The five large solar particle events during October–November 2003 presented an opportunity to test shock acceleration models with in-situ observations. We use solar particle spectra of H to Fe ions, measured by instruments on ACE, SAMPEX, and GOES-11, to investigate the Q/M-dependence of spectral breaks in the 28 October 2003 event. We find that the break energies scale as (Q/M)^b with b ≈ 1.56 to 1.75, somewhat less than predicted. We also conclude that SEP spectra >100 MeV/nucleon are best fit by a double power-law shape. ©2005 American Institute of Physic

Cohen, C. M. S.

Cummings, A. C.

Desai, M. I.

Haggerty, D. E.

Labrador, A. W.

Leske, R. A.

Li, G.

Looper, M. L.

Maclennan, C. G.

Mason, G. M.

Mazur, J. E.

Mewaldt, R. A.

Stone, E. C.

Wiedenbeck, M. E.

English

R. A. Mewaldt

Crossref

Solar Energetic Particle Spectral Breaks
   R. A. Mewaldta, C. M. S. Cohena, G. M. Masonb, A. W. Labradora,     
M. L. Looperc, D. E. Haggertyd, C. G. Maclennane, A. C. Cummingsa,
M. I. Desaib, R. A. Leskea, G. Lif,  J. E. Mazurc, E. C. Stonea,
and M. E. Wiedenbeckg
aCalifornia Institute of Technology, Pasadena CA 91125
bUniversity of Maryland, College Park, MD 20742
cThe Aerospace Corporation, Los Angeles, CA 90245
dJohns Hopkins University, Applied Physics Laboratory, Laurel MD 207232
eBell Laboratories, Lucent Technologies, Murray Hill, NJ 07974
fIGPP, University of California, Riverside, CA 92521
 gJet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91007
Abstract. The five large solar particle events during October-November 2003 presented an
opportunity to test shock acceleration models with in-situ observations. We use solar particle
spectra of H to Fe ions, measured by instruments on ACE, SAMPEX, and GOES-11, to
investigate the Q/M-dependence of spectral breaks in the 28 October 2003 event. We find that
the break energies scale as (Q/M)b with b ≈ 1.56 to 1.75, somewhat less than predicted.  We also
conclude that SEP spectra >100 MeV/nucleon are best fit by a double power-law shape.
INTRODUCTION
The Halloween 2003 period provided the opportunity to study the spectra of five
large solar energetic particle (SEP) events within a 10-day period, each associated
with an X-class flare and very fast (>1500 km/sec) CME.  An overview of this period
is shown in Figure 1, which includes oxygen intensities in several energy intervals. In
the two largest events (events 2 and 3), particles were still being accelerated to ~10
MeV/nuc when the shock reached 1 AU.  Two studies of these five events [1, 2] have
shown that elements from H to Fe have rather prominent spectral breaks in the energy
range from ~3 to ~30 MeV/nuc, similar to those in earlier studies by Tylka et al. [3, 4].
Li, Zank and Rice [5; hereinafter LZR] have recently extended the model of Zank,
Rice and Wu [6] to heavier ions.  In their model the break energy is proportional to the
square of the charge-to-mass ratio (Q/M), where Q is the charge state and M is the
ion’s mass number.  In this paper we combine measurements from instruments on
ACE, SAMPEX and GOES-11 to obtain SEP energy spectra for the five Halloween
events and the Jan. 20, 2005 event. We test the Q/M dependence predicted by LZR
with observations of spectral breaks for nine elements following the strong shock from
the Oct 28, 2003 SEP event. We also show that a double power-law shape provides
excellent fits to the high-energy (>100 MeV/nuc) spectra in these events.
227
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Figure 1:  Time history of energetic oxygen nuclei measured by the SIS and ULEIS instruments on
ACE (from Cohen et al. [1]). Five large SEP events are evident (numbered 1 to 5). Interplanetary
