Proton temperature anisotropy in the magnetosheath: comparison of MHD modeling with CLUSTER data

We compare the magnetosheath properties observed by the CLUSTER spacecraft, during four intervals lasting several hours, with the numerical 3-D double-adiabatic MHD model using upper limits of the proton temperature anisotropy T\perp p/T∥ p deduced from the kinetic thresholds of the proton-cyclotron and mirror instabilities (Samsonov et al., 2001). Generally the numerical predictions, where the input parameters are given by the solar wind ACE data, agree well with the observations, except that average values of the predicted density sometimes differ from the observed ones. The reason of this discrepancy could be a wrong approximation of the magnetopause shape in our local magnetosheath model. The predicted temperature anisotropy is equal to or slightly smaller than the observed one. Then we compare the observed temperature anisotropy with the theoretical kinetic thresholds, without MHD modeling. The considered thresholds are those for which the maximum growth rate, normalized to the proton cyclotron frequency, is γ_m/Ømega_p = 10-4 and γ_m/Ømega_p = 10-2. In the plane (β∥ p,T\perp p/T∥ p), the data points are close to the threshold of the proton- cyclotron instability for a relatively small β∥ p: what confirms that this instability constrains the temperature anisotropy. For a larger β∥ p, the data points are close to the thresholds of both the mirror and the proton-cyclotron instability, so that both constrain the anisotropy. We analyze several magnetic field power spectra between 0.003~Hz and 10~Hz both in low-β and in high-β regions. This analysis shows that the values of β∥ p and T\perp p/T∥ p are important but not the only parameters which determine the dominant mode (compressive or transverse, i.e. mirror or proton-cyclotron) at the proton scale in the magnetosheath. Other factors, such as the local percentage of α particles or the compression rate, could be also important.