Category: UKSP Nugget

132. Phase mixing of propagating Alfvén waves in a single-fluid partially ionized solar plasma.

Author: Max McMurdo at the Plasma Dynamics Group, University of Sheffield

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What Is The Coronal Heating Problem?

Imagine approaching a radiator that, although turned on, feels inexplicably cold to the touch. Yet, as you step away, the temperature begins to rise. In essence, this is what happens at our Sun. With a surface temperature of approximately 5800 K at the base of the photosphere to over a million K in the corona, the temperature gradient is exceptionally pronounced. This unsolved problem regarding plasma heating in the solar atmosphere is one of the most enigmatic questions that still eludes a definite answer. Modern ground and space-based instruments (DKIST, DST, Hinode, SDO, SST, Solar Orbiter), have provided observational evidence of waves with sufficient energy flux to heat the solar atmosphere. Despite this, analytical theory does not predict wave damping to occur over sufficiently short length scales, preventing them from being a dominant mechanism for effective plasma heating.

Pioneering work carried out by Heyvaerts & Priest (1983) first applied the theory of phase mixing as a mechanism to enhance the efficiency of Alfvén wave damping in the corona. Inhomogeneities in local plasma parameters causes the Alfvén speed to vary spatially. This in turn causes waves on neighbouring magnetic surfaces to propagate out of phase with one another leading to the development of large transversal gradients. These large gradients enhance the efficiency of resistive mechanisms leading to more dramatic wave damping, compared with a homogeneous plasma. Although significant progress has been made in advancing this theory, researchers often find themselves having to assume dissipative coefficients many orders of magnitude larger than theoretical formulae predict. This is typically justified by invoking the influence of turbulence, which is believed to amplify these values.

What Difference Do Neutrals Make?

In a partially ionized plasma, theory predicts the values of these dissipative coefficients can be as much as six orders of magnitude larger compared with the fully ionised corona, precisely the values required to provide effective plasma heating. Treating the plasma as partially ionised introduces a new dissipative process known as Ambipolar diffusion, closely related to the Cowling resistivity. Due to neutrals lack of interaction with magnetic forces, neutrals are decoupling from the magnetic field, and the magnetic field diffuses through the neutral gas. Figure 1 presents typical values for Cowling resistivity, shear viscosity, and magnetic resistivity in the lower solar atmosphere:

We introduce a parameter μ, which defines the ionisation degree of the plasma, determined by the relative number density of ions to the total number density of particles, and investigate the effects of varying this on the damping lengths of Alfvén waves. In what is to follow, we apply the theory of phase mixing to the partially ionised lower solar atmosphere and construct a numerical model to obtain solutions modelling the attenuation of propagating phase mixed Alfvén waves, demonstrating that the damping lengths and associated heating rates are sufficient to heat the solar chromosphere.

Numerical modelling

We present a numerical approach combining finite difference approximations, a Runge-Kutta 4th order time stepping algorithm, and sparse matrices to obtain solutions for phase mixed Alfvén waves in partially ionised plasmas. We vary the background Alfvén speed through an imposed inhomogeneous plasma density profile and investigate the damping of Alfvén waves for four different profiles, P1 − P4, increasing in gradient. We retain a homogeneous Alfvén speed (P1) for comparisons to a homogeneous base case. Our results show that the damping length is highly dependent on the gradient in the Alfvén speed as shown by Figure 2.

For the steepest profile, the damping length is approximately 1 Mm, while for the homogeneous case, the amplitude has not reduced to half its original value after 4 Mm of propagation, highlighting the efficiency of phase mixing on damping Alfvén waves (see Figure 3).

Heating Rates?

The heating rates are calculated for a wavelength of 400 km, for a range of ionization degrees that range from weakly ionised (large presence of neutral gas) to strongly ionised (very few neutrals). In order to estimate the efficiency of the phase-mixed Alfvén waves to heat the plasma, we use the estimated average heating rate of the quiet chromosphere. The radiative losses estimated from commonly used semi-empirical models of the quiet-Sun chromosphere is 4.3 kWm-2, which is shown by the black horizontal line in Figure 3.

Our analysis reveals that the maximum heating rate produced by Alfvén waves varies by more than one order of magnitude and it attains its maximum value for an ionisation degree of μ = 0.576. The results show that waves propagating in a partially ionised plasma with ionisation degrees in the range μ = 0.518 − 0.657 provide sufficient heating rates to balance chromospheric radiative losses. In the AL c7 atmospheric model, these values correspond to a ratio of neutrals to ions, nn/ni = 0.0567 − 0.917, respectively. The prevailing factor contributing to this heating is associated with the significant value of the Cowling resistivity, as indicated in Figure 1, showcasing the importance of neutrals on the damping of Alfvén waves and heating of the lower solar atmosphere.

Conclusions

  • A numerical code has been developed to study the damping of propagating phase mixed Alfvén waves in the presence of an arbitrary density inhomogeneity.
  • Investigations concluded that the damping lengths are heavily influenced by the levels of phase mixing and the proportional presence of neutrals.
  • The heating rates obtained for ionisation degrees that fall in the range μ = 0.518 − 0.657 provide sufficient energy flux to balance chromospheric radiative losses in the quiet Sun.
  • The location of maximal heating occurs at heights above the solar surface that correspond to the location of the transition region, where we find the rapid increase in atmospheric temperature.

References

  • Avrett, E. H., & Loeser, R. 2008, ApJS, 175, 229, doi: 10.1086/523671
  • Heyvaerts, J., & Priest, E. R. 1983, A&A, 117, 220
  • McMurdo, M., Ballai, I., Verth, G., Alharbi, A., & Fedun, V. 2023, ApJ, 958, 81, doi: 10.3847/1538-4357/ad0364
  • Vernazza, J.

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131. Swirls in the solar corona

Author: Cosima A. Breu at the University of St. Andrews.

