Research ArticleSPACE SCIENCES

Direct evidence of nonstationary collisionless shocks in space plasmas

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Science Advances  27 Feb 2019:
Vol. 5, no. 2, eaau9926
DOI: 10.1126/sciadv.aau9926
  • Fig. 1 Bow shock ramp substructure.

    An illustration of the magnetic profile (|B|) of the quasi-perpendicular terrestrial bow shock as a function of time and tangential (L) distance along the shock surface. The profile shows the following regions: upstream/solar wind, shock foot, ramp, overshoot, and the downstream/magnetosheath. The time series panel corresponds to cuts of artificial data in the plane perpendicular to the shock normal along L3 (red) and L4 (black). The blue trace represents the difference between the two cuts. It is this difference that is used to shade the shock surface to highlight the substructure location. It is clear that depending on the localized position of the spacecraft (in this case on electron scales), one may observe the structure and another will not. If the separation is too large, both may miss the structure or it will be impossible to correlate simultaneous measurements. In our case, the probe locations were at ideal locations and well suited to resolving the theoretically predicted scales.

  • Fig. 2 Bow shock wavelet spectrogram.

    Plotted in (A) are the time series of the magnetic field modulus measured by the Clusters 3 (red) and 4 (black) FluxGate Magnetometer instruments during the bow shock traversal. The blue trace shows the difference (4–3) between the measurements. (B) Wavelet spectrogram of the C4 bow shock crossing. (C) Wavelet spectrogram but computed with the difference data. The vertical lines in each panel indicate the location of the electron-scale substructure, which is the focus of this paper. There is a clear enhancement of wavelet power at the times corresponding to this structure (white dashed boxes). Since the difference data plotted in (C) have the shock ramp removed, then it is the direct evidence of an electron-scale ramp substructure within the ramp. For more evidence that this is associated with a nonstationary shock front, we provide a more detailed view of the shock crossing and the three-dimensional evolution of the magnetic field components during the ramp substructure in Fig. 3.

  • Fig. 3 Evidence of electron-scale subshock structure.

    (A) The magnetic field modulus of the bow shock crossing by C3 (blue) and C4 (red). The difference (|B4| − |B3|) is plotted in (B). The red shaded region marks a large difference in the shock ramp between C3 and C4. The structure in (B) is evidence that the shock ramp substructure varies over electron scales, because features in this dataset are dictated by the inter-spacecraft separation of 7 km. We have marked the spatial length scales of the ramp and the substructure (see the Materials and Methods section for how these lengths were derived). (C to E) Hodograms derived from the application of minimum variance analysis to the magnetic field differences in the shock frame. The variations appear elliptically polarized and propagate almost parallel to the shock normal, consistent with whistler waves on the predicted scales of the GC model of shock front reformation (17) (see the Materials and Methods section for technical details of the hodograms). UT, Universal Time.

  • Fig. 4 C4 Bow shock electric field on 24 January 2015.

    Indicated by the red trace is the electric field (Ey) measured by the C4 EFW instrument in the spacecraft frame. The start of the large oscillations marks the start of the shock transition region. The dotted black trace is the modulus of the magnetic field for reference. The large amplitude Ey variations occur in concert with the magnetic structure on the shock ramp indicated by the shaded red region. Note that the electric field structures take place on electron scales, which are theoretically predicted by the model of Krasnoselskikh et al. (17).

Supplementary Materials

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. C3 bow shock normal.
    • Fig. S2. C1 to C4 bow shock crossings.
    • Fig. S3. Cluster spacecraft constellation.

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