Thermal coupling of protons and neutral hydrogen in the fast solar wind

We investigate the coupling between neutral hydrogen atoms and protons in the corona for a range of proton temperatures reaching a maximum of 6×10⁶K, as recently inferred from observations of the Ly α spectral line profiles by Kohl et al. [1996]. We adopt the approach used by Olsen et al. [1994], whereby the neutral hydrogen atoms are treated as test particles in a background electron-proton solar wind. Charge exchange between neutrals and protons, radiative recombination, collisional ionization of the neutrals, and the effects of Alfvén waves, described by a single frequency or a spectrum, are included in the model. The computations show that an anisotropy in the neutral hydrogen temperature develops in the directions parallel and perpendicular to the magnetic field within 2-3 R_S for solar wind conditions, consistent with observational constraints of the fast wind. Although T_H^⊥ exceeds T_H^∥ (~T_p) in the inner corona, the anisotropy decreases as the peak proton temperature increases, with a temperature difference of <8×10⁵K when the protons reach 6×10⁶K. We find that the effective temperature T_H(eff)^⊥, incorporating both random and wave motions of the neutral hydrogen, and the calculated Ly α line profile are independent of wave frequency. The dominant contribution to the profiles comes from T_H(eff)^⊥ at the point of closest approach to the Sun along the line of sight (LOS), although the widths of the profiles are significantly narrowed by non-90° scattering along the LOS, broadened by outflow velocity, and narrowed or broadened by steep temperature gradients along the LOS. The proton and neutral hydrogen effective temperatures and velocities are comparable below ~3 R_S, thus implying that the measured Ly α profiles are equivalent to measurements of the velocity distribution of protons in that region. Beyond ~3 R_S, however, T_H(eff)^⊥ is found to be significantly lower than T_p(eff), and the measurement of T_H(eff)^⊥ provides a lower limit for T_p(eff) there.