1. Spectral Properties of Large Gradual Solar Energetic Particle Events
Paper No. SH041
35th ICRC
July 12-21, 2017
Busan, South Korea
Mihir I. Desai
Southwest Research Institute San Antonio, Texas
G. M. Mason, M. A. Dayeh, R. W. Ebert, D. J. McComas, G. Li, C. M. S. Cohen, N. A. Schwadron, R. A. Mewaldt, & C. W. Smith

2. Outline CME associated SEP events Model predictions/expectations
Spectral Properties
Q/M-dependence
Summary
Implications for SPP and SolO
Desai, M. I., et al. (2016a). The Astrophysical Journal, 816(2), 68.
Desai, M. I., & Giacalone, J. (2016). Living Reviews in Solar Physics, 1–132.
Desai, M. I., et al. (2016b). The Astrophysical Journal, 828(2), 1–19.

3. CME Shocks: SEPs and ESPs
CMEs drive shocks in the corona and the interplanetary medium
Accel. Near-SunSEPs
Accel. Near-EarthESPs
ESP
SEP
Reames.SSR, 1999

4. Q/M-dependent Spectral breaks
Heavy ion spectral breaks show a Q/M-dependence
Consistent with turbulence near and upstream of CME shock
Mewaldt et al. (2008)
Biggest Explosions (in tons of TNT equivalent)
Conventional TNT 3.8x103
Atomic bomb (Hiroshima) 1.3x104
Hydrogen bomb 2x107
Tunguska event (1908) 1x107
Mount Pinatubo (1991) 7x107
Largest earthquake (Chile 1960) 3x109
Asteroid that wiped out dinosaurs 1014
Comet Shoemaker-Levy 9 on Jupiter 1014
Largest solar flare 1016
Top right: Flare/CME eruption on July 11, Angstrom 500,000 to 2,000,000 K. This sequence of extreme ultraviolet images shows brightening and expansion of coronal loops accompanied by a violent ejection of material away from the Sun's surface. A bubble of hot, ionized gas or plasma as well as cooler, dark filamentary material, erupts from the solar corona and travels through space at a high speed. The cross-shaped pattern at the peak of the loop brightening is an artifact of the instrument response rather than a feature on the Sun.
Bottom left: Flare/CME eruption on July 11, Angstrom 4,000 to 10,000 K. This sequence of ultraviolet images shows the the same CME/flare event as seen in the chromosphere. The dark region at the center of the activity is a sunspot.
Image Credits: NASA/TRACE:

5. Latest Models
Acceleration at Perpendicular shockslower turbulence weaker Q/M-dependence
Acceleration at quasi-parallel shocks  enhanced turbulence stronger Q/M-dependence
Using scattering in interplanetary medium, Li & Lee (2016); Zhao et al (2016) predict double power-laws with weaker Q/M-dependence
Li et al. (2009)
Biggest Explosions (in tons of TNT equivalent)
Conventional TNT 3.8x103
Atomic bomb (Hiroshima) 1.3x104
Hydrogen bomb 2x107
Tunguska event (1908) 1x107
Mount Pinatubo (1991) 7x107
Largest earthquake (Chile 1960) 3x109
Asteroid that wiped out dinosaurs 1014
Comet Shoemaker-Levy 9 on Jupiter 1014
Largest solar flare 1016
Top right: Flare/CME eruption on July 11, Angstrom 500,000 to 2,000,000 K. This sequence of extreme ultraviolet images shows brightening and expansion of coronal loops accompanied by a violent ejection of material away from the Sun's surface. A bubble of hot, ionized gas or plasma as well as cooler, dark filamentary material, erupts from the solar corona and travels through space at a high speed. The cross-shaped pattern at the peak of the loop brightening is an artifact of the instrument response rather than a feature on the Sun.
Bottom left: Flare/CME eruption on July 11, Angstrom 4,000 to 10,000 K. This sequence of ultraviolet images shows the the same CME/flare event as seen in the chromosphere. The dark region at the center of the activity is a sunspot.
Image Credits: NASA/TRACE:

6. Survey of 46 large SEPs
Selected 46 SEP events from solar cycles 23 & 24 with no ESP or local shock accelerated component Mostly western events
Identified SEP sampling time intervals, taking account of velocity dispersion effects
Obtained ~ MeV/nucleon H-Fe energy spectra from ACE/ULEIS, ACE/SIS, GOES, SAMPEX, SoHO/ERNE
Fit the Band function (double-power law) to each species in each SEP event  obtain 2 power-law indices and a spectral break energy
Analyze spectral properties, spectral breakpoints vs. Q/M-dependence

7. Sampling Interval using 1/Ion speed
Sampling time intervals take account of velocity dispersion effects
Integrate over whole event

8. Spectral Fits Band Function
yields a low and a high-energy power-law index and a break energy for each species
Band et al., (1993); Tylka et al.(2001;2005); Mewaldt et al. (2005)