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Introduction

From water spiralling into a sink drain to mesmerising giant storms on Jupiter, vortex motions are present throughout the universe on scales from the very small to the very large. On the Sun, hot plasma bubbles up, only to sink back into the darker troughs between the bright granules, braiding and twisting the strong magnetic field that threads the solar atmosphere. Spiralling plasma winding up the magnetic field can generate large rotating flows higher up in the atmosphere, sometimes dubbed “magnetic tornadoes” [1]. Unlike the violent storms raging on Earth, however, these structures are held together by giant twisted magnetic funnels reaching up to low coronal heights, potentially channeling mass and energy into the corona.

Vortex motions on the Sun have been observed as rotational motions of magnetic bright points in the photosphere, as well as bright and dark spiral shapes in the chromosphere and low corona [1].  Furthermore, they have also been inferred from numerical simulations [2-4]. Due to their small scales, these structures are not easy to observe. New ground-based telescopes such as the Daniel K. Inouye Telescope (DKIST) allow us to resolve finer and finer structures on the solar surface down to tens of kilometers, increasing the importance of taking into account the contribution of small-scale motions inside magnetic flux concentrations to accurately estimate the energy flux into the solar atmosphere. Most existing studies focus on the photosphere and chromosphere. Here we present efforts to build a comprehensive model incorporating the energy transfer from the convection zone to the corona.

Numerical Simulations

We use 3D resistive magnetohydrodynamic simulations with the MURaM code [5] to study vortex motions in the interior of a coronal loop and their influence on energy transport. Computer simulations of the solar atmosphere are faced with competing demands between including regions of sizes of tens or hundreds of Mm with a realistic magnetic field geometry and resolving small-scale structures such as magnetic patches on the surface or current sheets in the atmosphere. To achieve a balance, we model an isolated loop as a straightened out magnetic flux tube in a Cartesian box rooted in a shallow convection zone at each foot point, allowing vortex motions to arise self-consistently from magnetoconvection [6,7]. While we have an intuitive notion of what a vortex is, finding an objective criterion to systematically identify vortices in a complex flow is not trivial. Here we employ the swirling strength criterion [8] that relies on the eigenvalues of the velocity gradient tensor to detect plasma locally spiralling around a point. Vortices exist on many scales, from a few tens of km to Mm. Since the swirling strength criterion depends on local gradients, we smooth out the velocity field to pick up rotational motions on larger scales.

Do swirls reach the corona?

We find that vortices can form coherent structures that reach far into the corona and funnel energy into the coronal loop, coupling different layers of the solar atmosphere from the photosphere to the corona. An example of a coherent magnetic structure harbouring a vortex is shown in Fig. 1. The coronal heating problem does not only involve the question of how energy is transported into the solar atmosphere, especially past the steep temperature and density gradients in the transition region, but also how it is converted into heat. To investigate general properties of swirls across a large
range of atmospheric heights, we conducted a statistical study of swirl properties in our simulation. Statistics for Poynting flux, density, heating rate and coronal emission are shown in Fig. 2. We find both an increased upward Poynting flux as well as enhanced heating in vortices.

Can we observe this?

We know that energy is dissipated in vortices, therefore this heating should lead to higher temperatures and thus cause the vortex to be brighter than its environment, potentially forming a coronal loop strand. The reality, however, seems to be less straightforward. While we find examples of brightenings at the edges of vortices, as shown in Fig. 3, some vortices are dark and the contrast between swirls and the environment is generally low with only about 5 % enhancement in X-rays (see Fig. 2). In addition to temperature, coronal emission has a strong density dependence and is determined by a complex interplay between the timescales of heating, cooling and chromospheric evaporation. We find the density to be enhanced in vortices in the chromosphere, but not the corona. While vortices are generally short lived, the cooling timescales of coronal plasma are on the order of half an hour, so a vortex causing a heating event might be long gone by the time denser material from the chromosphere evaporates into the corona and the loop brightens up.

Conclusions

Vortices can act as energy channels into the solar corona as well as sites of energy conversion and heat deposition. Spanning from spiralling plasma downflows in the intergranular lanes through the chromosphere up to the corona they connect different atmospheric layers. Vortices are in some cases associated with coronal brightenings and influence the visible coronal loop structure, although there is no one-to-one correspondence between a vortex tube and a bright coronal strand. The role vortices play compared to other mechanisms of energy transport and their dependence on the magnetic topology remains to be explored. Furthermore, observationally studying the 3D structure of vortices and the connectivity between different atmospheric layers poses a huge challenge due to the small spatial snd temporal scales involved, but new missions such as MUSE promise to allow a closer look at the complex plasma flows in the solar atmosphere. Finally, we can look beyond our own solar system and explore the role of vortices on other stars with convection zones and atmospheres different from our Sun.

This work was recently published in Astronomy and Astrophysics [9].

References

  • [1] Wedemeyer-Böhm, S., Scullion, E., Steiner, O., et al. 2012, Nature, 486, 505
  • [2] R., Cameron, R. H., & Schüssler, M.

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130. How do particles accelerated in solar flares escape into the heliosphere?

Authors: Mykola Gordovskyy University of Hertfordshire, Philippa Browning University of Manchester and Kanya Kusano Nagoya University.

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Introduction

High-energy particles carry a significant fraction of energy released in solar flares (e.g. [1]). Most of the energetic electrons and ions accelerated in solar flares precipitate in the corona, producing bright microwave, HXR and gamma-ray emissions, heating the corona and chromosphere and, in some cases, causing sunquakes. However, some of these particles propagate upward and escape into the heliosphere, becoming observable first via metric and deca-metric radio emission in the upper corona, then directly in the interplanetary space and near the Earth. These particles contribute to space weather and can be used as a diagnostic tool for the processes in flaring corona. Hence, we need to understand how energetic particles accelerated in solar flares escape into the heliosphere.

