating barrier. In both cases the loop is found to be stable: The loop is also unique to the extent that it relaxes to a state which is physically indistinguishable from its initial configuration. It is pointed out however, that a loop whose chromosphere is only marginally stable can evolve dynamically away from the initial static configuration.Finally, the observational consequences of the analysis are discussed. The differential emission measure profile is found to change its form as the loop cools, firstly, through an evaporative phase in which the coronal density increases; secondly, through a quasi-steady relaxation in which the enhanced coronal density gradually drains away to the chromosphere. This behaviour represents a possible observational test of the model.

On the consequences of a non-equilibrium ionisation balance for compact flare emission and dynamics

“…The smallest cell-width in both simulations is reached at about 120 s. In simulation A it is about 6 × 10 2 cm and in simulation B about 10 3 cm. According to Craig et al (1982), a heat flux on the order of 10 8 erg cm −2 s −1 carried by the transition region requires a resolution of less than 3 × 10 3 cm. In Fig. 2 the conducted heat flux peaks at just below 10 8 erg cm −2 s −1 .…”

The Influence of Numerical Resolution on Coronal Density in Hydrodynamic Models of Impulsive Heating

“…The treatment of shocks needs care, but is well understood. Despite early recognition of the problems (e.g., Craig et al 1982), the numerical treatment of thermal conduction, in particular the resolution of steep temperature gradients, remains a serious concern. This can be seen by considering a static equilibrium loop.…”

VIII. Theory of Flares

“…With a Lagrangian formalism, Craig et al (1982) show how a summit heat pulse raises the summit temperature and later (by evaporation) the summit density, after which both decline as the plasma drains back down. Antiochos S Sturrock (1982) suggest that supersonic downflows in the late phase could be driven by footpoint cooling.…”