Category: UKSP Nugget

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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122. Direct evidence that twisted flux tube emergence creates solar active regions

Author: David MacTaggart at the University of Glasgow, Chris Prior, Breno Raphaldini at Durham University and Paolo Romano, Salvo Guglielmino at INAF Catania.

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Introduction

Solar active regions are the nurseries of the most important dynamical events in the Sun’s atmosphere, including flares and coronal mass ejections. A fundamental constituent that helps to determine the evolution of an active region is the topology of its magnetic field. By this, we mean how the magnetic field lines are connected and twisted. A long-held assumption of active region formation is that they are created by large tubes of magnetic field with a net twist (rather like a large magnetic slinky). This assumption has been popular for two main reasons. The first is that twisted magnetic fields can survive in the solar convection zone better than untwisted fields, and are thus more likely to reach the photosphere and emerge as active regions. The second is that simulations of the emergence of twisted tubes are able to produce a variety of signatures that are found in solar observations, which match well with proxies of magnetic twist found in observations. However, despite many works suggesting the existence of twisted tubes creating active regions, the question of whether or not this is the case has remained open. This is because there exist plausible competing theories which suggest that the twist in active regions can be created in the atmosphere rather than emerge into it. Further, observational proxies used in support of the emergence of pre-twisted tubes can be reproduced by emerging magnetic fields that are not twisted tubes. What is needed is a direct measure of the magnetic topology.

Magnetic winding

One widely-used measure of magnetic topology is magnetic helicity. The flux of this quantity through the photosphere can be calculated in observations, and many studies of this have been made. No clear signature for twisted tube emergence has been found, however. One reason for this is that magnetic helicity represents a combination of two fundamental quantities, magnetic flux and field line topology, which together can introduce a confound. For example, a highly entangled field with a strong topological measure can have a very weak field strength. Thus, the magnetic helicity of such a field can be small and, therefore, not diagnose the topological complexity of the field clearly. It is not that magnetic helicity is giving an erroneous result, rather it is the interpretation of magnetic helicity as a direct measure of magnetic topology which is not correct in general. In order to find a direct measure, we can renormalize magnetic helicity to produce a quantity called magnetic winding [1]. This quantity is effectively the magnetic helicity with the field strength weighting removed, and thus represents a direct measure of magnetic field line topology.

Signatures in simulations and observations

The flux of magnetic winding can be calculated in both simulations and observations, just like magnetic helicity. The analysis of magnetic winding in simulations of twisted flux tubes emerging through a convective layer and into the solar atmosphere, reveals a consistent “rise and plateau” signature across a range of parameters [2]. This is not the case for magnetic helicity which does not provide a consistent signature, just as in observational studies. An example of the accumulation of magnetic winding in a flux emergence simulation is shown below.

Figure 1(a) shows field lines of an emerging twisted tube below and above the photospheric boundary (shown in red). There is no visible resemblance to a twisted flux tube due to the strong deformations caused by convective motion and the emergence into the atmosphere. That being said, the magnetic winding is robust enough to still detect that the magnetic field has a net twist, and this can be seen in Figure 1(b), which shows the accumulations of the total magnetic winding L, as well as the contributions to magnetic winding due to emergence, Lemerge, and photospheric braiding motions, Lbraid. What this signature is saying is that when the bulk of the twisted tube rises above the photosphere, it remains there. Even though convection drags down part of this field, no more topologically-significant field is passing through the photosphere. Thus, after the rise during emergence, there is a plateau which indicates that the main topological content has passed through the photospheric boundary (where the calculations are performed). Further, Lemerge dominates the contribution to L, which means that the signature is dominated by a pre-twisted magnetic field, rather than one whose twist is generated later by photospheric motions.

This magnetic winding signature for twisted tube emergence has now also been found in observations. As an example, Figure 2 shows the winding accumulations for the bipolar region AR11318.

The “rise and plateau” signature can be found for this region (even despite the period of missing data). AR11318 has been studied extensively [3] and many signatures had been found which are highly suggestive of twisted tube emergence though not conclusive. The magnetic winding signature is the last piece in the puzzle to confirm that the region is formed by a twisted magnetic flux tube.