Comparison of the characteristics of nonthermal electrons observed in situ near the Earth in impulsive solar energetic particle events (when particles are accelerated in solar flares) with the characteristics of electrons obtained from HXR observations shows that the energy spectra of these two populations are different [2]. It is not clear what caused this difference: acceleration in different places or different mechanisms. In addition, the spectra may change during particle transport, for instance, due to scattering, strongly non-uniform magnetic field, or the return current effect. To establish the effect(s) primarily responsible for the difference between particles in the corona and the heliosphere, we use computational models of individual solar flares combining magnetohydrodynamic and test-particle methods.

Solar flare models

Gordovskyy et al. [3] constructed an observationally-based model of a real solar flare, combining the magnetohydrodynamic (MHD) and test particle (TP) methods to simultaneously describe the evolution of the magnetic field, thermal plasma, and energetic particles. The synthetic observables (mainly HXR radiation) obtained from the model were in good agreement with the observations of the flare, demonstrating that MHD-TP is a viable approach for modeling individual flares. In the present study ( see Gordovsky et al. [4] for details), we used the MHD-TP approach to simulate two separate solar flares and investigate the behaviour of energetic particles in them to understand how particles accelerated in flares are transported into the heliosphere.

The MHD-TP simulation of an individual flare begins with a nonlinear force-free (NLFF) reconstruction of the magnetic field in the active region where the flare occurred. This is done using the approach developed by Inoue et al. [5] with HMI/SDO vector magnetograms observed approximately 1 hour before the event. The resulting NLFF magnetic field configuration is embedded in a plane-parallel gravity-stratified corona, thus, forming the initial conditions for MHD simulation.

Evolution of magnetic and parallel electric fields in the model of an X-flare that occurred on September 6, 2011 over the AR11283 active region is shown in Fig.1. The coronal magnetic field in this active region is determined by two close sunspots with magnetic field strengths of about 2.0 kG of opposite polarities, and mostly positive diffuse photospheric network flux. The total negative flux through the photosphere in this region is less than the total positive flux, and part of the photospheric positive flux opens towards the heliosphere. The energy release and particle acceleration region (i.e. the volume containing strong parallel electric field) is located approximately 10 Mm above the negative sunspot in closed magnetic field. As the reconnection progresses, the magnetic connectivity in the region changes. Importantly, some closed magnetic flux (solid lines in Fig. 1) becomes open (dashed lines in Fig. 1).

Particle transport

The resulting MHD models are used to trace a large number (~10^6) of test electrons and protons, which are initially statistically-representative of the thermal plasma in the MHD model. We are interested in particles accelerated to energies above 8 keV.

A comparison of populations of particles precipitating in the corona (i.e. lost through the lower boundary of the domain) and particles ejected towards the heliosphere (i.e. lost through the upper boundary of the domain) reveals two interesting features. First, only a small fraction of energetic electrons escape to the heliosphere (no more than 20% at any given time). This is due to the fact that practically all particles in the considered models are accelerated in closed magnetic fields. Particles ejected towards the heliosphere are accelerated in a closed field, but manage to drift across the magnetic field from closed to open magnetic flux.

The fraction of escaping electrons changes with time depending on the evolution of the magnetic field in the flaring corona. For instance, in the event shown in Fig.1 closed magnetic flux becomes open as the reconnection proceeds, and the fraction of escaping particles increases with time (Fig. 2).

Secondly, the energy spectra of escaping and precipitating particles are different: the energy spectra of escaping protons and electrons are softer in both events under consideration (Fig. 3). Thus, for the energy spectra approximated by the power functions E^-delta, the power-law indices delta are about 2 for precipitating electrons and about 2.5 for electrons escaping through the upper boundary. This is because particles with lower parallel (with respect to the magnetic field) velocities spend more time around the acceleration region, where they can drift from the closed magnetic field to the open one, and therefore are more likely to enter the open magnetic field and, hence, go to the upper boundary of the domain. This, in principle, can explain the difference in the energy spectra of precipitating electrons. If the HXR in this event was produced in a “thin target”, then its power-law index gamma would be ~3, i.e. ~0.5 units lower than the power-law index of the energy spectrum of escaping electrons, which is in a good agreement with observations [3].

Summary

Our models demonstrate how energetic particles accelerated predominantly in closed magnetic field in solar flares are transported into open magnetic field and escape into the heliosphere. It is shown that energetic particles precipitating in the corona and escaping into the heliosphere have different energy spectra, similar to those observed.… continue to the full article

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129. Are Internetwork Magnetic Fields in the Solar Photosphere Horizontal or Vertical?

Authors: Ryan Campbell and Michail Mathioudakis Queen’s University Belfast, Ricardo Gafeira Instituto de Astrofísica de Andalucía, Carlos Quintero Noda and Manuel Collados Instituto de Astrofísica de Canarias

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Introduction

For decades we have been making significant progress in developing our understanding of quiet Sun magnetism (see [1] for a review). At disk centre, we can access the horizontal component of the magnetic vector by measuring linear polarisation (LP), and the vertical component by measuring circular polarisation (CP). When trying to extract information about the magnetic vector from spectropolarimetric measurements in the quiet Sun, we are attempting to measure signals which are at the limit of our polarimetric sensitivity. At disk centre, for weak fields, accessing the horizontal component is more difficult than accessing the vertical component, because a vertical field produces a larger amplitude CP profile than the amplitude of a LP profile produced by a horizontal field of equal strength. Ultimately, this means there is a vital need to understand the influence of noise on our results.

