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

Abstract

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 $r\ge r_{\mathrm{crit}}$, 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 $Q_{\mathrm{flow}}/Q_{\mathrm{p}}$ 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.

14 pages, 10 figures, submitted to Astrophys. J

References in corpus (3)

• The Dispersion Relations and Instability Thresholds of Oblique Plasma Modes in the Presence of an Ion Beam
• Effects of alpha particles on the angular momentum loss from the Sun
• Magnetohydrodynamic Slow Mode with Drifting He${}^{++}$: Implications for Coronal Seismology and the Solar Wind

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