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

The Taylor hypothesis is an essential tool in studying space plasma with single point in situ observations. Its use and validity are generally well established for observations in the near-Earth solar wind. However, this is not the case for Parker Solar Probe observations in the inner heliosphere. The very high orbital velocity of the spacecraft, combined with the unusual plasma parameters very close to the sun, impose significant challenges in its use. We examine the validity of the Taylor hypothesis in throughout the Parker Solar Probe encounters so far. Specifically, we examine the ratio of the Alfven 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. We find that the necessary conditions appear to be satisfied for most of the orbit, with both these quantities remaining relatively small. However, at heliocentric distances smaller than 50 solar radii, the values 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, while both values remain generally low, at times we observe some periods of much higher values, either due to a change of the local plasma conditions or due to strong turbulent fluctuations, suggesting that the Taylor hypothesis may break down in such transient regions. An alternative formulation of the frozen-in hypothesis, which would be valid for outward-propagating dominant fluctuations, is also examined. Its conditions on the outward and inward propagating Elsasser modes are found to be satisfied near perihelion for encounters 1 and 2, and for parts of subsequent encounters. We conclude that the conditions for the validity of the Taylor hypothesis may not always to be satisfied in the inner heliosphere at distances below 50 solar radii, and that in such cases, alternative formulations may be successfully employed.