Conclusions

Magnetic winding is a robust measure of magnetic topology that can provide different information compared to magnetic helicity. Since it is a direct measure of field line topology, it has been used to show that pre-twisted tubes can emerge to create active regions. Therefore, the assumptions used in many flux emergence simulations now have an observational basis. For many more details and examples, together with a large set of relevant references, please consult [4]. Further developments of magnetic winding for use in flare prediction can be found in [5].

References

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121. Quasi-periodic problems; what’s going on with QPPs?

Author: Tishtrya Mehta from The University of Warwick

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What are QPPs?

Solar flares, driven by magnetic reconnection, describe the phenomenon of a rapid and localised energy release from an active region on the Sun. The intensity of the electromagnetic radiation produced increases rapidly, in what we call the impulsive phase of the flare, and then after reaching its maximum value gradually falls back down to its pre-eruptive level in what is known as the decay phase. Flares can also be observed on other stars, where they’re known as stellar flares.

Within the emission associated with these flares we often see another behaviour which we call a quasi-periodic pulsation (QPP), where the flare’s brightness oscillates over its duration. The properties of QPPs vary widely across different flares – they can be long or short lasting, but typically have average periods in the range of several seconds to a few minutes [1]. They may also exhibit amplitude modulation, and the pulsations can vary substantially in shape. QPPs are often observed across many wavelengths as can be seen in the well-reported and discussed ‘Seven Sisters QPP’ shown in Figure 1 [2].

Although it is accepted that QPPs are a common feature of both solar and stellar flares, there is still disagreement as to how prevalent they are, with QPPs being reported in 30 – 90% of solar flares [3] [4]. The lack of consensus on the prevalence of QPPs is partly due to there being no single definition of a QPP. Different analysis techniques will vary in their ability at identifying QPPs of different shapes, periods, and durations, which will substantially change the number of QPPs it finds.

Where are the non-periodic oscillations coming from?

As the name suggests, QPPs are rarely perfectly periodic. In fact many QPPs have been seen to have non-harmonic shapes, from triangular profiles to period or phase shifts over the duration of the flare. Some QPPs exhibit growth in their instantaneous period, the study of which could be key in determining the cause of quasi-periodic behaviour. Many different models have been proposed to explain the origin of QPPs (see [1] and references therein) but so far none have been definitively proven to be able to reproduce all of the variations in QPP behaviours that we observe.

Indeed, several of these models may be responsible but as of yet we don’t know which models are the most likely or accurate. Furthermore, it could be that different models can explain different classes of QPPs. In studying the prevalence and properties of non-stationary QPPs, we move one step closer to a full model of solar flares.

A case study of period growth in QPPs:

Let’s investigate a QPP case study which has shown evidence of period growth.
On the 19th of July 2012, the Sun produced an M7.7 class flare (which has since been reclassified as a X.1 class flare, following the removal of the SWPC scaling factors) and an accompanying coronal mass ejection, which gave rise to some beautiful coronal rain as seen here. This long duration flare lasted almost three hours and was observed by both the Geostationary Operational Environmental Satellites (GOES) X-ray Sensor and Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamics Observatory.

We detrend the flare, measured in soft X-ray (1-8 Angstrom) by GOES-15, using Empirical Mode Decomposition (EMD) and the resulting detrended signal can be seen in the top panel of Figure 2. The detrended flux shows oscillatory behaviour characteristic of the QPP phenomenon. The amplitude of the QPPs is modulated throughout the different stages of the flare; the QPPs’ amplitude grows during the impulsive phase, reaches a maximal value at flare maximum, and then decreases over the decay phase until around 07:10 where the amplitude of the QPP returns to the approximate noise level of the pre-flare signal.

The continuous wavelet spectrum of the normalised QPPs (found by dividing the detrended flux by its Savitzky-Golay Envelope) seen in the bottom panel of Figure 2 shows an increase in instantaneous period of the QPPs. The period grows from about 300 seconds at 06:00 to around 600 seconds at 07:00, with the rate of period growth appearing approximately linear.