High spatiotemporal resolution observations and visualisation tools

In a new study [2] we present optimised quiet Sun observations of the Fe I 15648.5 Å spectral line in the deep photosphere using the GREGOR telescope equipped with the GRIS-IFU instrument. Our goal was to reveal as much polarisation as possible in a dead-quiet region of the solar surface, while still obtaining a time-series with a good cadence. Our observations show exceptionally high polarization fractions, with polarization confidently detected above a 5σ threshold in 65% of the field of view (FOV). We refer to this 65% as the “magnetised” area. This includes 61% of the full FOV with CP signals, 23% with LP, and, significantly, 18% with both. Although we anticipated higher fractions of polarisation to be revealed, not least because our modelling with radiative hydrodynamic simulations predicted it was possible [3], these results exceeded our expectations.

We find small-scale magnetic loops, like that in Figure 1, which seem to be embedded in a sea of magnetism, and we are able to observe their evolution. We used the Stokes Inversion based on Response functions (SIR) code [4] to retrieve physical information about the thermodynamics, kinematics and magnetism of the plasma, performing over 45 million inversions. We find the median magnetic field strength is weaker than previous GRIS-IFU observations [5], indicating that we cannot explain the higher polarisation fractions by supposing that we observed a more active target.

Shown in Figure 2, we also developed an open-source tool called SIR Explorer (SIRE) for exploring SIR inversion outputs, which is available on GitHub: https://github.com/r-j-campbell/SIRExplorer.

A noisy problem

We interrogated the impact of two conflicting approaches to the treatment of noise:

  • Approach 1: the inversion proceeds without any attempt to remove Stokes Q, U, or V profiles that contain pure noise (no signal).
  • Approach 2: before inversion, for each pixel, any Stokes Q, U, or V profile which does not reach the 5σ threshold is set to zero at every wavelength. However, if one linear polarisation parameter was measured confidently, the other was not set to zero.

In both approaches, we only include magnetised pixels. This means we do not include the 35% of the scan which had no polarisation. A threshold this high is already quite stringent.

As Figure 3 shows, there are significant differences. The magnetic field strength distributions of each approach diverge below 600 G, with noise potentially resulting in the over-estimation of B. Further, in approach 1, the distribution of inclinations is overwhelmingly horizontal, with only about 10% of the pixels having γ >164 or γ <16 . One might conclude that the internetwork photosphere is evidently horizontal in nature. However, given that only 23% of the FOV had confidently measured LP signals while 60% had CP signals, we are circumspect about this interpretation. We argue this γ distribution is created by the inversion, as SIR interprets noise in Stokes Q and U as real signal. In the case where noisy profiles are removed (approach 2), the distribution looks very different – there are peaks at 0° and 180°, when a pixel has only Stokes V, and 90° when only Stokes Q and/or U were measured. The remainder have intermediate inclinations for those pixels with both LP and CP. Stokes I is also sensitive to γ, so this is an oversimplification of the problem, but it is nevertheless what is happening in many pixels.

Despite our very stringent approach to noise treatment, our analysis in approach 2 revealed an internetwork region with a majority (>60%) of magnetized pixels displaying a clear transverse component of the magnetic field, with an inclination in the range 15<γ<165. This result is in stark contrast to previous observations at disk centre, including the first GRIS-IFU observations of this spectral line [5], which had predominantly vertical magnetic fields in the deep photosphere. The result agrees with previous studies which examined the centre-to-limb variation in linear polarisation only, and therefore also circumvented the problem of measuring LP and CP simultaneously in an unbiased way, and found that the field orientation for the weakest magnetic fields is predominantly horizontal throughout the photosphere [6]. However, using a large 1.5m telescope, a highly magnetically sensitive spectral line, and with outstanding seeing conditions, we have been able to achieve this by analysing full-Stokes inversions at disk centre only (and despite having taken very stringent steps to remove noise contamination from our inversions!).

Conclusions

Our study highlights the importance of accounting for noise when conducting analyses of magnetic fields in the solar photosphere. The Daniel K. Inouye Solar Telescope (DKIST) and European Solar Telescope (EST) will be essential for advancing our understanding of the Sun’s magnetic field, because the higher spatial resolution provided could reveal even higher fractions of polarisation, or, at least, polarisation profiles with larger amplitudes. When it comes to the statistical analysis of data from these next-gen telescopes, we hope that our study will stir debate on how best to deal with noise in inversions.… continue to the full article

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128. Self-generated Turbulent Reconnection

Author: Raheem Beg, Alexander Russell and Gunnar Hornig (University of Dundee).

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Introduction

Over the last 15 years, steady-state reconnection models such as Sweet-Parker and Petschek have been replaced with dynamic ones, encompassing highly nonlinear phenomena such as plasmoids, turbulence and magnetic stochasticity. This work is advancing quickly, enabled by 3D simulations with Lundquist numbers exceeding a critical threshold of 104. These simulations produce self-generated and self-sustaining turbulent reconnection (SGTR) that is fully 3D and fast. Our recent paper [1] has examined the evolution, structure and topology of the SGTR layer. Here we highlight a few key facts about this type of reconnection.

Pathway to Fast Reconnection

Our 3D simulation starts from a 2.5D magnetic field, in which a current layer at y = 0 separates a pair of large twisted flux tubes [1,2]. The simulation shows three major stages:

  1. Laminar phase: The early evolution is 2.5D, laminar and slow. Reconnection is resistive Sweet-Parker. Magnetic islands form due to the tearing instability of the Sweet-Parker layer.
  2. Transition: The 2.5D symmetry breaks as 3D instabilities occur. A significant trigger in our simulation is the helical kink instability of a central flux rope formed by tearing. Magnetic stochasticity develops and spreads.
  3. SGTR phase: The system enters a final stage of self-generated turbulent reconnection that is fully 3D and quasi-stationary. The reconnection rate remains above 0.01.

Plasmoids-ish?

Figure 1 shows a zoomed horizontal cross-section through the reconnection layer, during the SGTR phase. The magnetic field is stochastic in the region between the white contours. The squashing factor, represented by the colour, reveals “lumpy” structures within the reconnection layer; these are reminiscent of plasmoids in 2.5D reconnection, but they are displaced above and below the centreline and do not form a neat chain.