shocks are indicated by vertical solid lines and X-class flares are shown along the top.
OBSERVATIONS
The shock from the 28 October 2003 event reached Earth within 19 hours followed
by driver gas traveling at ~2000 km/sec [7].   Upon arrival at 1 AU this shock was still
accelerating oxygen to ~10 MeV/nuc (see Figure 1) and protons to ~30 MeV [2].
Figure 2 shows energy spectra measured during the 6 hours following the arrival of
the shock. Note that all species show a relatively sharp break at energies ranging from
a few MeV/nuc to ~30 MeV/nuc.  The location of the breaks depends on species –
lighter species have higher break energies than heavier species like Fe (see also Tylka
et al. [3]). These spectra provide an excellent opportunity to test the prediction of LZR
[5] that the location of the breaks should scale as (Q/M)2.
The spectra in the left panel of Figure 2 were fit by a two-step procedure. In the
first step the points above and below the apparent break were individually fit with
power-laws, giving average power-law indices of –1.43 below the break and –4.1
above the break.  In the second step power-laws with these fixed, average slopes were
individually scaled to fit the points above and below the break, and the intersection of
the two power-laws was defined as the break energy.  The break energies ranged from
31 MeV for protons to 4.1 MeV/nuc for Fe.
Ellison and Ramaty [8] proposed that shock-accelerated SEPs would have spectra
of the form:
dJ/dE = KE
-γ exp(-E/Eo).  (1)
Here J is the intensity, K, Eo, and γ are constants, and we have treated E as energy/nuc.
This spectrum, which is a power-law at low energies with an exponential roll-over at
228
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high energies, has been used extensively by Tylka et al. [3, 4] to fit SEP spectra, and
we use this form to obtain a second estimate of the break energy. The average value of
γ was 1.3.  Using γ = 1.3 the spectra were then refit to determine Eo for each species,
which ranged from 31 MeV for protons to 3.5 MeV/nuc for Fe (see Figure 3).
FIGURE 2.  (Left) Spectra from the period following the shock on 29 October are fit with two power-
laws using a fixed slope of –1.43 at low energy and –4.1 at high energy. The intersection of these fits
determines the break energy.  (Right) The same data are fit with the Ellison-Ramaty spectral form using
a fixed value of –1.3 for the power-law index.  Data are from the SIS, ULEIS and EPAM instruments
on ACE, and the EPS sensor on GOES-11 (see Mewaldt et al. [2] for additional details). Each element
has been multiplied by a scale factor to separate the spectra.
In order to investigate the Q/M-dependence of the breaks we use charge-state
measurements from the same event by Labrador et al. [9] obtained using the
geomagnetic method with the MAST instrument on SAMPEX [10].  The energy
intervals range from 15 to 60 MeV/nuc for O to 27 to 90 MeV/nuc for Fe.  The two
estimates of the break energies are plotted against Q/M in Figure 3.
FIGURE 3. Break energies from Figure 2 are plotted versus Q/M.  Fits to the Z≥2 data give somewhat
weaker dependence on Q/M than is expected from the theory of LZR [6].
229
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FIGURE 4. H and He Fluence spectra for the Nov. 2, 2003 event are better fit with the double power-
law form of Band et al. [11; Right] than with the Ellison-Ramaty spectral form (Left).
The fluence spectra for the five Halloween events (integrated over the events) also
have spectral breaks [2, 1].  For these spectra the Ellison-Ramaty form is adequate up
to ~100 MeV/nuc, but fails to fit the spectra at higher energies [2].  Figure 4 illustrates
