Influence of the Deformation of Coronal Mass Ejections on Their in-Situ Fitting with Circular-Cross-Section Flux Rope Models

Understanding the properties, especially the magnetohydrodynamic (MHD) invariants, of coronal mass ejections (CMEs) measured in-situ is key to bridging the CME properties from the Sun to interplanetary space. In order to investigate CMEs based on in-situ measurements that provide a one-dimensional (1D) cut of the CME parameters over the spacecraft trajectory, various magnetic flux rope (MFR) models have been developed, among which the models with a circular cross section are the most popular and widely used. CMEs are found to be deformed during their propagation in interplanetary space, in which the cross section may be flattened in the direction of propagation, leading to the development of an elliptical or even pancake-like shape. We use numerical MHD simulations in 2.5D to investigate the influence of the CME deformation on the in-situ fitting using two linear force-free MFR models with a circular cross section, and we focus on the axial and poloidal magnetic fluxes, which are conserved in the ideal MHD frame. We quantitatively compare the fitted axial and poloidal fluxes with those in the simulations. We find that both models underestimate the axial flux compared to that in the simulations and that such underestimations depend on the CME deformation. However, the fitting of the poloidal flux is independent of the deformation. We discuss the reasons for the axial flux underestimation and the implication of the CME deformation for the CME in-situ fitting.