Deceleration of Alpha Particles in the Solar Wind by Instabilities and the Rotational Force: Implications for Heating, Azimuthal Flow, and the Parker Spiral Magnetic Field

Protons and alpha particles in the fast solar wind are only weakly collisional and exhibit a number of non-equilibrium features, including relative drifts between particle species. Two non-collisional mechanisms have been proposed for limiting differential flow between alpha particles and protons: plasma instabilities and the rotational force. Both mechanisms decelerate the alpha particles. In this paper, we derive an analytic expression for the rate $Q_{\mathrm{flow}}$ at which energy is released by alpha-particle deceleration, accounting for azimuthal flow and conservation of total momentum. We show that instabilities control the deceleration of alpha particles at $r< r_{\mathrm{crit}}$, and the rotational force controls the deceleration of alpha particles at $r> r_{\mathrm{crit}}$, where $r_{\mathrm{crit}} \simeq 2.5 \,\mathrm{AU}$ in the fast solar wind in the ecliptic plane. We find that $Q_{\mathrm{flow}}$ is positive at $r<r_{\mathrm{crit}}$ and $Q_{\mathrm{flow}} = 0$ at $r\geq r_{\mathrm{crit}}$, consistent with the previous finding that the rotational force does not lead to a release of energy. We compare the value of~$Q_{\mathrm{flow}}$ at $r< r_{\mathrm{crit}}$ with empirical heating rates for protons and alpha particles, denoted $Q_{\mathrm{p}}$ and $Q_{\alpha}$, deduced from in-situ measurements of fast-wind streams from the \emph{Helios} and \emph{Ulysses} spacecraft. We find that $Q_{\mathrm{flow}}$ exceeds $Q_{\alpha}$ at $r < 1\,\mathrm{AU}$, and that $Q_{\mathrm{flow}}/Q_{\rm p}$ decreases with increasing distance from the Sun from a value of about one at $r=0.29 - 0.42\,\mathrm{AU}$ to about 1/4 at 1 AU. We conclude that the continuous energy input from alpha-particle deceleration at $r< r_{\mathrm{crit}}$ makes an important contribution to the heating of the fast solar wind.