that spectra >100 MeV/nuc are better fit by a double power-law formula from Band et
al. [11], given by:
dJ/dE  = CE-
γ
a exp(-E/Eo)  for E ≤ (γb – γa)Eo;
   dJ/dE = CE-
γ
b{[(γb – γa)Eo](
γ
b-
γ
a) exp(γa – γb)} for E ≥ (γb – γa)Eo.         (2)
Here γa is the low-energy power-law slope and γb is the high-energy power-law
slope. Spectra from the five Halloween events are shown in Figure 5, along with the
Jan. 20, 2005 event, where the breaks are at lower energy, and the spectra above the
breaks are much harder.  In this event the H and He spectra above the breaks extend as
power-laws with an index ≈ -2.2 for about two decades in energy or more.
FIGURE 5.  (Left) Fluence spectra for the Oct.-Nov. 2003 events fit with the Band et al. shape
[11].  Spectral indices above and below the break are indicated. (Right) The 20 Jan. 2005 event had a
double power-law shape with a very hard spectrum.  Data are from ACE, SAMPEX and GOES-11 [2].
230
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DISCUSSION
In the model of LZR [5] streaming protons escaping upstream from the shock
generate enhanced turbulence in the form of Alfven waves that extends over ~2
decades in wave number (k; see Lee [12] and Ng, Reames, and Tylka [13], hereinafter
NRT]). The proton-amplified Alfven waves play a key role in scattering particles and
keeping them near the shock where they can be efficiently accelerated.  According to
LZR, the break in the power-law spectrum for a given species occurs at the maximum
achievable momentum/nuc (pmax) for which there is efficient acceleration, which
corresponds to the momentum/nuc that resonates with the minimum k-value (kmin) for
which there is enhanced turbulence.  Thus, for species i,
kmin = (Qi/Mi)(eB/c pmax), (3)
where B is the magnetic field strength, e the electron charge, and c the speed of light.
Converting from momentum/nuc to energy/nuc (E) the break-energy of species i
(Emax,i) is related to that of protons by
Emax,i
  =  (Qi/Mi)
2Emax,p . (4)
In the LZR model the sudden decrease in the turbulence level at k values below kmin
leads to a sudden increase in the diffusion coefficient, thus allowing higher-energy
particles to freely escape upstream from the shock.  There are similar, though less
sharp, breaks in the wave spectra calculated by NRT. Recently, evidence has been
reported for proton-amplified Alfven waves at 1 AU in large SEP events [14, 15].
The location of the breaks for He to Fe (Figure 3) are reasonably consistent with the
power-law behavior predicted by LZR, although the slope that we find (1.56 to 1.75)
is somewhat less than predicted.  Note that the proton break energy is low compared
with the fits to the heavy ions. Li and Zank (personal communication) have pointed
out that while heavy ions should act like test particles, protons may not, because
protons produce the waves that govern this process [5,  13].
Cohen et al. [1] analyzed the location of spectral breaks for 8 ≤ Z ≤ 26 ions in the
fluence spectra of the five Halloween events.  Using average SEP charge states
measured at lower energy they find that the breaks scale like (Q/M)b with b =  0.9 to
1.5.   Mewaldt et al. [2] found that breaks in the H and He fluence spectra suggest b =
0.7 to 1.3, similar to Tylka et al. [3].  It is possible that the expected Q/M dependence
in fluence spectra is washed out somewhat because the maximum energy (Emax) is
greater closer to the Sun than at 1 AU.  Fluence spectra from 1 AU inevitably include
particles accelerated close to the Sun as well as those accelerated locally [5].
There are also likely to be longitudinal differences in the break energies that may
depend on shock geometry [4].  In fluence spectra the magnetic connection point to