So now what?

Now that we’ve found proof of period growth in one QPP it’s not unlikely that we’ll find it in others. So the question remains – what’s causing this phenomenon? Is it due to one, or a combination, of the proposed QPP generation mechanisms already suggested? Or is it a result of something else- such as physical changes in the flaring region? We envisage that more in-depth studies of QPPs and their associated period drifts will hold the key to cracking this conundrum and pave the way for a better understanding of QPPs and flare events.

This UKSP Nugget is based on the work by L. Hayes and T. Mehta and is in final stages of preparation to be submitted for publication

References

  • [1] Zimovets et al., 2021, SSRv, 217, 5
  • [2] Kane et al., 1983, ApJ, 271, 376
  • [3] Inglis et al., 2016 ApJ, 833 284
  • [4] Dominique et al., 2018, SoPh, 293, 4

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120. NuSTAR observations of weak microflares

Author: Kristopher Cooper, Iain Hannah (University of Glasgow).

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What are microflares?

Solar flares release stored magnetic energy into mass flows, heating, and particle acceleration throughout the Sun’s atmosphere and occur in active regions (ARs) [1]. Small flares occur more frequently as energy release decreases with a flare frequency distribution consistent with a power-law. This allows for the possibility that the weaker flares actually contribute more net energy to the solar atmosphere than their brighter, but less frequent, counterparts. The energy release of flares spans decades of energies with microflares having energies between 1026–1028 erg and observed to have <10-6 W m-2 in GOES (1–8 Å) soft X-ray flux, with an A-class microflare being on the order 10-8 W m-2 [2,3]. We use the Nuclear Spectroscopic Telescope ARray (NuSTAR, [4]), an astrophysical focussing X-ray imaging spectrometer capable of observing the Sun, to probe these incredibly weak flares that are often very difficult to identify with other, even solar dedicated, instruments. For an overview of all NuSTAR solar observation campaigns and publications please visit Iain Hannah’s GitHub page.

NuSTAR observation overview: 2018 September 9 and 10

NuSTAR performed six hour-long solar observations on 2018 September 9 and 10, initially targeting a region already observed by the FOXSI-3 sounding rocket [5]. However, we find that AR12721, appearing on September 8, dominates NuSTAR’s field of view (FOV) shown in Figure 1 (panel e) [6]. Creating lightcurves of the extreme ultraviolet (EUV) AR emission (Figure 1, panel a), we find that there is no clear behaviour indicative of a microflare until we produce an FeXVIII proxy (panel b, [7]). Using the NuSTAR X-ray lightcurve, in combination with the FeXVIII proxy, we identify 10 microflares across both days with 7 taking place on September 9 (panel c). None of the NuSTAR observed microflares were easily visible in the corresponding GOES data itself and so were estimated to be GOES sub-A class from NuSTAR spectral analysis. During NuSTAR’s second orbit (10:26–11:26 UTC), AR12721 produces the brightest and weakest NuSTAR microflares of these data and are labelled as microflare 3 and 4, respectively.

Microflare 3: potential non-thermal signatures

The brightest NuSTAR microflare from these data was easily separated into a rise, peak, and decay time for further investigation via spectral analysis (Figure 2, [6]). Microflare 3 occurred in isolation and so a pre-flare time was also obtainable. We find that the FeXVIII proxy matches the lower X-ray range well (2.5–4 keV) while the higher X-ray energy range (4–10 keV) is more impulsive. This could indicate the existence of hot material at the very start of the microflare or the presence of non-thermal emission. During the pre-flare time, we find typical hot AR core temperatures at ~4 MK with the rise phase being the hottest reaching temperatures >7 MK. The microflare then progresses to show a slight, general decrease in temperature while increasing the emission measure by almost an order of magnitude. Microflare 3 is estimated to have an A0.1 GOES equivalent class.

