A model of coronal streamers with underlying flux ropes

We present global two-dimensional axisymmetric isothermal MHD simulations of the dynamic evolution of a coronal helmet streamer, driven at the lower boundary by the emergence of a twisted flux rope. By varying both the detached toroidal and poloidal fluxes emerged into the corona, but fixing the normal flux distribution at the surface at the end of the emergence, we obtain solutions that either settle to a new steady state of a stable helmet streamer containing a flux rope, or result in a disruption of the helmet with the underlying flux rope being expelled in a coronal mass ejection (CME)-like eruption. In all of the cases studied, we find that the transition from a stable to an eruptive state takes place at a magnetic energy that is very close to the Aly open field energy. Furthermore, we find that the transition from a stable to an eruptive end state does not occur at a single critical value of the total relative magnetic helicity, but depends on the profile of the underlying flux rope. Cases where the detached flux rope contains a higher amount of self-helicity, i.e., higher internal twist or detached poloidal flux, are found to become eruptive at a significantly lower total helicity. For the eruptive cases, the detached flux rope after emergence first rises quasi-statically due to a gradual opening of the field lines at the edge of the streamer and a slow reconnection below the flux rope, which continues to slowly increase the amount of the detached flux. This decreases the downward magnetic tension on the flux rope. The dynamic eruption is initiated when the magnetic pressure gradient no longer decreases fast enough to balance the decrease in the magnetic tension. Later rapid reconnections below the flux rope are important for accelerating the flux rope. For the stable helmets, we find that no cavities are formed due to the simplifying assumption of isothermal energetics and the uniform density lower boundary condition. However during the eruption we see the development of the 3-part structure of a CME.