# Revisiting the SHH and SEP Link

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Nugget
Number: 121
1st Author: James Grayson and
2nd Author: Säm Krucker
Published: 15 February 2010
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## Introduction

Two previous Nuggets have debated the possibility of a link between solar energetic particle (SEP) events and "soft-hard-harder" (SHH) spectral behavior in solar flares. In "Soft-Hard-Harder", Sam Krucker and Hugh Hudson discussed five RHESSI flares that confirmed this relation, but Gerry Share and Allan Tylka later questioned the link when considering five more RHESSI and Yohkoh events in "SEPs Link not Confirmed". In addition to these direct discussions, a [Nugget] by Sophie Masson and Ludwig Klein recently pointed out the complexity of this relationship in a recent remarkable "ground level event".

This correlation was originally studied by Alan Kiplinger, using 10 years of data from the Hard X-ray Burst Spectrometer aboard the Solar Maximum Mission. Kiplinger found that 96% of SEP-producing flares were predicted by non-thermal, hard X-ray (HXR) SHH behavior, suggesting that the two processes are somehow linked. This strong statistical correlation alone is interesting for space-weather prediction applications, but confirming or discrediting the link is also important for motivating further investigation into the actual dynamics that could relate the two phenomena. Kiplinger's discovery does not fit neatly into the widely-accepted picture that coronal/interplanetary shock waves, driven ultimately by coronal mass ejections, accelerate these high-energy particles, because the X-ray sources appear in the low corona long after the shock has appeared in the middle corona and gone on into the heliosphere.

Here we present the results of our recent study on the subject. Our findings appear to corroborate the statistical correlation between SHH and SEP occurrence, in agreement with Kiplinger's work.

## Online Catalog of Events

For this study, we initially gathered RHESSI observations of all 661 X- and M-class flares from 2002 February 12 through the end of Solar Cycle 23. Flares were then limited to solar locations between West 30o and West 90o, as these western longitudes are more likely to connect SEPs to Earth by interplanetary magnetic field lines. After eliminating flares without sufficient observational coverage by RHESSI and those without non-thermal HXR emission above background levels, we were left with 84 flares that were further analyzed for SHH behavior. SEP events were determined by particle flux observations at Earth. The data we used included GOES proton flux measurements and both proton and electron data from the 3DP instrument aboard WIND.

A full catalog of all our flares, along with SEP event data and SHH analysis is available online. The online catalog also serves as a quick general reference of all RHESSI observations of major flares, complete with spectrograms and accompanying GOES soft X-ray lightcurves.

## Spectral Analysis

In order to search for SHH behavior, we are required to analyze the HXR spectra at multiple time steps during each flaring event. A "harder" spectrum implies that there is a higher ratio of higher-energy emission, and is typical during periods of increased overall flare emission. The majority of events then return to "softer" spectra after emission lessens, and are therefore referred to as soft-hard-soft (SHS) flares. Soft-hard-harder (SHH) events instead show increasing ratios of higher-energy emission, even after overall emission subsides. Since a power-law spectrum is typically used to describe the HXR bremsstrahlung emission, plotting the spectral-index (γ) as a function of time is a good way to visualize spectral hardening and softening during a flaring event; lower γ values correspond to a flatter slope of the power-law on a log-log plot, and therefore a harder spectrum (the power-law form is

$I \propto E^{-\gamma}$,

where I is the count intensity and E is the emission energy). We took this approach to finding the spectral behavior of each flare by performing linear fits of the log-log spectra to find the slope (γ) at 4s intervals (see Figure 1 for an example of our fitting). We should mention that this is only one of many possible methods for quantifying spectral hardening and softening; for example, a ratio of counts from two energy ranges was used in "SEPs Link not Confirmed".

Figure 1: Spectra and power-law fits during two time steps of the 2004 September 19 flare. The later time step, on the right, shows a "harder" spectrum (and correspondingly lower γ value).

Samples of our analysis are shown for two flare events in Figures 2 and 3. Spectrograms (top panels) were useful for determining appropriate power-law energy ranges, which had sufficient non-thermal HXR emission for fitting. Lightcurves (middle panels) were compared to spectral-index (γ) progressions (bottom panels) in order to search for SHH events.

 Figure 2: The 2004 September 19 M1.9 flare, displaying distinct SHH spectral evolution. This is clear from the continuously decreasing spectral-index (γ) in the bottom panel. Figure 3: The 2002 August 03 X1.0 flare, showing the more typical SHS spectral behavior. The soft-hard-soft signature is seen in the spectral-index (γ) time-progression (bottom panel) as the inverse of the lightcurve (middle panel).

## Conclusion

After discarding flare observations whose spectral behavior or energetic particle occurrence were indeterminable, and those without visible SHH behavior but only partial RHESSI observational coverage, we were left with 37 events in our final results. The statistics are shown below:

$\left.\begin{array}{lcc} & \text{SEP} & \text{No SEP} \\ & \text{Event:} & \text{Event:} \\ \text{SHH:} & 12 & 6 \\ \text{No SHH:} & 0 & 19\end{array}\right.$

To summarize, we found that two-thirds of flares showing SHH behavior were associated with SEPs, while none of the flares without SHH behavior had an associated SEP event. Considering the complicated dynamics of the solar wind and magnetic field in interplanetary space, it is reasonable to expect that not all SEPs will be detected at Earth, and so the imperfect correlation of SHH flares with SEP events is not surprising. For a purely statistical analysis, the chi-square value was calculated when assuming the null hypothesis of no SHH/SEP correlation, and was found to be χ2 = 18.7. This corresponds to a rejection of the null hypothesis at more than 99.5% confidence. Therefore, these new results constitute a statistically significant result in favor of the SHH and SEP link proposed by Kiplinger.

Of course, as pointed out in SEPs Link not Confirmed, identifying SHH events is not yet an exact science. Without a full understanding of what causes SHH spectral behavior, and the possible relation to SEP production, it is impossible to determine what search criteria can be used when looking for SHH events. All similar studies are therefore limited by some inherent subjectivity. For example, while we cannot comment on the Yohkoh data in SEPs Link not Confirmed, one RHESSI flare used by both studies demonstrates the differing measures of SHH. The flare of 2003 November 2 (X8.3) is agreed to have been associated with an SEP event measured at Earth. However, while the previous study found no SHH behavior, our analysis appears to show distinct spectral hardening between 17:20 and 17:30. It is clear that more investigation into the underlying dynamics of both phenomena is required before a final ruling can be passed on the connection between soft-hard-harder flares and energetic particle events.

## Biographical Note

James Grayson is an undergraduate physics student at UC Berkeley, and has been working with Säm Krucker at the Space Sciences Lab since January 2009. This article is based on their recent publication in The Astrophysical Journal. Much thanks is owed to Hugh Hudson and the rest of the RHESSI team for their help in all stages of this work.