Inspecting the spectral profile of microflare 3’s rise time (~10:29–10:32 UTC), we observe an excess in the residuals >7 keV. This would suggest an additional model is needed to accurately represent the observed spectrum. Fitting an extra thermal model we find that unphysically high temperatures are required and so we then fit a power-law model to represent potential non-thermal emission (Figure 3, [6]). The power-law model removes the residual excess and estimates a non-thermal energy release of the same order of magnitude needed to produce the corresponding thermal model parameters.

Microflare 4: a wee flare

The weakest NuSTAR X-ray microflare to be observed in September 2018 was microflare 4 occurring at ~11:04 UTC [6,8]. Like microflare 3, microflare 4 occurred in isolation and a pre-flare time could be identified. Although its emission is very faint microflare 4 still measures 10–20 arcseconds across in SDO/AIA (Figure 4, [8]). Performing spectral fitting on the microflare time (~11:03–11:05 UTC), and fixing the model that best represents the pre-flare emission, we find that this incredibly faint microflare still reaches temperatures >6.5 MK and has a GOES class equivalent of approximately a thousandth of an A-class (Figure 5, [8]). The estimated instantaneous thermal energy release from microflare 4, at 1.1×1026 erg, makes it the weakest X-ray microflare from an AR currently in literature.

Unlike microflare 3, microflare 4’s spectrum is well represented with two thermal models with no detectable count excess. However, non-thermal emission could still be present, but hidden, within the noise of the data where we have counts and consistent with a null detection where we do not. Investigating the non-thermal models that fit these criteria, we find that there are non-thermal upper limits that could provide the required heating rate to the microflare.

Conclusions

  • Sensitive imaging and spectroscopic X-ray observations are crucial when investigating incredibly weak solar microflares as they are inconspicuous at many other wavelengths.
  • Although the NuSTAR X-ray microflares are extremely faint, sub-A class equivalent flares are not necessarily spatially small and can reach very hot temperatures.
  • Sub-A class microflares can have very strong evidence of, or can be consistent with, non-thermal emission with microflare 3 being one of the weakest non-thermal X-ray microflares in the literature.
  • With NuSTAR, an observatory that is not optimised for solar observation, we are approaching events close to nanoflare energies as opposed to microflare energies.

All microflares NuSTAR observed on 2018 September 9 and 10 are thoroughly discussed in [6], with microflare 4 studied further still in [8].

References

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119. Solar magnetic vortices

Author: Suzana S. A. Silva , Gary Verth, Viktor Fedun The University of Sheffield, Erico L. Rempel Aeronautics Institute of Technology, Sergiy Shelyag Deakin University, Luiz A. C. A. Schiavo Sao Paulo State University.

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Introduction

Photospheric flows play a crucial role in the dynamical evolution of the solar atmospheric as they are inherently coupled to magnetic fields, and this may lead to the generation of strong energetic events such as flares, coronal mass ejections, and solar tornados. The wide variety of photospheric plasma dynamics can create barriers in the plasma flow, impacting the magnetic field distribution, thereby influencing important aspects of energy and mass transport in the solar atmosphere. There is particular interest in studying the twisting of magnetic field lines due to photospheric motions, however, there is actually no universally accepted definition for a twisted magnetic flux tube. This inhibits the development of techniques to automatically identify twisted magnetic flux tubes and here we address this fundamental problem.

Methodology

Due to their geometry, we can define the twisted magnetic flux tube as a vortex in the magnetic field, the M-vortex. This is illustrated in Figure 1, where we see the geometry of a twisted flux tube from a realistic magneto–convection simulation performed using MURaM [1].

We performed our analysis on a time frame series of a simulated solar plage , covering 600 km from the solar surface to the lower chromosphere. The vortex boundaries were determined based on the Integrated Averaged Current Deviation (IACD method [2]. The IACD field was calculated by tracing the magnetic field line for each point starting in a selected height level and computing the current density along the line minus the spatial average of the current. The vortex boundary was defined as the outermost convex contour of the IACD field around the local maxima.

