In Chapter 5, the Neupert effect, which refers to the correlation between thermal soft X-ray emission (SXR) in solar flares and their hard X-ray counterpart (HXR), is used as an injection proxy in the transport model of Chap. 4. A wavy peak intensity is found for each injection in contrast to the Gaussian-like distribution from Parker HMF.
Introduction
The structure of the Sun
The solar core is located in the center of the Sun and has a radius of 0.25RJ. The surface of the Sun is called the photosphere and is the thinnest (between 100 and 300 km) of all the solar layers.
Solar activity
- Active regions and sunspots
- Solar prominences and filaments
- Coronal holes
- The solar wind
- The heliospheric magnetic field
The direction of the magnetic field is indicated in blue (inwards) and red (outwards) according to the configuration of the heliospheric flow blade (HCS) [McComas et al., 2003; The magnetic field is treated as “frozen” in the SW plasma, implying that V~ and B~ are parallel in the frame rotating with the sun.
Solar energetic particles (SEPs)
Kahler et al, which reinforced the idea that solar flares cannot be the only source of SEP events. Radio bursts associated with SEP events are discussed in more detail in Chapter 3.
Solar energetic particle transport
If a particle moves through a constant and uniform magnetic field of strength B0 and no electric field is present, then, according to equation 2.3, the particle will experience centripetal acceleration and rotate around the magnetic field. The frequency at which the particle will spin around the magnetic field is determined by.
Summary
This chapter focuses on SEP observations, including the wide range of electromagnetic frequencies and wavelengths used as diagnostic tools to observe and measure solar activity. The frequency ranges are complementary to each other, providing an in-depth picture of what processes take place from the photosphere to the corona.
Solar radio emission
Coronal type II radio bursts
The high-frequency part of the type II burst corresponds to the radio emission that is close to the Sun where the corona density is highest. There are several different types of type II radio bursts characterized by their respective wavelength domains.
Coronal type III radio bursts
Taking all these results into account, it can be concluded that the same shock accelerates the ions and electrons, which in turn produce the type II burst [ Gopalswamy , 2004 ]. Several type III burst simulation models have been developed to improve the predictability of space weather (SWx), see for example Li et al.[2006],Li[2007] and Lobzin et al.[2009].
Infra-red (IR) emission
Solar flares were also observed in He I1083nm, and observations of a two-band emission revealed that the He emission lines lasted more than 60 h [ Harvey and Recely , 1984 ]. The He I1083nm spectral line can therefore also be used to track solar activity and in turn warn of possible SEP events.
White-light emission and flares
Hα emission
Ultraviolet (UV) emission
Solar X-rays
SOLAR GAMA-RAYS Observatory (CGRO, Band et al. [1993]), a solar X-ray imager on board the geostationary.
Solar gamma-rays
The first mechanism is the continuum emission of electron bremsstrahlung produced by collisional bremsstrahlung from relativistic electrons that lose most of their energy through their interactions with protons and ions in the chromosphere. The second to last is the pion decay radiation where charged and neutral pions are produced by the interactions between >300 MeV protons and ions in the chromosphere, after which the charged pions decay into muons.
Ground level events (GLEs)
Spacecraft SEP observations
- Parker Solar Probe (PSP)
- Solar Orbiter (SolO)
- Past solar missions
- Current solar missions
- Future solar missions at L4 and L5
The Magnetometer (MAG) measures the strength and direction of the solar magnetic field through which the spacecraft moves [Horbury et al., 2020]. The Solar and Heliospheric Observatory (SOHO) is a sun-centric spacecraft mission with three main scientific objectives: i) to investigate the outer layer of the Sun, ii) to observe the solar wind, and iii) to study the inner structure of the Sun to investigate [Domingo et al., 1995].
Space weather (SWx)
Posner et al [2021] show that such a mission is indeed technically feasible and scientifically convincing. The L5 position is favorable for SWx monitoring and is equivalent to a geosynchronous orbit for weather satellites.