Oblique Frayed Flux Rope Structures

The 3D magnetic structures can be further explored using field lines. Figure 2 shows that the SGTR layer contains oblique frayed flux rope structures. These magnetic structures are coherent over short distances in z; however, they are made up of stochastic field lines that become highly intermixed over greater distances in z, causing the flux ropes to become “frayed”. This creates a dualism: globally, the magnetic field in the reconnection layer is stochastic, hence one might expect a Lazarian-Vishniac [3,4] type of reconnection; locally, however, reasonably coherent twisted flux ropes divide the reconnection layer into shorter segments by a similar principle to 2.5D plasmoid-mediated reconnection [5-8].

Mean Profiles and Effective Layer Thickness

Mean profiles provide a valuable top-level view of what is happening. Here, we examine variation in the y-direction across the reconnection layer during SGTR, taking averages over the whole z domain and intervals of t and x.

Figure 3 (left) shows contributions to the mean Ez. The reconnection flow pattern is supported by a fluctuation EMF (electromotive force) inside the reconnection layer, which allows the effective thickness (and hence reconnection rate) to be independent of resistivity and much greater than predicted by Sweet-Parker. Figure 3 (right) further reveals the existence of inner and outer thickness scales: the magnetic field is stochastic in a broad region, whereas the mean current density j, outflow |vx| and the fluctuation EMF have a much narrower peak. It is the inner thickness scale (associated with the main peak of the fluctuation EMF) that determines the reconnection rate.

Conclusions

Magnetic reconnection in the Sun is fast, fully 3D, dynamic and triggered. Simulations like the one shown above provide an exciting opportunity to finally address this long-standing and important problem.

How well do existing concepts of fast reconnection match up with simulation results? Two major frameworks are the Lazarian-Vishniac model, which is based on field-line wandering in 3D [3], and the 2D plasmoid-mediated model, which is based on a chain of marginally stable current layers [5-8]. We believe plasmoid-mediated physics is a better guide to this particular simulation, for several reasons. The reconnection rate matches the inner thickness scale, corresponding to the fluctuation EMF produced by the dynamics of flux rope structures, not the larger stochastic thickness. The reconnection rate is consistent with the ~Sc-1/2 of plasmoid-mediated reconnection. And Fig. 2 shows that the flux rope structures are locally coherent, allowing them to subdivide the global current layer into shorter segments.

In future, the plasmoid-mediated framework needs to be updated to address 3D effects, such as replacing plasmoids with oblique frayed flux ropes and incorporating field line stochasticity. New features are being discovered, such as the two thickness scales and the “SGTR wings” (regions where the fluctuation EMF reverses sign, see Fig. 3 right). It is also possible that different behaviour, such as a Lazarian-Vishniac regime, may exist for weaker guide field, so exploring parameter space is important further work.

Figures

Figures 2 & 3 in this nugget are reproduced from R. Beg , A. J. B. Russell, and G. Hornig 2022, “Evolution, structure, and topology of self-generated turbulent reconnection layers”, ApJ, 940, 94 https://doi.org/10.3847/1538-4357/ac8eb6 under the Creative Commons Attribution 4.0 licence. They are presented here at reduced resolution so they load quicker.

References

  • [1] Beg, R., Russell, A. J. B. & Hornig, G. 2022, “Evolution, structure, and topology of self-generated turbulent reconnection layers”, The Astrophysical Journal, 940, 94, https://doi.org/10.3847/1538-4357/ac8eb6.
  • [2] Huang, Y.-M., & Bhattacharjee, A. 2016, “Turbulent Magnetohydrodynamic Reconnection Mediated by the Plasmoid Instability”, The Astrophysical Journal, 818, 20, https://doi.org/10.3847/0004-637X/818/1/20.
  • [3] Lazarian, A., & Vishniac, E. T. 1999, “Reconnection in a Weakly Stochastic Field”, The Astrophysical Journal, 517, 700, https://doi.org/10.1086/307233.
  • [4] Kowal, G., Lazarian, A., Vishniac, E. T., & Otmianowska-Mazur, K. 2009, “Numerical Tests of Fast Reconnection in Weakly Stochastic Magnetic Fields”, The Astrophysical Journal, 700, 63, https://doi.org/10.1088/0004-637X/700/1/63.
  • [5] Bhattacharjee, A., Huang, Y.-M., Yang, H. & Rogers, B. 2009, “Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability”, Physics of Plasmas, 16, 112102, https://doi.org/10.1063/1.3264103.
  • [6] Cassak, P. A., Shay, M. A.

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127. The Lyman Continuum Formation during Solar Flares

Author: Shaun A. McLaughlin, Ryan O. Milligan Queen’s University Belfast.

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Introduction

The Lyman Continuum (LyC; <911.12Å) results from the free-bound transition of a free electron to the ground state of an ambient hydrogen nuclei. In the quiet-Sun, LyC forms at the top of the chromosphere/base of the transition region [1]. Therefore, the LyC is sensitive to chromospheric energy perturbations induced during solar flares, and since thermalization occurs very rapidly at the higher densities located here, its spectrum may reflect the local plasma temperature [2]. The LyC is a potentially powerful diagnostic tool of the chromospheric response to flare energy injection, but this potential is presently largely untapped.

Observational studies of the LyC have hypothesised two formation regions of the LyC during solar flares: a deeper-forming optically thick region that forms close to local thermodynamic equilibrium (LTE) and an overlying optically thin region in non-LTE that leads to an intensity enhancement in the LyC spectrum at shorter wavelengths (<750Å) [1, 2, 5].

