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 $Q_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}$ 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{c}\mathrm{r}\mathrm{i}\mathrm{t}$}$, and the rotational force controls the deceleration of alpha particles at $r>r_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}$, where $r_{$\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}$} \simeq 2.5 ,$\mathrm{A}\mathrm{U}$$inthefastsolarwindintheeclipticplane\mathrm{.}Wefindthat$Q_{$\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}$}$ispositiveat$r<r_{$\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}$}$and$Q_{$\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}$} = 0$at$r\geq r_{$\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}$}$, consistent with the previous finding that the rotational force does not lead to a release of energy. We compare the value of~$Q_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}$ at $r<r_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}$ 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 $Q_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}$ exceeds $Q_{\alpha }$ at $r<1\mathrm{A}\mathrm{U}$, and that $Q_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}\mathrm{/}{Q}_{\mathrm{p}}$ decreases with increasing distance from the Sun from a value of about one at $r=0.29-0.42\mathrm{A}\mathrm{U}$ to about 1/4 at 1 AU. We conclude that the continuous energy input from alpha-particle deceleration at $r< r_{$\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}$}$ makes an important contribution to the heating of the fast solar wind.