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 perpendicular to and T parallel to, in the directions perpendicular and parallel to the magnetic field, as well as the core parallel plasma beta, beta parallel to. The data are separately analysed for two distance ranges, R <= 0.4AU and R > 0.4AU, and divided into 24 bins for the plasma beta, in the range from beta parallel to =0.1 to beta parallel to = 10, and into 72 bins for the total temperature anisotropy, A= 1 - T perpendicular to/ T parallel to, 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. For 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.