Constraining Low-Frequency Alfvenic Turbulence in the Solar Wind Using Density Fluctuation Measurements

One proposed mechanism for heating the solar wind, from close to the sun to beyond 10 AU, invokes low-frequency, oblique, Alfven-wave turbulence. Because small-scale oblique Alfven waves (kinetic Alfven waves) are compressive, the measured density fluctuations in the solar wind place an upper limit on the amplitude of kinetic Alfven waves and hence an upper limit on the rate at which the solar wind can be heated by low-frequency, Alfvenic turbulence. We evaluate this upper limit for both coronal holes at 5 solar radii and in the near-Earth solar wind. At both radii, the upper limit we find is consistent with models in which the solar wind is heated by low-frequency Alfvenic turbulence. At 1 AU, the upper limit on the turbulent heating rate derived from the measured density fluctuations is within a factor of 2 of the measured solar wind heating rate. Thus if low-frequency Alfvenic turbulence contributes to heating the near-Earth solar wind, kinetic Alfven waves must be one of the dominant sources of solar wind density fluctuations at frequencies of order 1 Hz. We also present a simple argument for why density fluctuation measurements do appear to rule out models in which the solar wind is heated by non-turbulent high-frequency waves ``sweeping’’ through the ion-cyclotron resonance, but are compatible with heating by low-frequency Alfvenic turbulence.

💡 Research Summary

The paper investigates whether low‑frequency, oblique Alfvén‑wave turbulence can supply the energy required to heat the solar wind from the low corona out to beyond 10 AU. The authors focus on the fact that, as the turbulent cascade proceeds to perpendicular scales comparable to the ion gyroradius (ρ_i), the Alfvén waves become kinetic Alfvén waves (KAWs). KAWs are compressive: their density perturbations scale as δn ∝ k_⊥ δB_⊥, so a measurable level of electron‑density fluctuations directly constrains the amplitude of the KAW component of the turbulence.

Using the Goldreich‑Sridhar “critical‑balance” picture together with the analytic cascade model of Howes et al. (2008), the authors construct a one‑dimensional density‑fluctuation spectrum Φ₁Dₙ(k_⊥) that includes two contributions: (1) a passive scalar component arising from slow‑mode and entropy fluctuations that are mixed by the Alfvénic cascade (producing a k_⊥⁻⁵⁄³ spectrum at large scales), and (2) an active KAW component that dominates near k_⊥ ≈ ρ_i⁻¹ and yields a flatter k_⊥¹⁄³ scaling. The relative weight of the two components is parameterised by f = (δn_ps / n₀)/(δv_⊥ / v_A) evaluated at the outer driving scale.

The model predictions are compared with two sets of observations. In coronal holes at ≈ 5 R_⊙, density spectra derived from Venus‑probe radio scintillation (Coles & Harmon 1989) show a clear break near k_⊥ ρ_i ≈ 1, consistent with the transition to KAW‑dominated compressibility. Near 1 AU, in‑situ measurements from various spacecraft (e.g., Celnikier et al. 1987; Kellogg & Horbury 2005) exhibit a similar spectral break and a high‑frequency tail that matches the predicted KAW contribution.

From the observed δn/n₀ the authors infer the corresponding magnetic‑field fluctuation amplitude δB_⊥, then estimate the linear KAW parallel electric field δE_∥ ≈ (k_⊥/k_∥) δB_⊥/√(4πρ). Using the electron Landau/transit‑time damping rate γ_L ≈ k_∥ v_th,e, they compute the turbulent heating rate ε ≈ γ_L (δB_⊥²/8π). At 5 R_⊙ the resulting upper limit is ε_max ≈ 10⁻⁴ erg cm⁻³ s⁻¹, while independent estimates of the required coronal heating rate are ≈ 2 × 10⁻⁴ erg cm⁻³ s⁻¹. At 1 AU the limit is ε_max ≈ 10⁻⁶ erg cm⁻³ s⁻¹, compared with an empirically inferred heating rate of ≈ 5 × 10⁻⁶ erg cm⁻³ s⁻¹. In both cases the limits are within a factor of two of the required heating, demonstrating that low‑frequency Alfvénic turbulence can plausibly account for the observed solar‑wind heating.

The authors also discuss the alternative “sweeping” model, in which high‑frequency (kHz) waves launched from the Sun are damped by ion cyclotron resonance as they propagate outward. Because such waves are strongly damped before reaching the scales that would generate observable density fluctuations, the sweeping model predicts far lower density‑fluctuation levels than are measured. Hence the observed density spectra effectively rule out the sweeping scenario while remaining compatible with the low‑frequency turbulent cascade.

In summary, the paper provides a quantitative test of low‑frequency Alfvénic turbulence as a solar‑wind heating mechanism by linking KAW‑induced compressibility to measured electron density fluctuations. The derived upper limits on turbulent heating are consistent with, and in some cases tightly constrain, the heating rates required by observations, supporting the view that Alfvénic turbulence—rather than high‑frequency sweeping waves—is the dominant driver of solar‑wind heating.