On Fields and Mass Constraints for the Uniform Propagation of Magnetic-Flux Ropes Undergoing Isotropic Expansion

Abstract

An analytical 3-D magnetohydrodynamic (MHD) solution of a magnetic-flux rope (FR) is presented. This FR solution may explain the uniform propagation, beyond ∼ 0.05 AU, of coronal mass ejections (CMEs) commonly observed by today’s missions like The Solar Mass Ejection Imager (SMEI), Solar and Heliospheric Observatory (SOHO) and Solar Terrestrial Relations Observatory (STEREO), tracked to tens of times the radius of the Sun, and in some cases up to 1 AU, and/or beyond. Once a CME occurs, we present arguments regarding its evolution based on its mass and linear momentum conservation. Here, we require that the gravitational and magnetic forces balance each other in the framework of the MHD theory for a simple model of the evolution of a CME, assuming it interacts weakly with the steady solar wind. When satisfying these ansatze we identify a relation between the transported mechanical mass of the interplanetary CME with its geometrical parameters and the intensity of the magnetic field carried by the structure. In this way we are able to estimate the mass of the interplanetary CME (ICME) for a list of cases, from the Wind mission records of ICME encountered near Earth, at 1 AU. We obtain a range for masses of ∼ 109 to 1013 kg, or assuming a uniform distribution, of ∼ 0.5 to 500 cm−3 for the hadron density of these structures, a result that appears to be consistent with observations.