Study of Ion Temperature Anisotropy Boundaries in the Magnetosheath

The magnetosheath plasma often exhibits proton temperature anisotropy which may develop several instabilities. For anisotropy Tperp>Tpara, where Tperp and Tpara are the perpendicular and parallel (to the ambient magnetic field) proton temperatures, respectively, electromagnetic ion cyclotron (EMIC) and mirror mode instabilities can be excited, while for Tperp<Tpara, the parallel and oblique fire hose instabilities will occur. These instabilities in turn will limit the development of large anisotropies. A marginal condition for the proton temperature anisotropy instabilities has been obtained [Hellinger et al., 2006] with linear theory, by assuming bi-Maxwellian protons, in the form of Tperp/Tpara = 1+ a /(beta_para-beta_0)^b, where a, b, and beta_0 are fitting parameters for the threshold condition of maximum growth rate γmax =10^-3 ωcp, and ωcp is the proton cyclotron frequency. We have used plasma and magnetic field observations from several magnetosheath passes of THEMIS and Cluster spacecraft to examine the anisotropy boundary and compare the observations with the theoretical stability boundary. Three wave parameters |δB||/B0|, |δBperp/B0|, and the magnetic compressibility, δB||^2/( δB||^2+ δBperp^2), are calculated and distributions of their intensities on the Tperp/Tpara vs beta_para plane are examined. The data are shown to cluster around the thresholds of the mirror mode and the EMIC mode. For compressional waves there exist enhancements above the mirror mode threshold, which may indicate evolving process of the magnetosheath unstable plasma. The transverse variations are better constrained by the theoretical EMIC marginal curve. The distributions are notably different compared to previous observations of the solar wind fluctuations, which are enhanced along the temperature anisotropy thresholds of the four instabilities, indicating that the proton temperature anisotropy in the solar wind is constrained by the threshold defined in the above equation. We will discuss the interpretation of the results which may provide observational support or constraints on the theoretical and modeling developments of the marginal condition for the proton temperature anisotropy instabilities in the magnetosheath.