Spectral Structures of Type II Solar Radio Bursts and Solar Energetic Particles

More energetic CMEs can probably associate with type II bursts and SEP events (e.g., Gopalswamy et al. 2008). Conversely, we investigate the relationship between the frequency characteristics of type II bursts and SEPs in this study. In order to avoid the bias of the big flare/CME syndrome (Kahler 1982a), we selected CMEs that have similar characteristics observed by the Large Angle and Spectrometric Coronagraph (LASCO; Brueckner et al. 1995) on board the Solar and Heliospheric Observatory (SOHO) from the SOHO LASCO CME catalog⁶ (Yashiro et al. 2004). The selection criteria are as follows: a velocity between 1200 and 1800 km s⁻¹ and an angular width >120°. Because of the magnetic field connection governed by the Parker spiral, we expect a higher likelihood of observing SEPs if the CME is from the western hemisphere. Therefore, we limit the range of longitude for the CME source region to be between 0° and 120°. The scale of the associated SEP events is defined as the peak of the >10 MeV proton intensity observed by the Geostationary Operational Environmental Satellite (GOES) at 1 au. We exclude some CMEs that occurred during an elevated SEP background period owing to the previous events. During the period of 2016–2017 December, 26 CMEs met these criteria. Table 1 lists the 26 selected CME events. Even though those CME events have similar characteristics, the associated SEP flux at 1 au has high variability, from 0 to 1600 pfu.

The IP type II burst data were observed by the Radio and Plasma Wave Experiment (WAVES; Bougeret et al. 1995) on board the Wind spacecraft. In this study, we used 1 minute averaged Rad1 receiver data, which are observed in the frequency range between 20 and 1040 kHz, whose data units are in terms of ratio to the background. Figure 1 shows the radio dynamic spectra of the type II bursts on 2006 December 13 (up) and 2013 August 17 events (bottom). First, we identified type II radio emissions whose intensity is equal or more than 30% enhancement from the background level; they are indicated by the white contours in Figure 1. Weak radio emissions less than 30% enhancement were ignored. Subsequently, we removed the data periods that were contaminated by other radio emissions such as type III solar radio bursts and auroral kilometric radiations (AKRs). For example, the type II burst observed on 2006 December 13 (Figure 1(a)) overlapped with AKRs after 4:00 UT, so we could not measure the lower frequency boundary of the type II. Such periods were excluded from the analysis. The upper and lower boundaries of the identified type II burst components at a given time are indicated by the white rectangles in Figure 1.

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Following Richardson et al. (2014, 2018), this study investigated the IP type II bursts that were emitted below 1040 kHz (Rad 1 frequency band) because this radio emission frequency corresponds to the plasma frequency of the interplanetary space; therefore, they are more likely to be associated with the shocks of propagating CMEs. We investigated the type II characteristics in two frequency domains: one in the hectometric range (300–1040 kHz), which approximately corresponds to 7–25 solar radii (R_s) from the Sun, and the other in the kilometric range (lower than 300 kHz), which corresponds to 25 R_s and above according to the density model of the interplanetary space (Erickson 1964). Once the high-frequency side of the negatively drifting type II emission reached each observing frequency band, we began to derive the spectral characteristics of the type II component at any given time. The bandwidth and center frequency (indicated by the red crosses in Figure 1) of a given type II burst were derived from the difference between the highest and lowest frequencies of the burst component at a given time. Type II bursts sometimes have band-splitting structures (Vršnak et al. 2001). To derive the bandwidth of the type II emission, we considered both the upper and lower bands of the band-splitting. Hence, the difference between the upper side of the upper band and lower side of the lower band should give the bandwidth (see Figure 1(c)). Conversely, harmonic emissions were carefully distinguished from the fundamental emission, and we only used the fundamental (or harmonic) emission when both of them are present. The bandwidth-to-frequency ratio was defined as the ratio between the bandwidth and the center frequency, as in Aguilar-Rodriguez et al. (2005). The peak flux was the largest flux density relative to the cosmic background between the highest and lowest frequencies of the type II component. Therefore, the peak flux was not the flux of the center frequency. The spectral characteristics of type II bursts (e.g., bandwidth and intensity) change in time, and it takes more than 60 minutes for the typical type II bursts of interest in this study to pass the hectometric band (300–1040 kHz). Therefore, we derived the averages of the type II characteristics from the first 60 minutes observations in each frequency domain (i.e., 60 one-minute-averaged spectra) except the contaminated time period. For some events, 60 minute spectra could not be obtained because of contamination by other radio emissions. Herein, we used two types of averaging methods.

