On quantifying the impact of CME magnetic flux and mass erosion on geo-effectiveness 

Coronal mass ejections (CMEs) undergo erosion, deflection, and deformation upon interaction with the solar wind structures and with other transients during their propagation in the solar corona and heliosphere. In this work, we focus on the process of the erosion of CMEs in the heliosphere, which impacts their magnetic flux content, and its effect on altering their geo-effectiveness. To quantify the erosion of CME magnetic flux and mass in various solar wind environments, we employ 3D magnetohydrodynamic (MHD) simulations.  To create a simulated solar wind background resembling a solar minimum period (for simplistic cases), we utilize the EUropean Heliosphere FORecasting Information Asset (EUHFORIA, Pomoell and Poedts, 2018) model. Through this background, we evolved a CME from 0.1 au to 2 au using a linear force-free spheromak model. We employ two distinct methods to assess erosion of magnetic flux and mass.  First, the in-situ method, where the single point data at Earth or any other location is used to quantify the magnetic flux erosion. The orientation of the CME in the magnetic cloud frame of reference is determined through minimum variance analysis, and the accumulated axial and azimuthal flux is computed (Dasso et al, 2006). Imbalances in the flux profile serve as indicators of erosion.  The second method relies on 3D simulation data, tracking the mass of the magnetic cloud in three dimensions based on criteria developed by Asvestari et al, 2022 for the spheromak model. With this method we can identify the 3D volume of the spheromak, assess its orientation, rotation, and magnetic properties in 3D in the local frame of reference of the spheromak structure. This technique provides us with the magnetic flux content of the spheromak and how it changes in space and time.  Following a benchmarking process between the two erosion quantification methods, we conduct simulations to explore the sensitivity of CME erosion to variations in geometrical and magnetic field parameters. The study also investigates the influence of interactions with high-speed streams on erosion. Lastly, we apply an empirical Dst model (O’Brien and McPherron, 2000) to quantify geo-effectiveness and establish correlations with estimated erosion in all cases.