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

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

Mar 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990apj...352..326g&link_type=abstract

Astrophysical Journal v.352, p.326

Astronomy and Astrophysics

Astronomy

2

Hydromagnetics, Sun: Chromosphere, Sun: Corona

Scientific paper

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.

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