Estimates of magnetic cloud expansion at 1 AU
Abstract. In this study we analyze 53 magnetic clouds (MCs) of standard profiles observed in WIND magnetic field and plasma data, in order to estimate the speed of MC expansion (VE) at 1 AU, where the expansion is investigated only for the component perpendicular to the MCs' axes. A high percentage, 83%, of the good and acceptable quality cases of MCs (N(good)=64) were actually expanding, where "good quality" as used here refers to those MCs that had relatively well determined axial attitudes. Two different estimation methods are employed. The "scalar" method (where the estimation is denoted VE,S) depends on the average speed of the MC from Sun-to-Earth (<VS-to-E>), the local MC's radius (RO), the duration of spacecraft passage through the MC (at average local speed <VC>), and the assumption that <VS-to-E>=<VC>. The second method, the "vector determination" (denoted VE,V), depends on the decreasing value of the absolute value of the Z-component (in MC coordinates) of plasma velocity (|VZ|) across the MC, the closest approach distance (YO), and estimated RO; the Z-component is related to spacecraft motion through the MC. Another estimate considered here, VE,V', is similar to VE,V in its formulation but depends on the decreasing |VZ| across part of the MC, that part between the maximum and minimum points of |VZ| which are usually close to (but not the same as) the boundaries points. The scalar means of estimating VE is almost independent of any MC parameter fitting model results, but the vector means slightly depends on quantities that are model dependent (e.g. |CA|≡|YO|/RO). The most probable values of VE from all three means, based on the full set of N=53 cases, are shown to be around 30 km/s, but VE has larger average values of <VE,S>=49 km/s, <VE,V>=36 km/s, and <VE,V'>=44 km/s, with standard deviations of 27 km/s, 38 km/s, and 38 km/s, respectively. The linear correlation coefficient for VE,S vs. VE,V' is 0.85 but is lower (0.76) for VE,S vs. VE,V, as expected. The individual values of VE from all three means are usually well below the local Alfvén velocities, which are on average (for the cases considered here) equal to 116 km/s around the inbound boundary, 137 km/s at closest approach, and 94 km/s around the outbound boundary. Hence, a shock upstream of a MC is not expected to be due to MC expansion. Estimates reveal that the errors on the "vector" method of estimating VE (typically about ±7 km/s, but can get as large as ±25 km/s) are expected to be markedly smaller than those for the scalar method (which is usually in the range ±(15⇔20) km/s, depending on MC speed). This is true, despite the fact that |CA| (on which the vector method depends) is not always well determined by our MC parameter fitting model (Lepping et al., 1990), but the vector method only weakly depends on knowledge of |CA|.