Helicity analysis for expanding magnetic clouds:: A case study

Magnetic Clouds (MCs) are the interplanetary counterpart of coronal mass ejections (CMEs). They transport to the interplanetary medium the magnetic flux and helicity released in CMEs by the Sun. At 1 AU from the Sun, MCs are generally modeled as static flux ropes, i.e., considering them as rigid bodies traveling through the solar wind. However, the velocity profile of some MCs presents clear signatures of a significant expansion while observed in situ by a spacecraft in the heliosphere. We present here an analysis of the magnetic structure of an expanding magnetic cloud observed during the raising phase of solar cycle 23 by the spacecraft Wind. We consider a dynamical model, based on a self-similar behavior for the cloud radial velocity. We assume a free expansion for the cloud, and a cylindrical linear force free field (i.e., the Lundquist's field) as the initial conditions for its magnetic configuration. We derive theoretical expressions for the magnetic flux, across a surface perpendicular to the cloud axis, and for the magnetic helicity per unit length along the tube using the self-similar model. Finally, we compute these magnitudes fitting the free parameters of the expanding model to in situ magnetic observations, and compare them with those obtained from the linear force free static model.