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>1 >0.9 >0.8 >0.7 >0.6 >0.5 >0.4 >0.3 >0.2 >0.1 >0.0

Figure 8.16. Histogram of Walén slopes for 35 Cluster crossings of the magnetopause on July 5, 2001. Only crossings for which the magnitude of the Walen correlation coefficient exceeded 0.85 are included. There were 26 cases with a positive slope, implying reconnection sites tailward of Cluster, and 9 with negative slope, implying reconnection sites sunward of Cluster. (After Paschmann et al., 2004).

>1 >0.9 >0.8 >0.7 >0.6 >0.5 >0.4 >0.3 >0.2 >0.1 >0.0

Figure 8.16. Histogram of Walén slopes for 35 Cluster crossings of the magnetopause on July 5, 2001. Only crossings for which the magnitude of the Walen correlation coefficient exceeded 0.85 are included. There were 26 cases with a positive slope, implying reconnection sites tailward of Cluster, and 9 with negative slope, implying reconnection sites sunward of Cluster. (After Paschmann et al., 2004).

fairly rarely is the Walen slope near +1or — 1. A far more common situation is that it has smaller magnitude. If the correlation coefficient remains high, such a result indicates that the flow is still field-aligned but is sub-Alfvenic rather than Alfvenic. In the next Section, a number of reasons will be given why the stress balance in directions parallel to the magnetopause can involve, and even be dominated, by terms other than those in a one-dimensional RD, where a simple balance exists between the j x B force and the centrifugal force associated with the field aligned plasma flow. Thus smaller Walen slopes may still be consistent with reconnection, although scenarios are also possible where modest field-aligned flows occur without reconnection. Note also that slow shocks involve exclusively sub-Alfvenic flow, whereas the upstream and downstream states of an intermediate shock are super-Alfvenic and sub-Alfvenic, respectively. Walen slopes significantly larger than unity, with a high correlation coefficient, are essentially never seen.

The histogram in Figure 8.16 shows results of a statistical survey of Walen slopes for all those complete magnetopause crossings by C1 and C3 on July 5, 2001, that yielded a Walen correlation coefficient better than 0.85. A total of 35 crossings meeting this criterion were identified, of which 9 had negative slope and 26 had positive slope. The majority had slope magnitudes in the range 0.2-0.8. To the extent that these various slopes indicate that reconnection-associated plasma flow into the magnetosphere was occurring, the fact that there were many more cases having positive than negative slope would indicate that on this day the reconnection sites were located mostly tailward of Cluster or were originally created sunward, but had moved tailward by the time of the Cluster crossings (the spacecraft location is indicated in Figure 8.15a). In 9 cases the reconnection sites were located sunward of the spacecraft.

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