The connection between spicules’ acceleration, velocity and group height

Abstract

Abstract The acceleration and velocity (a,V) for solar jets such as spicules are often displayed as scattergraphs, which show a strong correlation between the two variables. This can be represented empirically by the equation, V = pa + q, where p and q are two arbitrary non-zero constants. This study aims to analyse the data for the acceleration, a, and velocity, V over a wide range of solar jets, in order to confirm an alternative proposal that there is a simpler relationship which directly links (a,V) to the mean height for the group of jets, requiring only one constant rather than two. The (a,V) data is subjected to a standard mathematical test – plotting log(a) against log(V), which allows us to establish whether V ~ a n and if so, the value of the index n. When this is done for a wide range of different types of jet the index n is consistently found to be close to 0.5 The nine groups of jets included spicules, macrospicules and dynamic fibrils. The result, V ~ a 0.5, or equivalently V 2 = ka, with only one constant, provides as good a match to the data as the equation V = pa + q, which requires two constants. It is further found that the constant k, is approximately twice the mean height, \(\stackrel{-}{s}\) ,of the group of jets being analysed. This then gives the well known equation for an object with constant acceleration, \({V}^{2}=2 a \stackrel{-}{s}\). This simpler (a,V) relationship links the acceleration and maximum velocity to a well defined constant - the mean height of the group of spicules. This single constant replaces the two undefined constants in the empirical equation.