Fig. 3: Wave activity along the Sun–Earth line.
From: Transmission of foreshock waves through Earth’s bow shock
a–c, Maps of the magnetic field strength (a) and its By (b) and Bz (c) components along the Sun–Earth line, as a function of x and time. The data have been high-pass filtered, with a cut-off at 40 s, to highlight the relevant frequencies, as indicated by the subscript “filt” in the variable names. The negative magnetic field strength values are due to this filtering. The cyan contour in a marks where the ion density reaches twice its solar wind value, a proxy for the shock position. The black contour in b and c marks where the magnetosonic Mach number Mms = 1. The coloured lines in the magnetosheath indicate streamlines originating from two locations associated with typical plasma velocities: bulk speed (green), Alfvén speed (blue) and fast magnetosonic speed (pink). The dashed lines correspond to an earthwards propagation in the plasma rest frame, and the dotted lines to a sunwards propagation. The outward motion of the bow shock is due to the two-dimensional (2D) setup of our simulation, as interplanetary magnetic field lines pile up in front of the magnetosphere. d, Time–position map of the magnetosonic Mach number. The white contour marks where Mms = 1. e,f, Dispersion plots obtained from the 2D Fourier transform of the magnetic field strength (e) and Bz component (f) between x = 6.5RE and x = 9RE, using unfiltered data to which a Hann window has been applied along both dimensions. On the horizontal axis, the frequencies are normalized to the ion cyclotron frequency Ωci and the wavenumber, on the vertical axis, to the proton inertial length dp. The solid yellow lines show the Courant–Friedrichs–Lewy (CFL) condition, which is the maximum speed at which information can travel in the simulation. The median bulk speed in the magnetosheath, at the locations used to calculate the 2D Fourier transform (\({v}_{{{{{\rm{bulk}}}}}_{x}}=48\) km s−1) is indicated by the dashed green line. The dash-dotted blue lines and the dotted pink lines indicate sunwards and earthwards propagation at the median Alfvén speed (vA = 145 km s−1) and median fast magnetosonic speed (vms = 360 km s−1), respectively, in the plasma rest frame.