Burst averaging: IP type II bursts occasionally show spontaneous emissions and patch-like spectral structures; these bursts are shown in Figures 1(c) and (d). We derived the averages from the period when the type II burst emitted, implying that the time periods when the burst components were not observed were excluded from the averaging denominator. Notably, we used only the first 60 minute spectra to detect the type II bursts for all the events. Therefore, averaging time is lower than 60 minutes in some patchy type II events. Hereafter, we call these characteristics "the burst-averaged (B.A.) characteristics."

Time averaging: we averaged the entire time period regardless of the detection of the burst components. For example, the bandwidth at the time without type II emission is treated as 0 Hz. Therefore, the time-averaged spectral characteristics of the patchy type II bursts became smaller than that of the burst-averaged values. Hereafter, we call these "the time-averaged (T.A.) characteristics."

In Figure 3, both the T.A. and B.A. bandwidths of the hectometric type II bursts correlate well with the peak flux of SEP. The two CCs have similar values (R_p = 0.64, and R_s = 0.60) and the P-value of R_s is very small (P = 0.001 ∼ 0.002) for both T.A. and B.A. bandwidth, suggesting high significance of the derived correlation. From these results, we can conclude that the correlations between the bandwidths of the type II bursts and peak fluxes of SEP should be significant regardless of the analysis method of the spectral data and statistical analysis methods. In the top panel of Figure 2, most CMEs with a B.A. bandwidth larger than 100 kHz (x-marks) are indicated above the regression line, while more than a half of the CMEs with a B.A. bandwidth smaller than 100 kHz (rectangles) are indicated below the regression line. This result also suggests that the CMEs associated with type II bursts characterized by larger B.A. bandwidth tend to generate more SEPs. From these results, we consider the bandwidth of the type II bursts at this frequency band to hold important information on the generations of SEPs.

The bandwidth of the plasma emissions may correspond to the density difference in the emission region, and the density difference may represent the spatial scale of the emission region under the gradual density distribution of the inner heliosphere. Therefore, a wider bandwidth could correspond to a larger emission region. The positive correlation between the type II bandwidth and the SEPs may suggest that, if the particle acceleration occurs on a larger spatial scale, more SEPs could be generated. Additionally, a wider bandwidth is explained via the larger density gradient at the radio source region. Such a region can be more turbulent and may lead to more efficient particle acceleration.

Another interpretation is possible using a model proposed by Vršnak et al. (2001) in which the band-splitting width of type II bursts corresponds to the density gap in the shock. In this model, the Alfvén Mach number of the shock can be estimated from the bandwidth of the splitting by assuming the density gradient along the shock trajectory. The correlation between the type II bandwidth and the SEP flux derived in this study may suggest that a shock with a larger Alfvén Mach number can produce more SEP particles, even though there are type II bursts without clear band-splitting on our list. Note that another theory has been proposed that appears to contradict this scenario (Du et al. 2014, 2015).

In Figures 3(e) and (f), the B.A. radio fluxes of hectometric type II bursts and SEPs have a relatively low correlation (R_p = 0.48); however, the correlation becomes better after time averaging (R_p = 0.62). Solar radio bursts generated by plasma emission contain many physical processes, such as plasma wave generation, radio wave emission, and propagation (e.g., Li et al. 2008). The modulation of the spectral structures of type II bursts can be explained by the modulation of the radio emission and the propagation processes along the trajectory of the shock (Schmidt & Cairns 2012, 2016). Therefore, a strong radio emission does not necessarily mean a strong shock, and it is not surprising that the peak flux of a type II burst has a low correlation with SEPs. Conversely, the better correlation with SEPs after time averaging suggests that the radio burst emission time may correspond to the acceleration time of the SEPs.

In Figure 2, the relationships between the CME speed and the type II spectral parameters (the burst-averaged bandwidth and the burst-averaged flux) are weak. Nevertheless, the spectral parameters of type II bursts are well correlated with SEPs. Therefore, we suggest that the electron beams of type II bursts and SEPs are generated by the same particle acceleration processes, but are controlled by something other than the CME speed.

The emission processes of IP type II bursts are beyond the scope of this study. Some studies have even suggested that wide-band IP type II emissions might be synchrotron emissions from trapped electrons within the CME (Bastian 2007; Pohjolainen et al. 2013). Different radio emission processes can excite different radio fluxes from the same amount of high-energy particles.

