Coulomb Collisions as a Candidate for Temperature Anisotropy Constraints in the Solar Wind

Many solar wind observations at 1 au indicate that the proton (as well as electron) temperature anisotropy is limited. The data distribution in the (Aa, βa,∥)-plane have a rhombic-shaped form around βa,∥ ∼ 1. The boundaries of the temperature anisotropy at βa,∥ > 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 βa,∥ < 1 is still under debate. One possible option is Coulomb collisions, which we revisit in the current work. We derive the relaxation rate ${\nu }_{{aa}}^{A}$ of the temperature anisotropy in a bi-Maxwellian plasma that we then study analytically and by observed proton data from WIND. We found that ${\nu }_{{pp}}^{A}$ increases toward small βp,∥ < 1. We matched the data distribution in the (Ap, βp,∥)-plane with the constant contour ${\nu }_{{pp}}^{A}=2.8\cdot {10}^{-6}$ 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 (Ap, βp,∥)-plane. Thus, Coulomb collisions are an interesting candidate for explaining the limitations of the temperature anisotropy in the solar wind with small βa,∥ < 1 at 1 au.