In this nugget, we present the analysis of synthetic LyC emission generated using the RADYN code as part of the F-CHROMA project. These profiles were extracted from model solar atmospheres that had been subjected to a large range of heating functions. Having a strong theoretical understanding of the LyC is vital for the interpretation of the readily available LyC flare observations from the Extreme-Ultraviolet Experiment (EVE) on board the Solar dynamic observatory (SDO), with potentially upcoming flare observations from the Spectral Imaging of the Coronal Environment (SPICE) on board Solar Orbiter, and the EUV High-throughput Spectroscopic Telescope (EUVST) instrument aboard Solar-C which will provide spectroscopic LyC observations (460-1220Å).

LyC formation regions

RADYN is a well-established resource that has been extensively used to model the response of the solar atmosphere to flare energy injection. When simulating flares driven by electron beams (the ‘standard model’), the non-thermal electron distribution is modelled as a power law characterised by the spectral index, δ, the low energy cut-off, Ec, and energy flux density, F [3].

The left-hand panel of Figure 1 shows synthetic LyC spectra from RADYN at various times, where an Eddington-Barbier approximation [4] has been applied to the head of the continuum (800-911Å) and to wavelengths extending down to the He I edge (505-911Å). The right-hand panel shows the goodness of fit (GoF) parameter as a function of time for the two fits, where a smaller GoF value corresponds to a better fit. Generally, we can see from the GoF parameter that the Eddington-Barbier approximation fits the head of the LyC better than the tail. The head of the continuum is dominated by emission from an optically thick LyC layer, while LyC intensities at shorter wavelengths are enhanced due to the presence of an overlying optically thin region. Using contribution functions, we found that optically thin LyC emission comes from narrow regions of increased density, that formed due to chromospheric evaporation and condensation, known as chromospheric bubbles [5, 6].

Between t=5-6s, the GoF parameter is at a maximum for both fits. In the left-hand panel, we can see that the spectra have an unexpected profile at these times, where the head of the continuum appears suppressed. This is due to an overlying region of high opacity forming between the beam heating region and transition region that is minimally heated. This region maintains a large population of hydrogen atoms in the ground state that can absorb LyC photons emitted from the deeper forming optically thick LyC layer, resulting in the suppression of the continuum head. During these times, the spectra can no longer be approximated as a blackbody, and the Eddington-Barbier relation breaks down. At later times, this region dissipates, and the spectrum behaves as expected again [6].

Values for the non-LTE departure coefficient of the first level of hydrogen (b1) and the colour temperature (Tc) can be determined from the Eddington-Barbier relation. Values for b1 and Tc are quoted at the top of Figure 1 for the 800-911Å fits at the various times shown in the left-hand panel. During quiescent times, we found that the LyC was optically thick forming at the base of the transition region in non-LTE (b1~103). Whereas during solar flares, we found that this region becomes strongly coupled to local plasma conditions (b1~1), forming deeper in the atmosphere, due to the evaporation of the upper chromosphere exposing a deeper region of the chromosphere. Tc was found to increase from 8-9kK to 10-16kK. When b1 is close to unity, Tc is assumed to be close to the electron temperature of the plasma, Te. In Figure 2 we show that when b1 was at a minimum, Tc was approximately equal to Te, in agreement with the literature [1, 6]. At the times when the Eddington-Barbier approximation breaks down, the values for b1 and Tc were found to be spurious.

Conclusions

We have shown that during quiescent periods, the LyC is optically thick and forms at the top of the chromosphere in non-LTE. During solar flares, the optically thick layer of the LyC forms deeper in the atmosphere and is strongly coupled to local conditions. Optically thin layers of the LyC form at higher altitudes due to chromospheric evaporation and condensation, resulting in enhancements in the LyC intensities at shorter wavelengths in agreement with observations [1, 2, 6].

SPICE on board the Solar Orbiter mission that was launched in 2020, provides EUV coverage in the 704−790Å and 973−1049Å wavelength ranges. This provides partial coverage of LyC. Therefore, SPICE observations may be used to determine b1 and Tc below the LyC head. However, the range covered by SPICE may be reflective of the optically thin LyC layers [1, 2, 6].

Our analysis paves the way for an interpretation of LyC solar flare observations taken by current and future missions. For more details see McLaughlin et al. (2023) [6].

References

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126. Successive interacting coronal mass ejections: How to create a perfect storm?

Author: Gordon Koehn (Imperial College), Ravindra Desai (University of Warwick, Imperial College), Emma Davies (University of New Hampshire), Robert Forsyth and Jonathan Eastwood (Imperial College), Stefaan Poedts (KU Leuven, Maria Curie-Skłodowska University).

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Introduction

Coronal mass ejections (CMEs) are large bundles of magnetic flux that erupt from the solar corona releasing vast amounts of energy across incredible short time periods. Several studies have examined multiple successive interplanetary CMEs and determined that preconditioning of the solar wind, where an initial CME clears the path for a second CME [1], and CME–CME collisions [2], can result in a significant increase in geo-effectivness, i.e., the severity of the impact on Earth. In this study, we model CME-CME interactions to address the question of what upstream conditions can produce a particularly geo-effective event, i.e. a “perfect storm” at the Earth.

MHD Simulations

We employ a magnetohydrodynamic (MHD) heliospheric model [1] and self-consistently model the solar wind evolving through the inner heliosphere as well as the insertion and evolution of multiple spheromak [3] flux rope CMEs. The baseline scenario has been chosen to be two CMEs with velocities of 500 km/s and 1500 km/s respectively, originating from the same active region and their interactions and the resultant geo-effectiveness characterised. Figure 1 shows the force-free implementation of the spheromak.

Parametric Study Outcomes

Stage 1 determined the most geo-effective tilt angle in the solar corona and showed how the southward magnetic field orientation and magnetic flux was well-conserved from initialisation through to 1 AU.

