Regularized Biot-Savart Laws for Modeling Magnetic Flux Ropes

TL;DR

This paper introduces a new analytical method using regularized Biot-Savart laws to efficiently model magnetic flux ropes with arbitrary shapes, aiding in the simulation of solar eruptions like CMEs.

Contribution

The authors developed a compact analytical form for magnetic flux ropes with arbitrary axes, enabling more realistic and efficient modeling constrained by observed solar magnetic data.

Findings

Successfully modeled pre-eruptive flux ropes for two CME events.

Demonstrated the method's flexibility and efficiency in CME simulations.

Constructed realistic flux rope configurations using observed magnetograms.

Abstract

Many existing models assume that magnetic flux ropes play a key role in solar flares and coronal mass ejections (CMEs). It is therefore important to develop efficient methods for constructing flux-rope configurations constrained by observed magnetic data and the morphology of the pre-eruptive source region. For this purpose, we have derived and implemented a compact analytical form that represents the magnetic field of a thin flux rope with an axis of arbitrary shape and circular cross-sections. This form implies that the flux rope carries axial current $I$ and axial flux $F$, so that the respective magnetic field is the curl of the sum of axial and azimuthal vector potentials proportional to $I$ and $F$, respectively. We expressed the vector potentials in terms of modified Biot-Savart laws whose kernels are regularized at the axis in such a way that, when the axis is straight, these laws define a cylindrical force-free flux rope with a parabolic profile for the axial current density. For the cases we have studied so far, we determined the shape of the rope axis by following the polarity inversion line of the eruptions' source region, using observed magnetograms. The height variation along the axis and other flux-rope parameters are estimated by means of potential field extrapolations. Using this heuristic approach, we were able to construct pre-eruption configurations for the 2009 February 13 and 2011 October 1 CME events. These applications demonstrate the flexibility and efficiency of our new method for energizing pre-eruptive configurations in simulations of CMEs.