The group height of spicules links their acceleration and velocity

Abstract

This study reveals a new feature of many solar jets: a group height, which links their acceleration and velocity.

The acceleration and velocity ($a$, $V$) for jets such as spicules, often displayed as scattergraphs, show a strong correlation. This can be represented empirically by the equation, $V = pa + q$, where $p$ and $q$ are two arbitrary non-zero constants.

This study reanalyses the ($a$, $V$) data for nine different groups of jets, in order to test an alternative proposal that a simpler relationship directly links ($a$, $V$) to the mean height for the group of jets, without needing the empirical constants $p$ and $q$. A standard mathematical test – plotting log($a$) against log($V$), tests whether $V\ \sim \ a^{n}$ and if so, gives the value of n. When this is done for a wide range of jets the index $n$ is consistently found to be close to 0.5

The nine groups of jets include spicules, macrospicules and dynamic fibrils. The result, $V\ \sim \ a$^0.5, or equivalently $V^{2} = ka$, with only one constant, provides as close a match to the data as the equation $V = pa + q$, which requires two unknown constants. It is found that the constant $k$, is a known quantity: just twice the mean height, $\overline{s}$, of the group of jets being analysed. This then gives the equation $V^{2} =2\ a\ \overline{s}$, for the jets in the group. This more succinct relationship links the acceleration and maximum velocity of every jet in the group to a well-defined quantity – the mean height of the group of spicules, without needing extra constants