Modeling of the three-dimensional motion of toroidal magnetic clouds in the inner heliosphere

¹ Center for Plasma Astrophysics, K.U.Leuven, 3001 Leuven, Belgium e-mail: Stefaan.Poedts@wis.kuleuven.be
² IZMIRAN, Troitsk, Moscow Region 142190, Russia
³ Solar Observatory of Prairie View A& M University, Prairie View 77446, USA
⁴ Astronomical Institute, Boční II 1401, 141 31 Praha 4, Czech Republic

Received: 9 August 2006
Accepted: 19 January 2007

Abstract

Context.The motion of a magnetic cloud through the heliosphere is governed by three main forces, viz. the diamagnetic force, the drag force, and gravity. Some recently derived formulas enabling the calculation of the ambient magnetic field around a toroidal magnetic cloud are applied to calculate the diamagnetic force acting on the cloud and to determine the cloud dynamics.

Aims.The aim is to determine the three dimensional velocity profiles and the trajectory of the magnetic cloud, as well as the evolution of the orientation of the cloud axis from the calculated moment of the force.

Methods.The method applied in this study consists of three steps. First, the r-component of the magnetic field at is derived from a spherical harmonic analysis. Next, the field distribution in the entire heliosphere, including the spiral structure, is reconstructed in a way that is consistent with this boundary condition at as well as with actual measurements at 1 AU. Then, a toroid is launched at a point obtained from solar observations of a specific event and the initial size, orientation, and velocity of this toroid is estimated from these observational data as well.

Results.The three dimensional velocity profiles and the trajectory of the magnetic cloud, as well as the evolution of the orientation of the cloud axis have been determined for a toroidally shaped cloud moving in the interplanetary medium taking into account a spiral magnetic field.