Stage 2 then examined waiting times between the release of the first and second CME of 12, 16, 20, and 24 hr which corresponded to full mergers of the CME sheath regions at ≈0.5, 0.7, and 0.9 AU, and just after Earth, respectively. The results are displayed in Figure 2. All other runs do not exhibit a merger within the simulation domain extending up to 1.1 AU. Thus, one may identify the first three simulations, 12–20 hr waiting times, as collision events and the last two, 32–36 hr waiting times, as preconditioning cases. The events in the middle of these exhibit features of both regimes. Figure 2 shows the minimum Bz and minimum Dst (Disturbance storm time index) is found to occur for a waiting time of 28 hr but the closest subsolar magnetopause stand-off distance is found for a waiting time of 20 hr. Rapid magnetopause compressions can have a dramatic effect on the Earth’s radiation belts [4] and the multiple geo-effectiveness measures thus highlight the multi-faceted nature of CME-CME interactions.

Stage 3 then examined the effect of the handedness or chirality of the CMEs with the results presented in Table 1. A clear trend from positive to negative handedness is identified and the handedness of the first CME has a higher influence than the handedness of the second CME. These differences in geo-effectiveness would already change the classification of the geomagnetic storm from strong to severe. It is thus a significant finding that the handedness of spheromak in CME–CME interactions can have such a dramatic effect on the geo-effectiveness.

To investigate the cause of this dramatic impact, Figure 3 shows the y-plane profiles of Bϕ and the 3D magnetic field lines projected onto that plane. Table 1 and Figure 3 shows that when the CME field lines orient in the same direction as the Parker spiral, this results in greater conservation of field lines within the spheromak. A negative handedness, H = −1, on the other hand, leads to field lines of spheromak and Parker spiral flowing in opposing directions on the outward radial side. This results in the greater erosion of the spheromak due to magnetic reconnection [5,6,7] and explains the de facto erosion of magnetic flux for the H:[−1, −1] case.

Conclusions

This study has conducted a parametric evaluation of successive interacting coronal mass ejections in a representative heliospheric environment. Our study demonstrates how two moderate CMEs can combine to produce an event with extreme characteristics and geo-effectiveness. Another major finding was that the handedness, or chirality in CME–CME interactions can have a significant effect on the geo-effectiveness and implicates the identification of CME chirality in the solar corona [8,9] as an important early diagnostic for forecasting the effects of geomagnetic storms involving multiple CMEs. This work highlights the need for self-consistent physics-based modelling approaches to capture the magnetized interactions within our heliosphere.

For more details see The Astrophysical Journal citation:
G. J. Koehn et al., 2022, ApJ, 941 139, doi 10.3847/1538-4357/aca28c.

References

  • [1] Desai R. T., Zhang H., Davies E. E. et al. 2020 SoPh 295 130
  • [2] Shiota D. and Kataoka R. 2016 SpWea 14 56
  • [3] Verbeke C., Pomoell J. and Poedts S. 2019 A&A 627 A111
  • [4] Blake J. B., Kolasinski W. A., Fillius R. W. and Mullen E. G. 1992 GeoRL 19 821
  • [5] McComas D. J., Gosling J. T., Hammond C. M. et al. 1994 GeoRL 21 1751
  • [6] Schmidt J. M. and Cargill P. J. 2003 JGRA 108 SSH 5-1
  • [7] Gosling J. T., Skoug R. M., McComas D. J. and Smith C. W. 2005 JGRA
  • [8] DeForest C. E., de Koning C. A. and Elliott H. A. 2017 APJ 850 130
  • [9] Palmerio E., Kilpua E. K. J., James A. W. et al. 2017 SoPh 292 39

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125. Density and temperature structure of plasmoids in jets

Author: Sargam Mulay at the University of Glasgow, Durgesh Tripathi at the Inter-University Centre for Astronomy and Astrophysics, Helen Mason and Giulio Del Zanna at the University of Cambridge, Vasilis Archontis at the University of St Andrews.

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Introduction

Solar jets [7,4] are a transient display of collimated plasma which show simultaneous radiative signatures at various wavelengths probing multiple layers of the solar atmosphere. A number of studies have observed the presence of multithermal dense plasma structures along the jet known as plasmoids [1,8,5,12,2]. Various numerical simulations have shown that such plasmoids are likely a result of a tearing mode instability at the current sheet region as part of the magnetic reconnection process [10,11,3].

Observations and results

We found a suitable source of recurrent jet activity that was observed on Oct. 31, 2011, between 14:30 and 15:30 UT, simultaneously by the Atmospheric Imaging Assembly (AIA) onboard SDO and the X-ray Telescope (XRT) onboard Hinode. Combining EUV images of the jet plasmoids from AIA along with X-ray images from XRT in the Differential Emission measure (DEM) analysis [9] (xrt_dem_iterative2.pro) facilitates the investigation of the temperature structure of the plasmoids observed along the jet and at the footpoint of the jet. This approach helped to constrain the high-temperature part of the DEM.

Fig. 1 shows an image of the jet along with plasmoids observed at the spire and footpoint. These plasmoids appeared to be brighter than ambient plasma. Most of the plasmoids that appeared at the footpoint of the jet followed the curved spire plasma to a certain distance and then disappeared/merge within the spire plasma. We used an artificial slit along the curved spire and created a time-distance plot (panel (b)) for one hour of the recurrent jet activity. The bright yellow stripes are the jets with measured plane-of-sky velocities ranging between 178 and 341 km s-1

We used six EUV AIA channels (94, 131, 171, 193, 211, and 335 Å) and near-simultaneous XRT Ti-poly images in the DEM analysis. Various plasmoids were identified (shown in Fig. 1, Panel (a)) at the footpoint, and the spire of the jet. The DEMs were measured for these regions and are shown in Panels (c-f). The uncertainties in the DEMs were measured using the Monte Carlo (MC) solutions by varying the input intensities. The 50%, 80%, and 95% of the MC solutions are indicated by blue, red, and yellow bars respectively. The black curves indicate best-fitting DEMs. The DEM plots indicate the temperature distribution along these plasmoids, and these curves confirmed that the plasmoids are multithermal. The DEM peaks at log T [K] = 6.1 (1.3 MK), 6.30 (2.0 MK), 6.35 (2.2 MK), and 6.25 (1.8 MK) for FP1, FP2, SP1, and spire regions, respectively. In this case, the spire-plasmoid was slightly hotter than the footpoint-plasmoid.

