Validation of single spacecraft methods for collisionless shock velocity estimation

The velocity of a collisionless shock (CS) is an important parameter in the determination of the spatial scales of the shock. The spatial scales of the shock determine the processes that guide the energy dissipation, which is related to the nature of the shock. During the pre-ISEE era, estimations of relative shock-spacecraft velocity (VSh) were based on spatial scales of the shock front regions, in particularly the foot. Multispacecraft missions allow more reliable identification of VSh. The main objective of this study is to examine the accuracy of two single spacecraft methods, which use the foot region of quasi-perpendicular shocks in order determine VSh. This is important for observational shock studies based on a single spacecraft data such as Venus Express (VEX) and THOR, a proposed single spacecraft mission of European Space Agency. It is shown that neither method provides estimates with an accuracy comparable to multipoint measurements of VSh. In the absence of alternative techniques to identify the VSh and therefore the spatial scales of the shocks, the methods can be used to provided order of magnitude estimations for the spatial scales of the shock front. Observations of the Venusian bow shock from VEX data have been used as an illustrative example for the application of these methods to estimate the shock spatial scale and the corresponding errors of this estimation. It is shown that the spatial width of the ramp of the observed shock is L ∼ 3.4 ± 1.4c/ωpe