the shock evolves with time, and this evolution depends on the event location. These
considerations, not accounted for in most theoretical models, complicate comparisons
such as these.  Presumably, contributions from particles accelerated closer to the Sun
or at different longitudes are minimized in the Oct. 29, 2003 shock period, where local
acceleration dominates, and the Q/M-behavior comes closest to the model predictions.
231
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     Cohen et al. [1] suggested that the location of spectral breaks in fluence spectra is
governed by diffusion processes, such as escape upstream from the shock.  In this
case, spectral breaks for different species should occur at the same value of the
diffusion coefficient [16].  Cohen et al. [1] found that the fluence spectra of 8 ≤ Z ≤ 26
ions in the Halloween events shared a common spectral shape (see also [2]).
Assuming a diffusion coefficient that scales as (M/Q)α, they found α = 0.8 to 2.7.
Following Droege [17], Cohen et al. related the value of α  to the spectrum of
interplanetary turbulence (taken to be a power-law in wave number, k-q).  They
concluded that SEP spectral breaks in these events were organized by wave spectra in
the range from k-1.2 to k0.7 (see also [2]), significantly flatter than a k-5/3 Kolmogorov
spectrum, consistent with a source of turbulence near the shock where the ions were
accelerated.  It is interesting that calculations by NRT [13] show that proton-amplified
Alfven waves in SEP events can produce broad features in the wave spectra with q≈0,
and that similar wave spectra have been reported in SEP events at 1 AU [14, 15].
Finally, we point out that the nature of spectra beyond the breaks has space-weather
implications.  The Band et al. form fits the Halloween spectra better than the Ellison-
Ramaty form [2], and a power-law above the break is clearly required for the Jan. 20,
2005 event.  Extrapolating these spectral forms results in significantly different
estimates of SEP radiation doses, especially behind several g/cm2 of shielding.  It is
therefore important to continue efforts to understand and eventually forecast not only
the location of spectral breaks, but also the nature of the spectra beyond the breaks.
ACKNOWLEDGMENTS
This work was supported by NASA under grants NNG04GB55G, NNG04088G,
and NAG5-12929.  We appreciate the availability of GOES-11 data from NOAA’s
Space Environment Center at http://www.sec.noaa.gov/Data/index.html.
REFERENCES
1. Cohen, C. M. S., et al., to be published in JGR, (2005).
2. Mewaldt, R. A., et al., submitted to JGR, (2005).
3. Tylka, A. J., et al., Ap. J., 558, L59-L63, (2001).
4. Tylka, A. J., et al., to be published in Ap. J., (2005).
5. Li, G., Zank, G. P., and Rice, W. K. M., to be published in JGR, (2005).
6. Zank, G. P., Rice, W. K. M., and Wu, C. C., JGR, 105, 25079-25095 (2000).
7. Skoug, R. M., et al., JGR 109, A9, DOI: 10.1029/2004JA010494 (2004).
8. Ellison, D. C., and Ramaty, R., Ap. J., 298, 400-408 (1985).
9. Labrador, A. W., et al., to be submitted to the 29th Internat. Cosmic Ray Conf., Pune, India, (2005).
10. Leske et al., Ap. J., 452, L149-L152 (1995).
11. Band, D., et al., Ap. J., 413, 281-292, (1993).
12. Lee, M. A., JGR, 88, 6109-6119, (1983).
13. Ng, C. K., Reames, D. V. and Tylka, A. J., 591, 461-485, (2003).
14. Bamert, K., et al., Ap. J., 601, L99-L102 (2004).
15. Kallenbach, R., et al., this volume (2005).
16. Cummings, A. C., Stone, E. C., and Webber, W. R., Ap. J. 287, L99-L103 (1984).
17. Droege, W., Ap. J. Suppl. 90, 567-576 (1994).
232
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Solar Energetic Particle Spectral Breaks

