Magnetic Reconnection in the Interior of Interplanetary Coronal Mass Ejections

Recent in situ observations of interplanetary coronal mass ejections (ICMEs) found signatures of reconnection exhausts in their interior or trailing edge. Whereas reconnection on the leading edge of an ICME would indicate an interaction with the coronal or interplanetary environment, this result suggests that the internal magnetic field reconnects with itself. In light of this data, we consider the stability properties of flux ropes first developed in the context of astrophysics, then further elaborated upon in the context of reversed field pinches (RFPs). It was shown that the lowest energy state of a flux rope corresponds to $\mathbf{\nabla }\times \mathbf{B}=\lambda \mathbf{B}$ with $\lambda$ a constant, the so-called Taylor state. Variations from this state will result in the magnetic field trying to reorient itself into the Taylor state solution, subject to the constraints that the toroidal flux and magnetic helicity are invariant. In reversed field pinches, this relaxation is mediated by the reconnection of the magnetic field, resulting in a sawtooth crash. If we likewise treat the ICME as a flux rope, any deviation from the Taylor state will result in reconnection within the interior of the flux tube, in agreement with the observations by Gosling et al. Such a departure from the Taylor state takes place as the flux tube cross section expands in the latitudinal direction, as seen in magnetohydrodynamic (MHD) simulations of flux tubes propagating through the interplanetary medium. We show analytically that this elongation results in a state which is no longer in the minimum energy Taylor state. We then present magnetohydrodynamic simulations of an elongated flux tube which has evolved away from the Taylor state and show that reconnection at many surfaces produces a complex stochastic magnetic field as the system evolves back to a minimum energy state configuration.

Figure 1

The in-plane magnetic field of the Taylor state solution in Eqs. (2)–(3). The field lines also act as contour levels of $B_z$ as defined in Eq. (4).

Figure 2

The equilibrium state for the $L_x=16$, $L_y=4$ case which satisfies Eq. (1) but only for nonconstant $\lambda$. The color bar shows $\lambda =4\pi \mathbf{J}·\mathbf{B}/B^2$, while contour lines depict the in-plane magnetic field $B_x-B_y$, as contours of the flux function $\psi$.

Figure 3

The total magnetic energy in the simulation of the $L_x=16$, $L_y=4$ flux tube as a function of time.

Figure 4

Puncture plots at (a) $t=50$ and (b) $t=200$. Note that (b) is a zoom into $-4<x<4$, $-1<y<1$ to emphasize the structure in that region, and each color corresponds to the punctures of a unique flux surface. Each flux surface is traced starting from its $x$ intercept at $x=1,2,\dots ,7$; i.e., the black puncture points correspond to a flux surface traced from $x=1$, $y=0$, the violet at $x=2$, $y=0$, etc.

Figure 5

The safety factor profile as a function of the $x$ intercept $x_0$ of a given flux surface. The diamond markers denote rational flux surfaces highlighted in Fig. 4: those with $q=5$ at $x_0\approx 2.8$, $q=9/2$ at $x_0\approx 4.0$, $q=3$ at $x_0\approx 5.5$, and $q=5/2$ at $x_0\approx 6.0$.