Summary
- The Parker HMF
- The magnetic focusing length
- The length of the Parker spiral
- The focused transport equation
- The injection function
From the particle speed (figure 4.2) and the length of the magnetic field lines (figure 4.1), the minimum travel time from the inner boundary at 0.05AU outwards along the Parker HMF is calculated for different solar wind speeds and shown in figure 4.3. It is assumed that perpendicular diffusion is efficient close to the Sun and therefore, as argued by Dr¨oge et al.[2010], the assumption that the ratioλ⊥/λ|| radial constant is not valid as the result would be a spatial distribution of particles at 1AU much wider than observed for SEP events. Dr¨oge et al.[2010].
Comparison between 2D and 3D simulations
A comparison between the 2D and 3D modeling approaches is shown in Figure 4.9, with the differential intensities compared in the upper panel and the resulting particle anisotropies in the lower panel. The simulation results compare very well, with the 2D model having a slightly faster start, being, of course, closer to the source in the reduced 2D geometry.
Gaussian modelling of SEPs
The lower axes, ∆φ, represent the difference (due to the helical HMF) between the injection azimuth angle at the Sun and the observation azimuth angle a radial distance away. The combined results of Figure 4.13 are shown in Figure 4.14 and provide a possible guide to answering the initial question of the interaction between perpendicular diffusion and injection width.
Particle onset comparison with Richardson et al.[2014]
This provides further justification for the Relativistic Electron Alert System for Exploration (REleASE) proposed by Posner et al. [2009] where electron fluxes are used to predict proton fluxes.
Towards simulating proton transport
The Sun (solid yellow circle) is located atr = 0.05AU and a magnetic field line is indicated by the dashed white line along which the SEPs propagate. The arrival time of the SEPs at each planet is shown at the top of each panel.
Summary
To illustrate the Neupert effect being used as an injection indicator, the series of consecutive solar events of May 28, 1980 are used as examples. The results from the Neupert effect are compared with those of an inversion method applied by Pacheco et al.[2019].
A brief history and background of the Neupert effect
In the context of this study, the Neupert effect refers to the result that the SXR time derivative is proportional to the HXR time profile. The Neupert effect is illustrated by noting that each peak in the time derivative (middle panels) closely matches the peaks of the HXR time profiles at the bottom.
Towards a SEP forecasting model using the Neupert effect
The points marked with crosses indicate the location of the ship's gain change point and these values were replaced by interpolated values. The dashed vertical line across all plots indicates the time of the highest HXR peak relative to the SXR plots.
Solar flare events of 28 May 1980
Inversion method used by Pacheco et al. [2019]
Agueda et al. Pacheco et al., 2017], and the novelty of this approach was that it took into account for the first time both the energetic response of the instrument, E6, as well as the angular response of its sectors. For the four events on 28 May 1980, the smoothing was applied only to the injections corresponding to the decay phase of the events.
Comparison between Neupert effect and full inversion method
In addition, the estimation using the time derivative cannot reflect the elongated tail of the injection, as concluded by Pacheco et al. [2019]. This could indicate a prolonged confinement of the particles in the flare, before slowly disappearing from a magnetic trap.
Further comparison: Short duration and extended events
Interestingly, Neupert's approach generally appears to compare much better with the inversion method when events exhibit short injection (release time histories of less than 30 min) [see again Pacheco et al., 2019, for a definition of short vs. extended]. This may be due to the trapping of electrons in the acceleration region [see e.g. Dresing et al ., 2018 ] or the SXR increase could be due to the burning of another active region that may not have produced electrons in situ at the used spacecraft position for inversion.
Simulation results
The results presented in Figure 5.8 therefore illustrate the effects of perpendicular diffusion and magnetic coupling on the simulation results: in Figure 5.8a, observer B is not magnetically coupled to the (small/narrow) source, while it is magnetically coupled to the (broad/broad) source in Fig. 5.8b. Also, the differential intensities on Earth (observer C) are lower than expected when comparing to the IMP-8 data for a narrow injection (5◦), while the wider injection (20◦) compares closer to the spacecraft data, but the underestimation of the decay phase still remains in both cases.
Discussion and Conclusions
The gradual increase in IMP-8 intensity measurements (which are about an order of magnitude smaller than expected intensities) is attributed to the large connection angle (∼50◦) between the spacecraft and the events. The simulation results are presented for 300 keV electrons, while comparing them to the soft channel (1-8A) of the GOES satellite.
