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Many solar wind observations at 1 au indicate that the proton (as well as electron) temperature anisotropy is limited. The data distribution in the (A(a), beta(a),(parallel to))-plane have a rhombic-shaped form around beta(a),(parallel to) similar to 1. The boundaries of the temperature anisotropy at beta(a),(parallel to) > 1 can be well explained by the threshold conditions of the mirror (whistler) and oblique proton (electron) firehose instabilities in a bi-Maxwellian plasma, whereas the physical mechanism of the similar restriction at beta(a),(parallel to) < 1 is still under debate. One possible option is Coulomb collisions, which we revisit in the current work. We derive the relaxation rate nu(A)(aa) of the temperature anisotropy in a bi-Maxwellian plasma that we then study analytically and by observed proton data from WIND. We found that nu(A)(pp) increases toward small beta(p),(parallel to) < 1. We matched the data distribution in the (A(p), beta(p),(parallel to))-plane with the constant contour nu(A)(pp) = 2.8 . 10(-6) s(-1), corresponding to the minimum value for collisions to play a role. This contour fits rather well the left boundary of the rhombic-shaped data distribution in the (A(p), beta(p),(parallel to))-plane. Thus, Coulomb collisions are an interesting candidate for explaining the limitations of the temperature anisotropy in the solar wind with small beta(a),(parallel to) < 1 at 1 au.
The general electromagnetic fluctuation theory is a powerful tool to analyze the magnetic fluctuation spectrum of a plasma. Recent works utilizing this theory for a magnetized non-relativistic isotropic Maxwellian electron-proton plasma have demonstrated that the equilibrium ratio of vertical bar delta B vertical bar/B-0 can be as high as 10(-12). This value results from the balance between spontaneous emission of fluctuations and their damping, and it is considerably smaller than the observed value vertical bar delta B vertical bar/B-0 in the solar wind at 1 au, where 10(-3) less than or similar to vertical bar delta B vertical bar/B-0 less than or similar to 10(-1). In the present manuscript, we consider an anisotropic bi-Maxwellian distribution function to investigate the effect of plasma instabilities on the magnetic field fluctuations. We demonstrate that these instabilities strongly amplify the magnetic field fluctuations and provide a sufficient mechanism to explain the observed value of vertical bar delta B vertical bar/B-0 in the solar wind at 1 au.