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

Abstract

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 , β a ,∥ )-plane have a rhombic-shaped form around β a ,∥  ∼ 1. The boundaries of the temperature anisotropy at β a ,∥  > 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 β a ,∥  < 1 is still under debate. One possible option is Coulomb collisions, which we revisit in the current work. We derive the relaxation rate of the temperature anisotropy in a bi-Maxwellian plasma that we then study analytically and by observed proton data from WIND . We found that increases toward small β p ,∥  < 1. We matched the data distribution in the ( A p , β p ,∥ )-plane with the constant contour 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 , β p ,∥ )-plane. Thus, Coulomb collisions are an interesting candidate for explaining the limitations of the temperature anisotropy in the solar wind with small β a ,∥  < 1 at 1 au.