Theoretical construction of solar wind proton temperature anisotropy versus beta inverse correlation

In situ observations from the Wind spacecraft that statistically analyzed the solar wind proton at 1 AU has indicated that the measured proton temperature anisotropies seems to be regulated by the oblique instabilities (the mirror and oblique firehose). This result is in contradiction with the prediction of linear kinetic theory that the ion-cyclotron (for ${\beta}_{\parallel}$ < 2) and parallel firehose (for ${\beta}_{\parallel}$ <10) would dominate over the oblique instabilities. Various kinds of physical mechanisms have been suggested to explain this disagreement between the observations and linear theory. All of the suggestions consider the solar wind as a unoform magnetized plasma. However the real space environment is replete with the intermediate spatio-temporal scale variations associated with various physical quantities, such as the magnetic field intensity and the solar wind density. In this paper we present that the pervasive intermediate-scale temporal variation of the local magnetic field intensity can lead to the modification of the proton temperature anisotropy versus beta inverse correlation for temperature-anisotropy-driven instabilities. By means of quasilinear kinetic theory involving such temporal variation, we construct the simulated solar wind proton data distribution associated the magnetic fluctuations in (${\beta}_{\parallel}$, $T_{\perp}/T_{\parallel}$) space. It is shown that the theoretically simulated proton distribution and a general trend of the enhanced fluctuations bounded by the oblique instabilities are consistent with in situ observations. Furthermore, the measure magnetic compressibility can be accounted for by the magnetic spectral signatures of the unstable modes.