On modeling ICME cross-sections as static MHD columns

TL;DR

This study tests the common assumption that magnetic cloud cross-sections are static in MHD models by analyzing in-situ data, finding they are nearly static and well-described by MHD, but with heating rates too low to explain observed plasma heating.

Contribution

The paper provides empirical evidence supporting the static MHD approximation for MC cross-sections and evaluates the plasma heating rates, highlighting potential limitations of MHD in explaining heating.

Findings

MC cross-sections expand very slowly, about 0.03-0.06 times the Alfvén speed.

High Lundquist number (~10^13) indicates MHD is valid inside MCs.

Computed Joule heating rates are much lower than needed for plasma heating.

Abstract

Solar coronal mass ejections are well known to expand as they propagate through the heliosphere. Despite this, their cross-sections are usually modeled as static plasma columns within the magnetohydrodynamics (MHD) framework. 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 $\approx 0.06$ times the Alfv\'en speed inside the MCs while the most probable cross-section expansion speeds for the Helios events is $\approx 0.03$. MC cross-sections can thus be considered to be nearly static over an Alfv\'en crossing timescale. Using estimates of electrical conductivity arising from Coulomb collisions, we find that the Lundquist number inside MCs is high ($\approx 10^{13}$), 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 near the Earth. While the (low) heating rates we compute are consistent with the MHD description, the discrepancy with the heating requirement points to possible departures from MHD and the need for a better understanding of plasma heating in MCs.