Magnetic flux rope versus the spheromak as models for interplanetary magnetic clouds

TLDR: In this article, the authors compare and contrast two models for the global magnetic field line topology of magnetic clouds: a magnetic flux tube geometry, on the one hand, and a spheromak geometry (including possible higher multiples), on the other.

Abstract: Magnetic clouds form a subset of interplanetary ejecta with well-defined magnetic and thermodynamic properties. Observationally, it is well established that magnetic clouds expand as they propagate antisunward. The aim of this paper is to compare and contrast two models which have been proposed for the global magnetic field line topology of magnetic clouds: a magnetic flux tube geometry, on the one hand, and a spheromak geometry (including possible higher multiples), on the other. Traditionally, the magnetic structure of magnetic clouds has been modeled by force-free configurations. In a first step, we therefore analyze the ability of static force-free models to account for the asymmetries observed in the magnetic field profiles of magnetic clouds. For a cylindrical flux tube the magnetic field remains symmetric about closest approach to the magnetic axis on all spacecraft orbits intersecting it, whereas in a spheromak geometry one can have asymmetries in the magnetic field signatures along some spacecraft trajectories. The duration of typical magnetic cloud encounters at 1 AU (1 to 2 days) is comparable to their travel time from the Sun to 1 AU and thus magnetic clouds should be treated as strongly nonstationary objects. In a second step, therefore, we abandon the static approach and model magnetic clouds as self-similarly evolving MHD configurations. In our theory, the interaction of the expanding magnetic cloud with the ambient plasma is taken into account by a drag force proportional to the density and the velocity of expansion. Solving rigorously the full set of MHD equations, we demonstrate that the asymmetry in the magnetic signature may arise solely as a result of expansion. Using asymptotic solutions of the MHD equations, we least squares fit both theoretical models to interplanetary data. We find that while the central part of the magnetic cloud is adequately described by both models, the 'edges' of the cloud data are modeled better by the magnetic flux tube. Further comparisons of the two models necessarily involve thermodynamic properties, since real magnetic configurations are never exactly force-free and gas pressure plays an essential role. We consider a polytropic gas. Our theoretical analysis shows that the self-similar expansion of a magnetic flux tube requires the polytropic index gamma to be less than unity. For the spheromak, however, self-similar, radially expanding solutions are known only for gamma equal to 4/3. This difference, therefore, yields a good way of distinguishing between the two geometries. It has been shown recently that the polytropic relationship is applicable to magnetic clouds and that the corresponding polytropic index is approximately 0.5. This observational result is consistent with the self-similar model of the magnetic flux rope but is in conflict with the self-similar spheromak model.