Global and local expansion of magnetic clouds in the inner heliosphere

Abstract: Observations of magnetic clouds (MCs) are consistent with the presence of flux ropes detected in the solar wind (SW) a few days after their expulsion from the Sun as coronal mass ejections (CMEs). Both the \textit{in situ} observations of plasma velocity profiles and the increase of their size with solar distance show that MCs are typically expanding structures. The aim of this work is to derive the expansion properties of MCs in the inner heliosphere from 0.3 to 1 AU.We analyze MCs observed by the two Helios spacecraft using \textit{in situ} magnetic field and velocity measurements. We split the sample in two subsets: those MCs with a velocity profile that is significantly perturbed from the expected linear profile and those that are not. From the slope of the \textit{in situ} measured bulk velocity along the Sun-Earth direction, we compute an expansion speed with respect to the cloud center for each of the analyzed MCs. We analyze how the expansion speed depends on the MC size, the translation velocity, and the heliocentric distance, finding that all MCs in the subset of non-perturbed MCs expand with almost the same non-dimensional expansion rate ($\zeta$). We find departures from this general rule for $\zeta$ only for perturbed MCs, and we interpret the departures as the consequence of a local and strong SW perturbation by SW fast streams, affecting the MC even inside its interior, in addition to the direct interaction region between the SW and the MC. We also compute the dependence of the mean total SW pressure on the solar distance and we confirm that the decrease of the total SW pressure with distance is the main origin of the observed MC expansion rate. We found that $\zeta$ was $0.91\pm 0.23$ for non-perturbed MCs while $\zeta$ was $0.48\pm 0.79$ for perturbed MCs, the larger spread in the last ones being due to the influence of the environment conditions on the expansion.