Hopf Bifurcations in Coronal Loops. II. Nonlinear Evolution of Instabilities

D. Gomez, A. Sicardi Schifino, C. Ferro Fontan
1990 Astrophysical Journal  
We study the coupling between the hot plasma confined in a coronal loop and the much colder chromospheric plasma at the footpoints. Considering the coronal heating rate as a control parameter, we find that the static equilibrium becomes unstable for heating rates below a critical value, giving rise to the appearance of a stable limit cycle. Starting from the hydrodynamic equations, we derive a model which generalizes the analysis of Kuin and Martens and consistently takes into account the
more » ... sation-evaporation process. In this paper, we linearize our equations in order to find the bifurcation point where the stability of the static equilibrium is lost. We also show that this model can provide a natural explanation for the excess widths of EUV spectral lines formed in the transition region. Moreover, we can predict the observed reduction in the broadening of these lines when they form in certain active regions, like quiescent prominences or sunspots. ABSTRACT In a previous paper, we have modeled the coupling between corona and chromosphere and derived a nonlinear set of equations, where the global stability properties of the coronal plasma can be studied. The linear stability analysis indicates that the static equilibrium is stable unless the heating rate falls below a certain critical value. In the present paper, we study the nonlinear evolution of our equations both analytically and numerically. Applying a perturbative technique around the critical point, we find that a subcritical Hopf bifurcation takes place. The numerical integration of the equations agrees satisfactorily with the analytical results when they are compared close to the bifurcation. The nonthermal Doppler widths of EUV lines forming in the transition region can be explained by the existence of relatively low amplitude limit cycles.
doi:10.1086/168539 fatcat:pm3qrhbm5becfgjviwnxehteiq