Electron temperature in the solar wind: Generic radial variation from kinetic collisionless models

Abstract

We calculate analytically the radial profile of the average electron temperature in the solar wind with a kinetic collisionless model. The electron temperature profile at large distances r is the sum of a term ~r^-4/3 plus a constant, with both terms of the same order of magnitude near r~1AU. This result is generic as it is weakly dependent on the particle velocity distributions in the corona. It provides a natural explanation for the observed electron temperature profile near 1 AU, which is in the low or middle part of the range between isothermal and adiabatic behaviors. The r^-4/3 term comes from the isotropically distributed electrons confined by the heliospheric electric potential, which is found to have a similar radial variation. The constant term comes from the parallel temperature of the electrons energetic enough to escape. The calculated profile flattens as r increases and tends to be flatter in the high-speed wind. We also give simple explicit expressions for the electron temperature and density at large distances and for the terminal wind velocity as a function of coronal parameters when the electron velocity distribution is a Kappa function, which is close to a Maxwellian with a suprathermal tail.