Solar Energetic Particle Spectral Breaks   R. A. Mewaldta, C. M. S. Cohena, G. M. Masonb, A. W. Labradora,     M. L. Looperc, D. E. Haggertyd, C. G. Maclennane, A. C. Cummingsa,M. I. Desaib, R. A. Leskea, G. Lif,  J. E. Mazurc, E. C. Stonea,and M. E. WiedenbeckgaCalifornia Institute of Technology, Pasadena CA 91125bUniversity of Maryland, College Park, MD 20742cThe Aerospace Corporation, Los Angeles, CA 90245dJohns Hopkins University, Applied Physics Laboratory, Laurel MD 207232eBell Laboratories, Lucent Technologies, Murray Hill, NJ 07974fIGPP, University of California, Riverside, CA 92521 gJet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91007Abstract. The five large solar particle events during October-November 2003 presented anopportunity to test shock acceleration models with in-situ observations. We use solar particlespectra of H to Fe ions, measured by instruments on ACE, SAMPEX, and GOES-11, toinvestigate the Q/M-dependence of spectral breaks in the 28 October 2003 event. We find thatthe break energies scale as (Q/M)b with b ≈ 1.56 to 1.75, somewhat less than predicted.  We alsoconclude that SEP spectra >100 MeV/nucleon are best fit by a double power-law shape.INTRODUCTIONThe Halloween 2003 period provided the opportunity to study the spectra of fivelarge solar energetic particle (SEP) events within a 10-day period, each associatedwith an X-class flare and very fast (>1500 km/sec) CME.  An overview of this periodis shown in Figure 1, which includes oxygen intensities in several energy intervals. Inthe two largest events (events 2 and 3), particles were still being accelerated to ~10MeV/nuc when the shock reached 1 AU.  Two studies of these five events [1, 2] haveshown that elements from H to Fe have rather prominent spectral breaks in the energyrange from ~3 to ~30 MeV/nuc, similar to those in earlier studies by Tylka et al. [3, 4].Li, Zank and Rice [5; hereinafter LZR] have recently extended the model of Zank,Rice and Wu [6] to heavier ions.  In their model the break energy is proportional to thesquare of the charge-to-mass ratio (Q/M), where Q is the charge state and M is theion’s mass number.  In this paper we combine measurements from instruments onACE, SAMPEX and GOES-11 to obtain SEP energy spectra for the five Halloweenevents and the Jan. 20, 2005 event. We test the Q/M dependence predicted by LZRwith observations of spectral breaks for nine elements following the strong shock fromthe Oct 28, 2003 SEP event. We also show that a double power-law shape providesexcellent fits to the high-energy (>100 MeV/nuc) spectra in these events.227Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jspFigure 1:  Time history of energetic oxygen nuclei measured by the SIS and ULEIS instruments onACE (from Cohen et al. [1]). Five large SEP events are evident (numbered 1 to 5). Interplanetaryshocks are indicated by vertical solid lines and X-class flares are shown along the top.OBSERVATIONSThe shock from the 28 October 2003 event reached Earth within 19 hours followedby driver gas traveling at ~2000 km/sec [7].   Upon arrival at 1 AU this shock was stillaccelerating oxygen to ~10 MeV/nuc (see Figure 1) and protons to ~30 MeV [2].Figure 2 shows energy spectra measured during the 6 hours following the arrival ofthe shock. Note that all species show a relatively sharp break at energies ranging froma few MeV/nuc to ~30 MeV/nuc.  The location of the breaks depends on species –lighter species have higher break energies than heavier species like Fe (see also Tylkaet al. [3]). These spectra provide an excellent opportunity to test the prediction of LZR[5] that the location of the breaks should scale as (Q/M)2.The spectra in the left panel of Figure 2 were fit by a two-step procedure. In thefirst step the points above and below the apparent break were individually fit withpower-laws, giving average power-law indices of –1.43 below the break and –4.1above the break.  In the second step power-laws with these fixed, average slopes wereindividually scaled to fit the points above and below the break, and the intersection ofthe two power-laws was defined as the break energy.  The break energies ranged from31 MeV for protons to 4.1 MeV/nuc for Fe.Ellison and Ramaty [8] proposed that shock-accelerated SEPs would have spectraof the form:dJ/dE = KE-γ exp(-E/Eo).  (1)Here J is the intensity, K, Eo, and γ are constants, and we have treated E as energy/nuc.This spectrum, which is a power-law at low energies with an exponential roll-over at228Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsphigh energies, has been used extensively by Tylka et al. [3, 4] to fit SEP spectra, andwe use this form to obtain a second estimate of the break energy. The average value ofγ was 1.3.  