Spectral characteristics of type II bursts in the kilometric range have lower correlations with SEPs compared to those in the hectometric range, as shown in Figures 3 and 4. Fast CMEs, such as the ones accommodated in this study, tend to decelerate in the LASCO field of view, suggesting that the shock waves driven by them become weaker at greater distances from the Sun. That may suggest that these shock waves have higher particle acceleration efficiencies in regions closer to the Sun. For well-connected high-energy SEP events at hundreds of MeV, the first arriving particles often correspond to CME heights of a few R_s (Reames 2009), and the SEP peaks are reached when CMEs are at heights of 5–15 R_s (Kahler 1994). SEPs at lower energies such as >10 MeV may have similar corresponding CME heights unless the time profiles are dominated by energetic storm particles. Therefore, we may expect better correlations of spectral characteristics of type II bursts at wavelengths shorter than the kilometric range (see Figures 3 and 4). There is another possibility that explains the lower collation between the frequency characteristic of the kilometric type II bursts and SEPs. The plasma frequency of the hectometric range in this study (300–1020 kHz) corresponds to up to 0.1 au from the solar surface. Therefore, the distance between the radio source region and the Earth should be approximately 0.9–1.0 au regardless of the location of the radio source region. Conversely, plasma emission in the kilometric range corresponds to 0.1–1 au. The distance between the Earth and the emission region can vary significantly depending on the longitudinal difference between the Earth and the radio source region. This likely explains the lower correlation between the kilometric flux and the SEPs.

Given that the CME-driven shock is stronger closer to the Sun, it is possible that type II bursts at higher frequencies than those sampled by the RAD1 receiver of Wind/WAVES, that is, above 1 MHz, may be equally relevant for SEP studies. We therefore examined the same set of type II bursts observed by the RAD2 receiver, which covers 1–14 MHz. However, we found it difficult to conduct the same analysis described in Section 2.2, largely because we would need the same type II bursts to be observed in the metric range so that we could define the upper frequencies for the bandwidth. In many cases, this was apparently impossible, since the radio dynamic spectra tend to be complex in the metric range with the presence of type III (and IV) bursts observed in overlapping times and frequencies with type II bursts (e.g., Nitta et al. 2014). We also note that a few type II bursts in our sample are hardly noticeable in the 1–14 MHz range. These observational constraints have unfortunately prevented us from statistically studying the spectral characteristics of type II bursts above 1 MHz. On the other hand, reasonably high correlations of the bandwidth of hectometric type II bursts with the SEP peak flux have established the potential importance of this frequency range in predicting the magnitude of SEP events.

Figure 5 shows a white-light coronagraph image and the radio dynamic spectra on 2013 October 28. Two CMEs (CME1 and CME2) occurred, which are indicated by the black arrows. The white vertical line in the right panel indicates the time when the coronagraph image in the left panel was taken. It appears that the type II burst appeared to be significantly enhanced immediately after the CME–CME interaction began. Type II enhancements during CME–CME interactions have been reported in multiple studies (e.g., Gopalswamy et al. 2002; Al-Hamadani et al. 2017). Pohjolainen et al. (2016) reported that some CME–CME interactions do not generate SEP enhancements. They explained that the earlier CMEs and shocks change the propagation paths or prevent the propagation of SEPs because the type III bursts observed after a CME–CME interaction stop at much higher frequencies than those at the earlier events. As shown in the left panel in Figure 5, type III radio bursts around 7–9 UT stopped at much higher frequencies than the earlier type III bursts. This behavior can be explained by the hypothesis proposed by Pohjolainen et al. (2016). In addition, the type III bursts also stopped at higher frequencies than the simultaneous type II bursts, suggesting a lack of open field lines beyond the shock. Alternatively, the stop of type III bursts can be related to the change of the excitation conditions of plasma emission and/or radio emission due to the CME–CME interaction. That situation may also prevent derivation of the relationship between the type II radio bursts and SEPs. Therefore, we removed this event from the statistical analysis although it is still listed in Table 1. Note that the kilometric counterpart of this type II burst event was not significant probably because the CME–CME interaction had already finished when the CME reached the plasma emission region of kilometric bursts (>70 R_s).

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Another exceptional event in our list is the SEP event on 2017 September 4. In Table 1, this event might be recognized as the SEP event without any type II bursts. Figure 6 shows the radio dynamic spectra for 2017 September 4. Numerous hectometric type III bursts in the frequency range below 1040 kHz were observed during the time when a type II burst should have been observed. Although some emissions similar to type II were observed in that band, contamination by type III bursts prevented the detection of type II burst emission. Note that type II emissions were observed at frequencies above 1040 kHz.

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