Fig. 5: Experimental wave properties obtained from MMS observations.
From: Transmission of foreshock waves through Earth’s bow shock
The data set includes all events listed in Extended Data Table 1. a–d Orientation of the wavevectors, with negative kx corresponding to earthwards propagation, as a function of the angle θkB between the wavevector and magnetic field. The data are divided between four ranges of θkB values to distinguish between nearly parallel (θkB ≈ 0° or θkB ≈ 180°), nearly perpendicular (θkB ≈ 90°) and intermediate propagation direction. The percentage in each panel indicates the fraction of data points within this θkB range. The data points marked in red (blue) correspond to those points found within the red (blue) areas in e–h and are thus consistent with the fast wave (Alfvén wave) solution from linear Vlasov theory. The points outside both areas are left in black. e–h, Recovered plasma frame wave frequencies (normalized to the ion cyclotron frequency Ωci) as a function of the wavevectors (normalized to the proton inertial length dp). These are separated by the orientation of the wavevector with respect to the mean-field direction. The red areas denote the fast wave solutions from linear Vlasov theory, and the blue areas denote the solutions expected for the Alfvén wave solutions. The percentages in red (blue) indicate the fraction of data points found within the red (blue) area. The solutions are calculated using the extreme θkB values for each angle range and isotropic ion and electron temperatures. The extremes of proton and electron plasma β are βp = [5, 20], and βe = [1, 3], and the ratio of Alfvén speed to the speed of light is 2 × 10−4. The error bars on ω are derived from the s.d. of the velocity component in the direction of the obtained wavevector.