The meaning of the vortex boundary defined by IACD is illustrated in Fig. 2 where we can see the following:

  • The boundary delimits a region where the vortex boundary lines are twisted and preserve their coherence for the length used to compute the IACD field,
  • The magnetic field lines inside the vortex are also twisted, forming a coherent twisted flux tube,
  • The lines traced from points inside the M-vortex (green lines) do not cross the vortex boundary (blue lines).

Therefore, IACD provides a proper physical definition for twisted magnetic flux tubes and automatically detects those structures.

Results

We computed the plasma variables across the M-vortices and averaged them along the azimuthal direction, considering a cylindrical coordinate system where the origin is placed at the vortex centre. We found that inside M-vortices mainly downflows are present and that they locally concentrate the vertical magnetic field and current [3]. Based on the ratio of magnetic energy (Em) and kinetic energy (Ek), we classify the M-vortices as: type I M-vortex (Em/Ek >1); and type II M-vortex (Em/Ek ≤1).

Examples of both types of vortices are given in Figure 3, where we see the magnetic field lines of the M-vortex in blue and the surrounding velocity field lines in red. From Figure 3, we see that the different types of M-vortex also present different geometries. Moreover, we see that the M-vortices appear in regions with shear flows[3].

In order to compare M-vortices and kinetic (plasma flow) vortices, which we denote as K-vortice, we also applied Instantaneous Vorticity Deviation to identify K-vortices for the time interval of the analysis as described in [4]. Figure 4 displays a 3D view of the domain with the detected K- and M- vortices at t= 1424 seconds.

The magnetic field lines of all detected M-vortices are represented by white lines and the red lines show the velocity field streamlines from detected K -vortices. On average, over a time period of 500s, the densities of ~13 and ~28 per Mm2 were detected for M- and K-vortices, respectively. The K-vortices are located in low plasma-β regions and the M -vortices are present in regions of the flow with higher plasma-β. We find that K -vortices and M-vortices have a mean lifetime of 84.7s and 54.1 seconds, respectively, i.e., the plasma supports more K -vortex long-duration structures than M-vortices [3].

Conclusions

  • M-vortices are observed in parts of the intergranular lanes with the plasma-beta >1. K-vortices appear in low plasma-beta intergranular lanes.
  • M-vortices locally concentrate the vertical magnetic field due to the gas pressure gradient between the vortex boundary and its centre, forcing a new magnetic field into the M-vortex.
  • There are two types of M-vortices: they show differences between their shape, magnetic and kinetic energy ratio.
  • M- vortices appear if two conditions are simultaneously present: (i) shear flow, (ii) plasma-beta >1
  • Further numerical studies and high-resolution observations at different spatial and temporal scales are essential to correctly describe the interplay between the magnetic field and K-vortices and the interconnectivity between structures at different height levels.

References

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118. Tour de France of compressive waves in the Sun’s corona

Author: Dmitrii Y. Kolotkov and Valery M. Nakariakov from the University of Warwick.

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What makes solar coronal waves wavy?

The intrinsically filamentary nature of the coronal plasma plays a crucial role in the dynamics of magnetohydrodynamic (MHD) waves. In particular, the waves could be guided along the plasma inhomogeneities. Due to this waveguiding effect, coronal MHD waves are known to be subject to effective dispersion manifested through the dependence of the wave speed on the wavenumber (frequency), which is most pronounced for fast magnetoacoustic (MA) waves. Similarly to a mass-start in road cycling, where all cyclists begin the race at the same time and position, an impulsively excited ensemble of fast MA harmonics, initially localised in space and time, disperses along the waveguide and forms a quasi-periodic fast-propagating perturbation of the local plasma parameters (see Fig. 1, for example). Such rapidly propagating trains of fast waves, guided by field-aligned plasma non-uniformities, are confidently observed both near the base and at higher heights of the Sun’s corona [1].

We determine characteristic signatures of fully developed fast wave trains in the time domain, obtained from theoretical modelling of fast MA waves in a coronal plasma non-uniformity. We demonstrate the link between the time history of a fast wave train and parameters of the hosting waveguide, which gives important and sometimes unique seismological information about the cross-field structuring of the coronal plasma.

