On the validity of the Taylor Hypothesis in the inner heliosphere as observed by the Parker Solar Probe

Abstract

We study the validity of the Taylor “frozen-in” hypothesis in the inner heliosphere during the orbit of Parker Solar Probe. We examine the ratio of the Alfv´en velocity to the apparent solar wind velocity, and the magnitude of the turbulent fluctuations of the velocity of the solar wind, as observed by the spacecraft in its own reference frame. The necessary conditions appear to be satisfied for most of the orbit, with both these ratios being far below unity. However, at heliocentric distances smaller than ∼ 50 solar radii, these ratios are observed to rise above 0.1, and can consistently exceed 0.3, leading to the conclusion that the Taylor hypothesis may begin to break down in these inner regions. At larger distances, both ratios remain generally low. However, we observe some periods where the plasma conditions change significantly, either due to a lower plasma density or much stronger turbulent fluctuations, leading to much higher values, suggesting that the Taylor hypothesis may break down in such transient regions. An alternative formulation of the frozen-in hypothesis, which could be valid for outward-propagating dominant fluctuations, is also examined. Its conditions, namely that the Els¨asser variable corresponding to inward propagating fluctuations is much smaller than both the perpendicular spacecraft velocity, and the outward propagating fluctuation, were found to be satisfied near perihelion for encounters 1 and 2 and for parts of the encounters 4 and 5. We conclude that although the basic conditions for the validity of the Taylor hypothesis may cease to be satisfied in the inner heliosphere at distances below ∼ 50 solar radii, alternative frozen-in hypotheses may be successfully employed.