The same analysis was performed for the other six time slots, and we found that the footpoint plasmoid temperatures range between log T [K] = 6.0 and 6.4 (1.0-2.5 MK), which are found to be similar to the temperatures that are obtained for spire-plasmoids (which range between log T [K] = 6.0 and 6.35 (1.0-2.24 MK)). For the spire, a lower limit to the electron number densities, Ne ranged from 2.6 to 3.2×108 cm-3 whereas for FPs (SPs), it ranged from 3.3 to 5.9×108 cm-3 (3.4-6.1×108 cm-3).

We studied the temporal evolution of temperature and density in the spire plasmoid by tracking its movement along the spire until it disappears. The double-peaked nature of DEM confirms the low (0.5 MK) as well as high temperatures (2.5 MK) plasma in spire plasmoids. The peak temperatures ranged from 1.2 to 2.24 MK and showed an initial increase and then a decrease in temperatures. A systematic rise and fall in the electron number densities were observed at the spire-plasmoid as it travels. The densities range between 2.3 and 5.0×108 cm-3.

Conclusions

Our study provided observational evidence for the formation of plasmoids at the base of the jets and suggest that plasmoids are induced by a tearing-mode instability. This thorough investigation shed light on the temperature and density structure of the plasmoids at the spire and the footpoint. We believe that these observational constraints provide a basis for future numerical experiments. These results were recently published in Mulay et al. (2023) [6].

References

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124. The independence of kink oscillation periods on noise

Author: Valery Nakariakov, Dmitrii Kolotkov and Sihui Zhong at the University of Warwick.

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Introduction

The launching of the TRACE spacecraft ushered in a new era of high-resolution observations, boosting the confident detection of MHD waves and their use for probing unknown physical parameters in the coronal plasma, known as MHD seismology. In particular, this technique is crucial for the estimation of the magnetic field in corona where the Zeeman effect could not be resolved.

Solar coronal loops are known to host several types of waves and oscillations, among which kink oscillations are the most intensively applied in seismology [1]. The kink oscillation period is determined by the time-varying displacement extracted from time-distance maps. Then, the period is used to derive the kink and Aflvén speeds, the magnetic field strength, scale height of loop density, and transverse density structure etc., by assuming that the observed period is interpreted as the period of a standing kink wave.

Kink oscillations appear in two regimes; decaying and decayless. The former is triggered by impulsive energy releases, while the latter appears without a visible driver, and displays ubiquitously in coronal loops. Decayless kink oscillations are a promising tool for routine diagnostics of the quiescent corona. In addition, its undamped nature arouses interest in how the energy is continuously input into the loop system to balance the damping by e.g. resonant absorption. So far, decayless kink oscillations have been interpreted as self-oscillations sustained by a quasi-steady flow moving across the loop footpoints [2], or random motions of loop footpoints [3]. Alternatively, it is described as an apparent periodic brightness because of the Kelvin-Helmholtz instability and resonant absorption.

Typical dynamic processes of the corona are coloured noises manifesting as power-law-like Fourier power spectra of observables. In the context of MHD seismology, it is of interest to understand whether the noise affects the quality of seismological inversions. The self-oscillatory model of decayless kink oscillations could include noises associated with random footpoint and coronal motions which sustain the oscillations. Therefore, it is necessary to know to what extent the kink oscillation period is influenced by the existence of the noise.

In this work, we combine the randomly driven and self-sustained oscillation models of decayless kink oscillations of coronal loops to demonstrate that the oscillation period is almost insensitive to the noisy dynamics around the oscillating loop and its footpoints.

Results

We construct a zero-dimensional model describing the decayless kink oscillations based on a randomly driven Rayleigh oscillator with random coefficients. The model accounts for negative friction responsible for the interaction of the loop with external non-periodic flows, and random motions of footpoints. Both processes could compensate the damping. The governing equation includes multiplicative and additive noises which represent chromospheric and coronal noisy processes. The noises are independent of each other.

In the absence of noise, the governing equation reduces to the standard Rayleigh equation, which has an asymptotically stationary (decayless) oscillatory solution with constant period and amplitude.

In the presence of essentially broadband red noise, the oscillatory patterns are found to be almost monochromatic. For both multiplicative and additive noises of the amplitudes up to 120% of the corresponding model coefficients, the oscillation period is found to depart from the noise-free value by less than two percent (Figure 1).

In the noisy cases, the oscillation amplitude experiences fluctuations around the mean value. Random fluctuations of the coefficients associated with the external flows are found to result in a symmetric modulation of the oscillation pattern, while random footpoint motions lead to antisymmetric modulation. When both multiplicative and additive noises are present, the amplitude modulation is a superposition of the symmetric and antisymmetric modulations, see Figure 2. Such modulations are also qualitatively consistent with the observed behaviour, see Figure 3.

The results obtained justify the seismological diagnostics based on the kink oscillation periods, e.g., the construction of Alfvén speed and magnetic field maps of pre-flaring coronal active regions [4].

Conclusions

In terms of a zero-dimensional model based on a randomly driven Rayleigh oscillator with random coefficients, we investigate the effect of noise on decayless kink oscillations of solar coronal loops. It was found that the period of kink oscillations is practically independent of noises, justifying the coronal seismology techniques based on kink oscillation periods. Moreover, in the presence of noise, kink oscillatory signals experience long-durational amplitude modulations which are consistent with observational findings.

This work has been published in MNRAS. The full version could be found here.

References

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123. Transverse Oscillations of Spicules and Estimating Their Energy Flux

Author: William Bate at Queen’s University Belfast.

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Introduction

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).

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.

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.… continue to the full article

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