Limits on the core temperature anisotropy of solar wind protons

We analyse the temperature anisotropy of the protons in the solar wind and thereby concentrate on plasma data obtained in the year 1976 of the Helios 1 and Helios 2 missions. We derive the core proton temperatures T perpendicularto and T parallel, in the directions perpendicular and parallel to the magnetic field, as well as the core parallel plasma beta, β parallel. The data are separately analysed for two distance ranges, R≤0.4 AU and >0.4 AU, and divided into 24 bins for the plasma beta, in the range from β parallel =0.1 to β parallel =10, and into 72 bins for the total temperature anisotropy, A=1-T perpendicularto /T parallel, which is here considered in the range from -0.9 to 0.9. The number of spectra in each bin is determined to obtain distributions. The statistical results are presented in two-dimensional histograms. Fore each column we define a critical upper and lower limit of the anisotropy. The resulting empirical points are compared with the known theoretical instability thresholds. The protons are found to come with increasing radial distance closer to the fire-hose instability threshold