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