From fast magnetoacoustic tadpoles to boomerangs

We model fast MA waves in a low-β plasma slab stretched along the z-axis in the linear regime (e.g., [2]). In the model, the direction of the equilibrium magnetic field coincides with the slab axis, and the cross-field profile of the plasma density (in the x-direction) is given by a continuous function with varying steepness. Thus, the waveguide is characterised by two free parameters, its depth (i.e. ratio of the plasma densities or Alfven speeds inside and outside) and steepness (i.e. smooth or sharp boundary), which determine the dynamics of fast MA waves in this model.

For smooth transverse density profiles, the group speed of fast MA waves varies with the parallel wavenumber monotonically between the Alfven speeds inside and outside the waveguide, CAi and CAe; and it has a well-pronounced minimum for steeper waveguide boundaries (see Fig. 2). The former means that among the impulsively excited ensemble of fast MA waves in a waveguide with sufficiently diffuse boundaries, all guided parallel harmonics will propagate at their own group speeds (between CAi and CAe), eventually forming a quasi-periodic pattern seen in the Morlet wavelet power spectrum as a tadpole with a narrow-band tail and broader-band head [3]. In steeper waveguides, in contrast, there will be a relatively narrow interval of parallel harmonics propagating at the highest group speeds CAi < Vgr < CAe (a quasi-periodic phase I in Fig. 1); pairs of harmonics with distinctly different wavelengths travelling at the same group speed Vgrmin < Vgr < CAi (a multi-periodic or a peloton phase II in Fig. 1); and a single parallel harmonic trailing behind all other guided harmonics at Vgrmin (Airy phase III in Fig. 1). Such a structure of the wave train is seen as a boomerang shape in the wavelet spectrum with two well-pronounced arms at shorter and longer periods (bottom panel in Fig. 1). The revealed multi-phase structure of fast MA wave trains is consistent with the suggestion of [4], based on the analogy with Pekeris waves in an ocean layer.

Observational example

The high time resolution traditionally available in the radio band seems to be most suitable for the detection of these boomerang-shaped fast MA wave trains in observations.

For example, [5] observed signatures of a fast wave train in the decimetric radio emission at 973-1025 MHz, with a frequency drift of Δf/Δt = 8.7 MHz/s towards lower frequencies which could be interpreted as an upward propagation of the wave train at the speed about 870 km/s (see Fig. 3). The shape of the wavelet spectrum of this wave train is seen to change from a tadpole at higher frequencies (lower heights) with a narrow-band tail around 81-s oscillation period and a broader-band head to a boomerang at lower frequencies (higher heights) with two well-pronounced arms around 81 s and 30-40 s. These observational properties are consistent with the theoretical scenario described in our work for the development of a fast MA wave train in a waveguide with a steep transverse density profile.

Prospects for coronal seismology

A synergy of observations of such boomerang-shaped wave trains with theory offers a unique possibility for probing simultaneously the plasma waveguide depth (Alfven speed ratio CAe/CAi) and steepness. According to the model, one can estimate CAe/CAi from the observed duration of phase I (see Fig. 1). Likewise, the duration of peloton phase II gives the ratio CAi/Vgrmin which is sensitive to the waveguide steepness. Thus, the time history of fast-propagating quasi-periodic wave trains carries important information about the transverse structuring of the coronal plasma which opens up interesting perspectives for coronal seismology, using high-resolution and high-sensitivity observations from existing (e.g. AIA/SDO, LOFAR) and upcoming (e.g. SKA, METIS/SO, ASPIICS/Proba-3) instruments.

The work has been published in MNRAS, 2021, DOI.

References

  • [1] Li et al. 2020, SSRv, 216, 136
  • [2] Hornsey et al., 2014, A&A, 567A, 24
  • [3] Nakariakov et al. 2004, MNRAS, 349, 705
  • [4] Roberts et al. 1983, Nature, 305, 688
  • [5] Meszarosova et al., 2011, SoPh, 273, 393

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