9. Scatterplot of Band-fit slopes
γa<γb
i.e., spectra steepen with increasing energy

10. H, Fe, O Low-energy slopes
Spectral slopes are correlated
All species have similar slopes during an event

11. H, Fe, O High-energy slopes
Range: 2-7
Spectral slopes are correlated
All species have similar slopes during an event

12. Types of Q/M-dependence
Both axes on right normalized to H
Modest Q/M-dependence (α~1)
Average Large SEP Q-states (Klecker et al 2000)

13. Types of Q/M-dependence
Weak Q/M-dependence (α~0.2)

14. Types of Q/M-dependence
GLE event
Strong Q/M-dependence (α~2.8)
Strong scattering

15. Histogram of alpha EB/EX∝[Q/M]α
α – power-law exponent of the Q/M-dependence of spectral break energy
α is constrained within 0.2-2;
Mean and median ~1
α >2 in 3 events; 2 are GLEs
Consistent with Li et al. (2009); Schwadron et al. (2015)

16. Alpha vs. CME speed Larger α for faster CMEs
6 GLE-associated SEPs have larger α; 2 events α>2
At odds with models that predict double power-laws in GLEs are due to scatter-dominated transport (Li & Lee; 2015; Zhao et al.2016)

17. Alpha vs. ~0.2 Fe/O Weak correlation
Larger α and higher Fe/O for “extreme” SEPs

18. Alpha vs. 3He/4He No overall trend 21 events are 3He-rich
5 of the 9 extreme SEPs are also 3He-rich
SW Value

19. Observations/Results Conclusions/Implications
Summary
Observations/Results
Conclusions/Implications
SEP spectra are well-represented by double power-laws with species-independent spectral slopes that steepen above break energies
Formation of double power-laws is consistent with CME shock acceleration (Li et al., 2009; Schwadron et al., 2015)
Break energies exhibit Q/M-dependence that scales as EB/EX∝[Q/M]α
Consistent with the equal diffusion coefficient or resonance condition (Li et al. 2009; Schwadron et al., 2015)
α is constrained within 0.2-2, and α ≥1.4 in extreme SEPs
Consistent with acceleration-dominated (Li et al. 2009) models rather than transport-dominated models (Li & Lee 2015; Zhao et al 2016)
Many extreme events are Fe- and 3He-rich, and have large values of α (≥1.4)
Enhanced wave power enable near-Sun CME shocks to accelerate flare-rich material more efficiently than the ambient coronal material (Desai et al. 2016a;b)
Measurements of SEP energy spectra for multiple species over a broad energy range can remotely probe the geometry, turbulence, and acceleration conditions at near-Sun shocks

20. Probes of near-Sun CME shocks
H<4 for most events
Weak correlation with CME speed
Higher compression ratios for extreme events

21. Probe near-Sun CME shocks
H<4 for most events
Weak correlation with CME speed
Higher compression ratios for extreme events
Extreme events in red
Stronger wave power than Kolmogorov -5/3 index

22. Conclusions
Interplanetary turbulence levels are not likely to be strong enough to produce the strong Q/M-dependence of spectral break energies that result in α ≥1.4 in GLE events
Rather, the spectral breaks are consistent with Q/M-dependent acceleration at near-Sun CME shocks
Future Outlook: Simultaneous measurements of SEP spectra (SPP/IS⊙IS and SolO/EPD), plasma parameters, and fields closer to the regions where the acceleration processes begin, will unravel the roles of variable seed populations, self-excited waves, turbulence, and shock geometry
Data from these missions will provide the ground truth and definitive tests for acceleration and transport-dominated models of SEP spectral properties

23. Thank You

24. Alpha vs. γb-γa
Events with α>1.4 have harder spectra at high and low-energies

25. O EB vs. γb-γa
Two groups?
Extreme SEPs: EB Increases as γb-γa1; flat spectra at high and low energy
Second group: EB increases as γb-γa increases

26. H, O, Fe Break Energies Range: ~0.2-100 EH>EO>EFe
Break energies are also generally correlated within events

27. Alpha vs. γb-γa
Events with α>1.4 have harder spectra at high and low-energies

28. H-Fe Spectral Break Energies
EB for H is generally larger than other species

29. Distribution of Break Energies
In a given SEP event, spectral variability due to break energy
Large spread in break energies

30. Histograms of all Spectral Slopes
All species are shown
Some overlap
Low-energy slopes <2.5
Most high-energy slopes>2

31. H-Fe Low-energy slopes
Low-energy spectral slopes are correlated within events

32. H-Fe High-energy slopes
High-energy spectral slopes are correlated within events

33. α in large SEPs Estimated α for each event
33 events have α ranging between >0.2-3

34. Distribution of spectral slopes
In a given event, the low- and high- energy spectral slopes are species-independent