Extended Data Fig. 5: Wave phase speeds from MMS observations.
From: Transmission of foreshock waves through Earth’s bow shock
Total magnetic power as a function of the wave phase speeds vph = ω/k. The phase speeds correspond to the recovered points obtained from the Bellan method and are organised as a function of the orientation of the wavevector, with a negative speed indicating earthward propagation. The data points in black are the same as shown in Fig. 5, for which the current density was obtained from the particle measurements. Those in red are based on the current density calculated using the curlometer method. The results from both approaches are in excellent agreement. The vertical blue line denotes the Alfvén speed. The dashed lines denote the phase speeds for largest and smallest phase speeds \({v}_{{{{\rm{A}}}}}\cos ({\theta }_{{{{\rm{kB}}}}})\) and the shaded cyan area denotes the region where the speeds are consistent with Alfvén waves or advected structures.
