Non-stationarity of the quasi-perpendicular bow shock: comparison between Cluster observations and simulations

We have performed full particle electromagnetic simulations of a quasi- perpendicular shock. The shock parameters have been chosen to be appropriate for the quasiperpendicular Earth's bow shock observed by Cluster on 24 January 2001 (Lobzin et al., 2007). We have performed two simulations with different ion to electron mass ratio: run 1 with m(i)/m(e) = 1840 and run 2 with m(i)/m(e) = 100. In run 1 the growth rate of the modified two- stream instability (MTSI) is large enough to get excited during the reflection and upstream gyration of part of the incident solar wind ions. The waves due to the MTSI are on the whistler mode branch and have downstream directed phase velocities in the shock frame. The Poynting flux (and wave group velocity) far upstream in the foot is also directed in the downstream direction. However, in the density and magnetic field compression region of the overshoot the waves are refracted and the Poynting flux in the shock frame is directed upstream. The MTSI is suppressed in the low mass ratio run 2. The low mass ratio run shows more clearly the non-stationarity of the shock with a larger time scale of the order of an inverse ion gyrofrequency (Omega(ci)): the magnetic field profile flattens and steepens with a period of similar to 1.5 Omega(-1)(ci). This non-stationarity is different from reformation seen in previous simulations of perpendicular or quasi-perpendicular shocks. Beginning with a sharp shock ramp the large electric field in the normal direction leads to high reflection rate of solar wind protons. As they propagate upstream, the ion bulk velocity decreases and the magnetic field increases in the foot, which results in a flattening of the magnetic field profile and in a decrease of the normal electric field. Subsequently the reflection rate decreases and the whole shock profile steepens again. Superimposed on this ' breathing' behavior are in the realistic mass ratio case the waves due to the MTSI. The simulations lead us to a re-interpretation of the 24 January 2001 bow shock observations reported by Lobzin et al. (2007). It is suggested that the high frequency waves observed in the magnetic field data are due to the MTSI and are not related to a nonlinear phase standing whistler. Different profiles at the different spacecraft are due to the non-stationary behavior on the larger time scale.