Using γ = 1.3 the spectra were then refit to determine Eo for each species,which ranged from 31 MeV for protons to 3.5 MeV/nuc for Fe (see Figure 3).FIGURE 2.  (Left) Spectra from the period following the shock on 29 October are fit with two power-laws using a fixed slope of –1.43 at low energy and –4.1 at high energy. The intersection of these fitsdetermines the break energy.  (Right) The same data are fit with the Ellison-Ramaty spectral form usinga fixed value of –1.3 for the power-law index.  Data are from the SIS, ULEIS and EPAM instrumentson ACE, and the EPS sensor on GOES-11 (see Mewaldt et al. [2] for additional details). Each elementhas been multiplied by a scale factor to separate the spectra.In order to investigate the Q/M-dependence of the breaks we use charge-statemeasurements from the same event by Labrador et al. [9] obtained using thegeomagnetic method with the MAST instrument on SAMPEX [10].  The energyintervals range from 15 to 60 MeV/nuc for O to 27 to 90 MeV/nuc for Fe.  The twoestimates of the break energies are plotted against Q/M in Figure 3.FIGURE 3. Break energies from Figure 2 are plotted versus Q/M.  Fits to the Z≥2 data give somewhatweaker dependence on Q/M than is expected from the theory of LZR [6].229Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jspFIGURE 4. H and He Fluence spectra for the Nov. 2, 2003 event are better fit with the double power-law form of Band et al. [11; Right] than with the Ellison-Ramaty spectral form (Left).The fluence spectra for the five Halloween events (integrated over the events) alsohave spectral breaks [2, 1].  For these spectra the Ellison-Ramaty form is adequate upto ~100 MeV/nuc, but fails to fit the spectra at higher energies [2].  Figure 4 illustratesthat spectra >100 MeV/nuc are better fit by a double power-law formula from Band etal. [11], given by:dJ/dE  = CE-γa exp(-E/Eo)  for E ≤ (γb – γa)Eo;   dJ/dE = CE-γb{[(γb – γa)Eo](γb-γa) exp(γa – γb)} for E ≥ (γb – γa)Eo.         (2)Here γa is the low-energy power-law slope and γb is the high-energy power-lawslope. Spectra from the five Halloween events are shown in Figure 5, along with theJan. 20, 2005 event, where the breaks are at lower energy, and the spectra above thebreaks are much harder.  In this event the H and He spectra above the breaks extend aspower-laws with an index ≈ -2.2 for about two decades in energy or more.FIGURE 5.  (Left) Fluence spectra for the Oct.-Nov. 2003 events fit with the Band et al. shape[11].  Spectral indices above and below the break are indicated. (Right) The 20 Jan. 2005 event had adouble power-law shape with a very hard spectrum.  Data are from ACE, SAMPEX and GOES-11 [2].230Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jspDISCUSSIONIn the model of LZR [5] streaming protons escaping upstream from the shockgenerate enhanced turbulence in the form of Alfven waves that extends over ~2decades in wave number (k; see Lee [12] and Ng, Reames, and Tylka [13], hereinafterNRT]). The proton-amplified Alfven waves play a key role in scattering particles andkeeping them near the shock where they can be efficiently accelerated.  According toLZR, the break in the power-law spectrum for a given species occurs at the maximumachievable momentum/nuc (pmax) for which there is efficient acceleration, whichcorresponds to the momentum/nuc that resonates with the minimum k-value (kmin) forwhich there is enhanced turbulence.  Thus, for species i,kmin = (Qi/Mi)(eB/c pmax), (3)where B is the magnetic field strength, e the electron charge, and c the speed of light.Converting from momentum/nuc to energy/nuc (E) the break-energy of species i(Emax,i) is related to that of protons byEmax,i  =  (Qi/Mi)2Emax,p . (4)In the LZR model the sudden decrease in the turbulence level at k values below kminleads to a sudden increase in the diffusion coefficient, thus allowing higher-energyparticles to freely escape upstream from the shock.  There are similar, though lesssharp, breaks in the wave spectra calculated by NRT. Recently, evidence has beenreported for proton-amplified Alfven waves at 1 AU in large SEP events [14, 15].The location of the breaks for He to Fe (Figure 3) are reasonably consistent with thepower-law behavior predicted by LZR, although the slope that we find (1.56 to 1.75)is somewhat less than predicted.  Note that the proton break energy is low comparedwith the fits to the heavy ions. Li and Zank (personal communication) have pointedout that while heavy ions should act like test particles, protons may not, becauseprotons produce the waves that govern this process [5,  13].Cohen et al. [1] analyzed the location of spectral breaks for 8 ≤ Z ≤ 26 ions in thefluence spectra of the five Halloween events.  