The structured solar wind
The hourly averaged magnetic field data have a length scale of 0.014 AU (defined by Taylor's hypothesis [Taylor, 1938]) and are shown in Figure 6.2 by the red dashed vertical line. The gray-shaded region represents small-scale turbulence that will not be observed in the 1-h mean resultant magnetic field data.
Mapping magnetic field lines
Consequently, the magnitude of the magnetic field B at a point~ ~r between the Sun and the Earth, in or near the solar equatorial plane, can be determined using the observed magnetic field magnitude B~ = (Br, Bφ ), at 1 AU and using equations 6.4 and 6.5 to calculate Br(rs, φs) and Bφ = (rs, φs) on the SWSS and then predicting Br(r, φ) and Bφ(r, φ), again using the same equation. Further details of the algorithm used to map the magnetic field can be examined in section 2.2 of Li et al.
Mapping field lines for CR 1895
Earth's orbit (1AU) is indicated by the white dotted lines in all graphs. DIVERGENCE OF THE MAGNETIC FIELD Figures 6.6b and 6.6c show normalized contour plots of the radial V and the azimuthal Vφcom-.
Divergence of the magnetic field
It is immediately clear that the divergence is not zero, but (very) close to zero for most of the map. There are certain points where the divergence increases locally (red points) and the mean field is assumed to be divergence-free.
Preparations for the transport model
The focussing length
The top panel of Figure 6.8 shows for 180◦ the inverted contour map of the inverse focus length, L−1, as explained in the next section. The bottom panel of Figure 6.8 shows L−1 for the standard Parker model (assuming constant solar wind speed Vsw = 400kms−1) and.
The winding angle
The top panel of Figure 6.9 is a closer look at the top panel of Figure 6.8, where a dashed black circle shows an orbit at 0.03 AU. Labels A1, A2, A3, and A4 indicate regions of focusing and reflection effects and correspond to the bottom panel of Figure 6.9 where L−1 is shown as a function of azimuthal angle.
Conclusion
This chapter discusses the results of simulated SEP transport in a structured solar wind using the SEP transport model of Strauss and Fichtner[2015] while incorporating the modeled magnetic field of Li et al.[2016]. Multiple injection sites at different azimuth angles are used to simulate SEP transport in the slow and fast solar wind.
SEP intensities in a structured solar wind
Figures 7.5a and 7.5b show the omnidirectional differential particle intensity for 100 keV electrons in the modeled magnetic field and the maximum particle intensity at 1AU at all azimuth angles, respectively, for the case where the initial injection is at φ0 = 0◦ (indicated by the vertical dotted line in Figure 7.5b). Figures 7.6a and 7.6b show the omnidirectional differential particle intensity for 100 keV electrons in the modeled magnetic field and the maximum particle intensity at 1AU at all azimuth angles, respectively, for the case where the initial injection is at φ0 = −90◦ (indicated by the vertical dotted line in Figure 7.6b).
Discussion
The necessary background related to the solar structure, from the solar core to the chromosphere, was discussed. The results of the 2D model were compared with the results of the 3D model and it was concluded that the 2D model is sufficient for the study of SEP transport.
The solar telescopes
The Center for Space Research (CSR) at North-West University (NWU), South Africa, started a solar telescope project in 2017. The weather in Potchefstroom is ideal for solar observations most of the year, especially during the dry winter months, and is 1340 meters above sea level.
Solar observations
Active regions and sunspots
The white light image (right panel) shows the AR of the sunspots, with the shadows and penumbra clearly visible. On August 18, 2017, one large filament was also observed on the solar disk, shown in Figure 8.3a.
Mercury transit - 11 November 2019
Annular solar eclipse - 26 December 2019
The lunar disk (black) is covering the solar disk (red) with the solar limb still visible. Solar cycle 24 ended in December 2019 and thus this eclipse was observed at the limit of solar minimum.
Community engagement activities
The North-West University solar telescope dome
The enclosed solar telescope dome installed on the roof of the CSR building in Potchefstroom, South Africa.
Future work
Agueda, N., et al., Release time scales of solar particles in the low corona, Astronomy and Astrophysics,570, A5, 2014. Kovaltsov, Anisotropic three-dimensional focused transport of solar particles in the inner heliosphere, Astrophysical Journal.
