On modeling ICME cross sections as static MHD columns

Solar coronal mass ejections (CMEs) are observed to expand during their propagation through the solar wind. However, their cross-sections are usually modeled as static plasma columns within the framework of magnetohydrodynamics (MHD). In this study, we test the validity of this approach using in-situ plasma data from 151 magnetic clouds (MCs) observed by the WIND spacecraft and 45 observed by the Helios spacecrafts. We find that the most probable cross-section expansion speeds for the WIND events are only ≈ 0.06 times the Alfvén speed inside the MCs while the most probable cross-section expansion speeds for the Helios MCs is ≈ 0.03. Hence, the MC cross-sections can be considered approximately static over an Alfvén crossing timescale. Using estimates of electrical conductivity arising from Coulomb collisions, we find that the Lundquist number inside MCs is high ( ≈ 10¹³), suggesting that the MHD description is well justified. The Joule heating rates using our conductivity estimates are several orders of magnitude lower than the requirement for plasma heating inside MCs at 1 AU. The low heating rates are consistent with the MHD description which assumes no dissipation. However, the discrepancy with the heating requirement suggests possible departures from MHD and the need for a better understanding of plasma heating inside MCs.