Consequences of the force‐free model of magnetic clouds for their heliospheric evolution

2009

A&A

148

191

Context. A magnetic cloud (MC) is a magnetic flux rope in the solar wind (SW), which, at 1 AU, is observed ∼2-5 days after its expulsion from the Sun. The associated solar eruption is observed as a coronal mass ejection (CME). Aims. Both the in situ observations of plasma velocity distribution and the increase in their size with solar distance demonstrate that MCs are strongly expanding structures. The aim of this work is to find the main causes of this expansion and to derive a model to explain the plasma velocity profiles typically observed inside MCs. Methods. We model the flux rope evolution as a series of force-free field states with two extreme limits: (a) ideal magnetohydrodynamics (MHD) and (b) minimization of the magnetic energy with conserved magnetic helicity. We consider cylindrical flux ropes to reduce the problem to the integration of ordinary differential equations. This allows us to explore a wide variety of magnetic fields at a broad range of distances to the Sun. Results. We demonstrate that the rapid decrease in the total SW pressure with solar distance is the main driver of the flux-rope radial expansion. Other effects, such as the internal over-pressure, the radial distribution, and the amount of twist within the flux rope have a much weaker influence on the expansion. We demonstrate that any force-free flux rope will have a self-similar expansion if its total boundary pressure evolves as the inverse of its length to the fourth power. With the total pressure gradient observed in the SW, the radial expansion of flux ropes is close to self-similar with a nearly linear radial velocity profile across the flux rope, as observed. Moreover, we show that the expansion rate is proportional to the radius and to the global velocity away from the Sun. Conclusions. The simple and universal law found for the radial expansion of flux ropes in the SW predicts the typical size, magnetic structure, and radial velocity of MCs at various solar distances.

Section: Comparison To Previous Studiessupporting

confidence: 82%

Section: Comparison To Previous Studiessupporting

confidence: 61%

Section: Comparison To Previous Studiesmentioning

confidence: 99%

See 1 more Smart Citation

Causes and consequences of magnetic cloud expansion

Démoulin¹,

2009

A&A

148

191

“…Such radial evolution is otherwise available only from a statistic analysis of a large number of MCs observed individually at various distances (Liu et al 2005;Wang et al 2005a;Leitner et al 2007;Gulisano et al 2010), with possible bias coming from the selection of MCs with different properties. Another application of line-up spacecraft is to derive the evolution of global magnetohydrodynamic (MHD) quantities, such as magnetic flux and magnetic helicity (Dasso 2009).…”

Section: Introductionmentioning

confidence: 99%

Dynamical evolution of a magnetic cloud from the Sun to 5.4 AU

Nakwacki

Démoulin

et al. 2011

A&A

Context. Significant quantities of magnetized plasma are transported from the Sun to the interstellar medium via interplanetary coronal mass ejections (ICMEs). Magnetic clouds (MCs) are a particular subset of ICMEs, forming large-scale magnetic flux ropes. Their evolution in the solar wind is complex and mainly determined by their own magnetic forces and the interaction with the surrounding solar wind. Aims. Magnetic clouds are strongly affected by the surrounding environment as they evolve in the solar wind. We study expansion of MCs, its consequent decrease in magnetic field intensity and mass density, and the possible evolution of the so-called global ideal-MHD invariants. Methods.In this work we analyze the evolution of a particular MC (observed in March 1998) using in situ observations made by two spacecraft approximately aligned with the Sun, the first one at 1 AU from the Sun and the second one at 5.4 AU. We describe the magnetic configuration of the MC using different models and compute relevant global quantities (magnetic fluxes, helicity, and energy) at both heliodistances. We also tracked this structure back to the Sun, to find out its solar source. Results. We find that the flux rope is significantly distorted at 5.4 AU. From the observed decay of magnetic field and mass density, we quantify how anisotropic is the expansion and the consequent deformation of the flux rope in favor of a cross section with an aspect ratio at 5.4 AU of ≈1.6 (larger in the direction perpendicular to the radial direction from the Sun). We quantify the ideal-MHD invariants and magnetic energy at both locations, and find that invariants are almost conserved, while the magnetic energy decays as expected with the expansion rate found. Conclusions. The use of MHD invariants to link structures at the Sun and the interplanetary medium is supported by the results of this multi-spacecraft study. We also conclude that the local dimensionless expansion rate, which is computed from the velocity profile observed by a single-spacecraft, is very accurate for predicting the evolution of flux ropes in the solar wind.

“…The simplest solution is obtained with a cylindrical boundary; this is the so-called Lundquist model (Lundquist 1950). It was, and is still, widely used to fit the magnetic field observed in MCs and to derive global quantities such as the magnetic flux and helicity (e.g., Burlaga 1988;Lepping et al 1990;Dasso et al 2003;Lynch et al 2003;Dasso et al 2005b;Mandrini et al 2005;Dasso et al 2006;Leitner et al 2007). An extension of this model to an elliptical boundary was realized by Vandas & Romashets (2003).…”

Section: Introductionmentioning

confidence: 99%

Magnetic cloud models with bent and oblate cross-section boundaries

Démoulin¹,

2009

A&A

Context. Magnetic clouds (MCs) are formed by magnetic flux ropes that are ejected from the Sun as coronal mass ejections. These structures generally have low plasma beta and travel through the interplanetary medium interacting with the surrounding solar wind. Thus, the dynamical evolution of the internal magnetic structure of a MC is a consequence of both the conditions of its environment and of its own dynamical laws, which are mainly dominated by magnetic forces. Aims. With in-situ observations the magnetic field is only measured along the trajectory of the spacecraft across the MC. Therefore, a magnetic model is needed to reconstruct the magnetic configuration of the encountered MC. The main aim of the present work is to extend the widely used cylindrical model to arbitrary cross-section shapes. Methods. The flux rope boundary is parametrized to account for a broad range of shapes. Then, the internal structure of the flux rope is computed by expressing the magnetic field as a series of modes of a linear force-free field. Results. We analyze the magnetic field profile along straight cuts through the flux rope, in order to simulate the spacecraft crossing through a MC. We find that the magnetic field orientation is only weakly affected by the shape of the MC boundary. Therefore, the MC axis can approximately be found by the typical methods previously used (e.g., minimum variance). The boundary shape affects the magnetic field strength most. The measurement of how much the field strength peaks along the crossing provides an estimation of the aspect ratio of the flux-rope cross-section. The asymmetry of the field strength between the front and the back of the MC, after correcting for the time evolution (i.e., its aging during the observation of the MC), provides an estimation of the cross-section global bending. A flat or/and bent cross-section requires a large anisotropy of the total pressure imposed at the MC boundary by the surrounding medium. Conclusions. The new theoretical model developed here relaxes the cylindrical symmetry hypothesis. It is designed to estimate the cross-section shape of the flux rope using the in-situ data of one spacecraft. This allows a more accurate determination of the global quantities, such as magnetic fluxes and helicity. These quantities are especially important for both linking an observed MC to its solar source and for understanding the corresponding evolution.