Using average SEP charge statesmeasured at lower energy they find that the breaks scale like (Q/M)b with b =  0.9 to1.5.   Mewaldt et al. [2] found that breaks in the H and He fluence spectra suggest b =0.7 to 1.3, similar to Tylka et al. [3].  It is possible that the expected Q/M dependencein fluence spectra is washed out somewhat because the maximum energy (Emax) isgreater closer to the Sun than at 1 AU.  Fluence spectra from 1 AU inevitably includeparticles accelerated close to the Sun as well as those accelerated locally [5].There are also likely to be longitudinal differences in the break energies that maydepend on shock geometry [4].  In fluence spectra the magnetic connection point tothe shock evolves with time, and this evolution depends on the event location. Theseconsiderations, not accounted for in most theoretical models, complicate comparisonssuch as these.  Presumably, contributions from particles accelerated closer to the Sunor at different longitudes are minimized in the Oct. 29, 2003 shock period, where localacceleration dominates, and the Q/M-behavior comes closest to the model predictions.231Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp     Cohen et al. [1] suggested that the location of spectral breaks in fluence spectra isgoverned by diffusion processes, such as escape upstream from the shock.  In thiscase, spectral breaks for different species should occur at the same value of thediffusion coefficient [16].  Cohen et al. [1] found that the fluence spectra of 8 ≤ Z ≤ 26ions in the Halloween events shared a common spectral shape (see also [2]).Assuming a diffusion coefficient that scales as (M/Q)α, they found α = 0.8 to 2.7.Following Droege [17], Cohen et al. related the value of α  to the spectrum ofinterplanetary turbulence (taken to be a power-law in wave number, k-q).  Theyconcluded that SEP spectral breaks in these events were organized by wave spectra inthe range from k-1.2 to k0.7 (see also [2]), significantly flatter than a k-5/3 Kolmogorovspectrum, consistent with a source of turbulence near the shock where the ions wereaccelerated.  It is interesting that calculations by NRT [13] show that proton-amplifiedAlfven waves in SEP events can produce broad features in the wave spectra with q≈0,and that similar wave spectra have been reported in SEP events at 1 AU [14, 15].Finally, we point out that the nature of spectra beyond the breaks has space-weatherimplications.  The Band et al. form fits the Halloween spectra better than the Ellison-Ramaty form [2], and a power-law above the break is clearly required for the Jan. 20,2005 event.  Extrapolating these spectral forms results in significantly differentestimates of SEP radiation doses, especially behind several g/cm2 of shielding.  It istherefore important to continue efforts to understand and eventually forecast not onlythe location of spectral breaks, but also the nature of the spectra beyond the breaks.ACKNOWLEDGMENTSThis work was supported by NASA under grants NNG04GB55G, NNG04088G,and NAG5-12929.  We appreciate the availability of GOES-11 data from NOAA’sSpace Environment Center at http://www.sec.noaa.gov/Data/index.html.REFERENCES1. Cohen, C. M. S., et al., to be published in JGR, (2005).2. Mewaldt, R. A., et al., submitted to JGR, (2005).3. Tylka, A. J., et al., Ap. J., 558, L59-L63, (2001).4. Tylka, A. J., et al., to be published in Ap. J., (2005).5. Li, G., Zank, G. P., and Rice, W. K. M., to be published in JGR, (2005).6. Zank, G. P., Rice, W. K. M., and Wu, C. C., JGR, 105, 25079-25095 (2000).7. Skoug, R. M., et al., JGR 109, A9, DOI: 10.1029/2004JA010494 (2004).8. Ellison, D. C., and Ramaty, R., Ap. J., 298, 400-408 (1985).9. Labrador, A. W., et al., to be submitted to the 29th Internat. Cosmic Ray Conf., Pune, India, (2005).10. Leske et al., Ap. J., 452, L149-L152 (1995).11. Band, D., et al., Ap. J., 413, 281-292, (1993).12. Lee, M. A., JGR, 88, 6109-6119, (1983).13. Ng, C. K., Reames, D. V. and Tylka, A. J., 591, 461-485, (2003).14. Bamert, K., et al., Ap. J., 601, L99-L102 (2004).15. Kallenbach, R., et al., this volume (2005).16. Cummings, A. C., Stone, E. C., and Webber, W. R., Ap. J. 287, L99-L103 (1984).17. Droege, W., Ap. J. Suppl. 90, 567-576 (1994).232Downloaded 02 Oct 2007 to 131.215.225.176. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp

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Solar Energetic Particle Spectral Breaks

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