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Fig. 6.

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Double logarithmic plot showing the average proton density, Np, of the different ICME structures and upstream solar wind (SW) versus solar distance, R, in au. The linear regression lines for each structure from our study are obtained with: Np, SW(R) = 7.0  ×  R−2.1; Np, ME(R) = 7.1  ×  R−2.4; Np, sheath(R) = 22.3  ×  R−1.7; Np, LE(R) = 26.6  ×  R−1.5. The uncertainty ranges for the ME density are derived from previous Helios results from Liu et al. (2005), Wang et al. (2005), Leitner et al. (2007). For the SW density estimate we added model results given in Scolini et al. (2021). For the sheath density we use as upper and lower uncertainty the standard deviation as derived in this study. Extrapolating the Helios based fits for SW, ME and sheath density, three intersection sectors are derived (1, 2a–2b, 3a–3b which are marked by black arrows). 1: between sheath density and upstream solar wind density at about 0.06 au – which can be interpreted as average starting distance for sheath formation; 2a–2b: between sheath density and ME density ranging from 0.09–0.28 au; 3a–3b: between ME density and the upstream solar wind density ranging from 0.45–1.18 au. Complementary we show PSP sheath and ME density measurements for a set of five events supporting the general trend derived from Helios observations. In addition, we provide results for the mean calculated ME density (solid gray line with upper and lower limit, i.e., standard deviation, marked as light gray dashed lines) over 0.07–0.14 au based on indirect ME density measurements derived by Temmer et al. (2021).

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