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Figure 5.1. Bow shock normals (short lines) deduced from four spacecraft timings, plotted extending from their measured locations (circles). The three panels show the projection of the positions and normals onto the X-Y, X-Z and Y-Z GSE planes. Note that shocks near the nose are not sampled due to the polar Cluster orbit. From Horbury et al. (2002).

Figure 5.1. Bow shock normals (short lines) deduced from four spacecraft timings, plotted extending from their measured locations (circles). The three panels show the projection of the positions and normals onto the X-Y, X-Z and Y-Z GSE planes. Note that shocks near the nose are not sampled due to the polar Cluster orbit. From Horbury et al. (2002).

Figure 5.2. Histograms of angular difference between different estimates of quasi-perpendicular bow shock normals. Left: comparison of Cluster four-spacecraft timing normals with normals from a parameterised bow shock model (Peredo et al., 1995). The agreement is good, implying both are typically reliable estimators of the normal. Middle: comparison of timing normals with magnetic field coplanarity. Right: comparison of timing-based normal estimates using magnetic field and spacecraft potential to calculate timings. Left and middle panels from Horbury et al. (2002). Right panel provided by T. S. Horbury and S. D. Bale.

mals for dBn ~ 90°, is apparent in Figure 5.3, which shows the deviation of coplanarity vectors from timing-based normal estimates for the shocks considered by Horbury et al. (2002): when dBn ~ 90°, the scatter is very large. However, Horbury et al. found that deviations were still large (on average 22° ± 4°) for shocks with dBn < 90°. This implies that coplanarity estimates of shock orientation can have significant errors even for moderate dBn and they must therefore be treated with caution when using single spacecraft data. This is an example of how Cluster multi-spacecraft analysis can help us to interpret other, single spacecraft, data sets.

Horbury et al. (2002) used magnetic field profiles to estimate the shock crossing time at the Cluster spacecraft. However, other parameters can be used: for example, Maksimovic et al. (2003) and Bale et al. (2003) used the spacecraft potential, a

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