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 spacecraft. We find that the most probable cross-section expansion speeds for the WIND events are only \(\approx 0.06\) times the Alfvén 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 Alfvén 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.
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Acknowledgments
We acknowledge the reviewer for constructive criticism that helped improve the manuscript. DB acknowledges a PhD studentship from the Indian Institute of Science Education and Research, Pune. DB also acknowledges the NAMASTE+ programme (funded by DAAD) and the ICASEC for providing the scholarship during his visit to Georg-August Universität Göttingen, Göttingen, Germany. DB is thankful to Dr. Niclas Mrotzek for his help and valuable discussions.
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Appendix A: Data Tables
Appendix A: Data Tables
1.1 A.1 Events from the WIND ICME Catalogue
1.2 A.2 Events from the Helios Observation
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Bhattacharjee, D., Subramanian, P., Bothmer, V. et al. On Modeling ICME Cross-Sections as Static MHD Columns. Sol Phys 297, 45 (2022). https://doi.org/10.1007/s11207-022-01982-x
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DOI: https://doi.org/10.1007/s11207-022-01982-x