The group height of spicules links their acceleration and velocity

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

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

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

The nine groups of jets include spicules, macrospicules and dynamic fibrils. The result, $V\sim a$ $V\ \sim \ a$ ^0.5, or equivalently $V^2=ka$ $V^{2} = ka$ , with only one constant, provides as close a match to the data as the equation $V=pa+q$ $V = pa + q$ , which requires two unknown constants. It is found that the constant $k$ $k$ , is a known quantity: just twice the mean height, $\bar{s}$ $\overline{s}$ , of the group of jets being analysed. This then gives the equation $V^2=2a\bar{s}$ $V^{2} =2\ a\ \overline{s}$ , 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