On the origin of solar wind MHD turbulence: Helios data revisited

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Abstract
We study the fluctuations of density, magnetic and velocity fields in the frequency range from (1 day)−1 ≈ 1.2×10−5 Hz to (2.8 min)−1≈ 6×10−3 Hz, as measured by the primary Helios mission (118 days), at heliocentric distances ranging from 0.3 to 1 AU. We address the question of the existence of nonlinear cascades in the observed turbulence, possibly separate for the two “inward” and “outward” components, corresponding to opposite directions of propagation along the large‐scale magnetic field. We consider energies per unit mass, not per unit volume, in order to work with variables which are not very sensitive to the heliocentric distance variations. We find that while the whole spectrum of total (kinetic plus magnetic) turbulent energy undergoes very large daily variations both in its amplitude and spectral shape the instantaneous spectrum follows a power law in the frequency range 10−4 to 6×10−3 Hz. We show that both the amplitude and the spectral index m depend on the proton temperature, in a monotonic way, so that a large temperature (thermal speed about 60 km/s) leads to a low level of turbulence with a steep, Kolmogorov‐like spectrum (m ≈ −1.8), while a low temperature (thermal speed about 16 km/s) leads to a flatter spectrum (m ≈ −1.2) with a high level of turbulence. This relation is independent from heliocentric distance, at least between 0.3 and 1 AU. Decomposing the turbulent energy into two components, “outward” and “inward,” we find that the spectrum of the outward component also follows very closely the daily proton temperature variations, while the inward component's spectrum is less sensitive to the temperature but also varies with the relative level of rms proton density fluctuations. As a consequence, Alfvénic periods (in which energy is dominated by the outgoing component) occur mainly when density fluctuations are low and temperature is high, which does not contradict the classical view that they are found in the “trailing edges of high‐speed streams” (Belcher and Davis, 1971). The existence of inertial ranges controlled by the level of density fluctuations is not completely new (see the numerical simulations of purely hydrodynamic turbulence by Pouquet and Passot (1987)), but the strong dependence of both turbulent energy level and spectral slope on temperature is a new, unexpected property of solar wind turbulence which remains to be explained.

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