123. Transverse Oscillations of Spicules and Estimating Their Energy Flux

Author: William Bate at Queen’s University Belfast.

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Spicules are dense and narrow jets of chromospheric plasma which rise from the chromosphere and can reach up to coronal heights. They have relatively short lifetimes, typically less than ten minutes, and are extremely common. Spicules are typically understood to outline near-vertical magnetic field. When the solar limb is viewed in certain wavelengths, such as H-alpha, they appear as a dense forest of straw-like features. This “forest of spicules” is visible in the left panel of Figure 1 above the limb.

One of the major questions of solar physics is the so-called “coronal heating paradox”, where the solar atmosphere is at a higher temperature than would be expected through conventional means. However, it may be more appropriate to call it the “chromospheric heating paradox”, as the energy required to heat the corona is around an order of magnitude less than that required to heat the chromosphere, with an energy flux of 103–104 W m−2 required to balance the radiative losses of the chromosphere [6]. One of the proposed resolutions of this paradox is propagation and dissipation of wave phenomena, also known as the AC heating mechanism (as opposed to the DC heating mechanism believed to be caused by magnetic reconnection).

Figure 1. Left panel: An image taken in H-alpha with the Hydrogen-alpha Rapid Dynamics camera (HARDcam) showing a forest of spicules visible above the solar limb. Right panel: A time-distance diagram captured using a curved slit at a height of 6850km above the solar limb. Each bright streak is a feature passing through the slit, with the clear oscillatory features representative of transverse motions displaying a range of amplitudes and periods. [1]

Transverse Oscillation Property Analysis

These spicules, as dense tubes of plasma, are of particular interest when it comes to the transfer of energy from the photosphere into the higher levels of the solar atmosphere. Due to their topology, with their lengths being much greater than their widths, spicules can generally be described by the magnetic cylinder model [3]. This allows their behaviour to be interpreted and modelled in terms of the magnetohydrodynamic (MHD) modes of a magnetic cylinder.

Perhaps the most straightforward sort of wave behaviour that spicules can exhibit is their transverse oscillations. Spicules can be seen to “sway” across the plane of sky above the solar limb (with motions in along the line of sight likely also present). These can be interpreted as the kink mode of a magnetic cylinder which displaces the axis of the entire flux tube. These transverse oscillations are typically observed having mean periods of 50-300s, displacement amplitudes on the order of 100km, velocity amplitudes on the order of 10 km s-1, often with 50-1000 examples found within an individual dataset. For a more comprehensive review of the properties of these oscillations, see Section 5 of [4].

By placing slits at different positions along the length of a spicule, it is possible to create a time-distance diagram showing the side-to-side motion of the spicules as bright streaks against the dark background of space. An example time distance diagram is shown in the right panel of Figure 1, with oscillatory behaviour noticeable in many of these spicules. By tracking the centre of these bright streaks over time and applying tools such as wavelet and/or Fourier analysis it is possible to measure oscillation properties such as displacement amplitude, velocity amplitude and period.

Performing similar analysis for slits placed along the length of the spicule, it becomes possible to analyse how these properties evolve as a function of height. In recent work [1] it has been found that period seems relatively independent of distance along the spicule. However, displacement and velocity amplitude appear to increase with distance (or height as the spicules are near vertical). This is not entirely unexpected, as the density of spicules is thought to decrease exponentially with height. At greater heights, the lower density plasma can be moved further and faster with similar energy to smaller heights. Through further analysis of waves within the same spicule at different heights along the spicule, the phase lag between adjacent heights can be found, allowing for calculation of phase speeds and propagation direction.

Figure 2. Energy flux estimations as a function of atmospheric height for all propagating waves (upper panel), upwardly propagating waves (middle panel), and downwardly propagating waves (lower panel). The total energy flux provided by short/long period waves is shown in black, while the energy fluxes for short- (<50s) and long-period (>50s) waves are shown in red and blue, respectively. The energy fluxes provided by the full set of waves (including upwardly and downwardly propagating) and for all upwardly propagating waves are depicted, using a linear line of best fit, as a dashed black line in the upper and middle panels, with gradients equal to -12,600W m-2/Mm and -13,200W m-2/Mm, respectively. [1]

Energy Flux Estimates

Using velocity amplitude, phase velocity, and an estimate of plasma density, it is possible to calculate an estimate for the energy flux carried by these waves. It is extremely important that care is taken when choosing what wave mode to interpret the transverse motions of the spicules as. For example, when treating their observed transverse motions as bulk Alfvén waves, [2] estimated the energy flux carried by them to be 4000-7000 W m-2. However, by reanalysing these motions as kink modes and assuming that spicules take up around 5% of the local chromospheric volume (also known as a filling factor), this energy flux estimate was reduced to 200-700 W m-2 [5].

Sticking with the kink mode interpretation and 5% filling factor, another set of transverse waves within spicules have been found to carry significant energy upwards through the solar atmosphere [1]. The energy flux estimations for different heights are presented in Figure 2. These are broken up into the total energy flux in the top panel, the energy flux carried by the upwards propagating waves in the middle panel, and the energy flux carried by the downwards propagating waves in the bottom panel. For all waves examined, it can be seen that there is a decrease in energy flux with height. A black dashed line in the upper panel represents a linear line of best fit, with a gradient of -12,600 W m-2/Mm. This is due to the decrease with height of energy flux carried by the upwardly propagating waves (middle panel), whilst the energy flux carried by the downwardly propagating waves remains approximately constant with height. It can also be seen from that the energy flux of the short-period (<50s, red) waves is greater than that of the long-period (>50s, blue) waves for the full set of propagating waves.

The Future

An important topic of further investigation is what causes this decrease in energy flux with height. This could be due to a number of factors, including but not limited to: physical thermalisation of wave energy into localised heat via dissipation mechanisms; damping of detectable transverse waves through the process of mode conversion; and reflection of the waves downward at varying heights above the solar limb. Through complementary theory, simulation, and more high spatial and temporal resolution observation work it is hoped that the contributions of these mechanisms can be better understood.

Whatever the case, it is clear that transverse waves within spicules carry a substantial amount of energy up into the solar atmosphere and further study of these waves can help contribute to our better understanding of the resolution of the “coronal heating paradox”.