Minor Ions as a Diagnostic of Solar Wind Heating: Inverted Mass-to-Charge Scaling in Imbalanced Turbulence

Abstract: Alfvénic turbulence is vital to powering the solar wind and corona, yet eludes a comprehensive understanding of the kinetic processes by which it dissipates. Minor ions are sensitive tracers of these processes, showing extreme perpendicular temperatures and mass-weighted temperature trends that can either correlate or anticorrelate with mass-to-charge ratio, $A_i/Z_i$. We use a combination of quasilinear theory and 3D hybrid-kinetic simulations to explain these features and their correlations with properties of turbulence in the fast solar wind. When Alfvénic turbulence is imbalanced, its cascade to ion-Larmor scales is throttled by the helicity barrier. This barrier ultimately leads to high-frequency proton-cyclotron waves (PCWs), both oblique and parallel, the latter of which produce very flat electric-energy spectra ($\mathcal{E}{E{\perp}}\sim k_\parallel^{-η}$ with $η<2$) over the range of scales that are cyclotron resonant with minor ions. While steeper spectra lead to a positive correlation of heating with $A_i/Z_i$, the shallower spectra cause the dependence to invert, with $Q_i\propto Q_{\mathrm{p}}A_i(A_i/Z_i)^{η-2}$. Six simulations of balanced and imbalanced turbulence spanning $β{\rm p0}={1,0.3,1/16}$ corroborate this prediction, showing minor-ion heating rates that follow $(A_i/Z_i)^a$. Minor-ion heating is strongest and most perpendicular in our lowest $β{\rm p0}=1/16$ simulation of imbalanced turbulence, reaching $T_{\perp{\rm O}^{5+}}/T_{\perp{\rm p}}\approx40$ and $T_{\perp{\rm O}^{5+}}/T_{\parallel{\rm O}^{5+}}\approx10$, consistent with low-coronal observations. Future minor-ion measurements should test whether intervals in which minor-ion thermal speeds decrease with increasing mass-to-charge ratio are associated with a history of large cross helicity, enhanced power in parallel PCWs, and a steep transition-range spectrum.