On the Energy Dependence of Ionic Charge States in
Solar Energetic Particle Events
B. Klecker1, E. Mobius2, M.A. Popecki2, M.A. Lee 2, and A.T.
Bogdanov3
(1) Max-Planck-Institut fur extraterrestrische Physik, 85741 Garching, Germany
(2) Space Science Department and Department of Physics, University of New Hampshire, Durham,
03824, NH, USA
(3) Technische Universitdt Braunschweig, 38106 Braunschweig, Germany
ABSTRACT In large, gradual, interplanetary shock related solar energetic particle events an increase of the mean
ionic charge of heavy ions with energy is often observed. There are large event to event variations. For Fe, for
example, the observed variation in the energy range 0.1-1 Mev/nuc ranges from ~ 1 — 2 charge units to about 4
charge units. Large increases of the mean ionic charge with energy could be explained by acceleration at low
coronal altitudes and charge stripping in this sufficiently dense environment. However, some of the events show
evidence for local acceleration at interplanetary shocks. In this low-density environment the charge stripping
mechanism would not work. We investigate rigidity dependent effects at quasi-parallel shocks, that could be due
to mass per charge dependent effects of the acceleration, propagation, or loss processes, resulting in a mass per
charge dependent exponential cutoff of the energy spectra. We show that a mass per charge dependent cutoff as
observed recently in large, gradual solar energetic particle events will also result in an increase of the mean ionic
charge with energy.
INTRODUCTION
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Fe Mean
The ionic charge composition of suprathermal ions is a
sensitive indicator for the temperature of the source
region. Besides that, the acceleration and transport
processes depend significantly on velocity and rigidity,
i.e. on the mass and ionic charge of the ions. With
experiments onboard the SAMPEX, SOHO and ACE
spacecraft earlier measurements with ISEE-3 (e.g.
Hovestadt et al, 1981; Luhn et al, 1985) of the ionic
charge composition of suprathermal ions accelerated at
coronal or interplanetary shocks have been extended
over a much larger energy range. With SAMPEX an
increase of the mean ionic charge at energies > 10
MeV/nuc has first been observed for two gradual solar
energetic particle events (SEP) in October / November
1992 (Mason et al., 1995; Leske et al., 1995; Oetliker et
al., 1997, s. a. Fig. 1). New measurements with
improved resolution and sensitivity with SOHO and
ACE showed that the mean ionic charge in the energy
range ~ 30 to 500 keV/nuc increases with energy in
many events, with a large event-to-event variability
(Mobius et al., 1999; Mazur et al., 1999, Bogdanov et
al., 2000; Klecker et al., 2000). The increase of the
mean ionic charge between solar wind energies and ~ 60
MeV/nuc is most noticeable for heavy ions (e.g. Si, Fe).
Figure 1 shows as an example for the range of the
energy dependence of the mean ionic charge of Fe the
observations for 3 events in 1992, 1997, and 1998.
10
-Nov6, 1997 (ACE) /
———————— * */
'UTT
T '** "
J"
W '4^/™««iji.>.../
T
T j ----\/
12
i
/
Oct+-Novl992 (SAMPEX) -
• May 1, 1998 (SQHQ+ACE)
4
10"2
10"1
10°
101
E (MeV/nuc)
FIGURE 1. Typical cases of the energy dependence of
the mean ionic charge of Fe as observed for 3 gradual
SEP events in 1992, 1997 and 1998. The dotted line
shows the energy dependence as computed for charge
stripping low in the corona. The dashed line is taken
from Fig. 3; for details see the text.
CP598, Solar and Galactic Composition, edited by R. F. Wimmer-Schweingruber
© 2001 American Institute of Physics 0-7354-0042-3/017$ 18.00
317
The November 1992 event shows an almost constant Fe
mean ionic charge of ~ 11 at energies < 3 MeV/nuc with
a large increase to - 17 at - 60 MeV/nuc. In the
November 6, 1997 event, on the other hand, the mean
ionic charge of Fe increases from ~ 10 to 14.5 at low
energies, in the energy range 0.18 - 0.54 MeV/nuc, with
a further increase up to ~ 18.5 in the energy range 12 60 MeV/nuc (Cohen, et al, 1999). However, it should
be noted that in this case the mean ionic charge at high
energies has been inferred from M/Q dependent
composition arguments and has not been directly
measured. The third example (May 2, 1998) shows the
Fe mean ionic charge as determined for a particle
intensity increase at energies < 1 MeV/nuc that was
closely related to the passage of an interplanetary shock,
and the acceleration most likely occurred in interplanetary space (Klecker al., 2000). In this case a
moderate increase of the mean ionic charge from solar
wind values (~ 10) at suprathermal energies (30 - 70
keV/nuc) by ~ 2 charge units to ~ 12 at ~ 400 keV/nuc
was observed. For this event no ionic charge state
measurements at higher energies are available.
INTERPRETATION OF AN ENERGY
DEPENDENT IONIC CHARGE
DISTRIBUTION
Stripping low in the Corona
A monotonic increase of the mean ionic charge with
energy in the sub-MeV/nuc energy range would be a
natural consequence if the particles are propagating in a
sufficiently dense environment low in the corona. This
has been pointed out by Reames et al., 1999. It is well
established from laboratory measurements that energetic
ions rapidly approach an equilibrium mean ionic charge
when traversing small amounts of matter of the order of
~ jig/cm2 (e.g. Betz, 1972). This equilibrium charge Qeq
(Z,v) increases with energy and depends on the ion
atomic number, Z, and velocity, v and it is the basis of
our understanding of the stopping power and ranges of
heavy ions in matter (see e.g. Ziegler, 1980 and
references therein). Semi-empirical expressions for Qeq
(Z, v) have been derived for the propagation of heavy
ions through neutral solids and gases and have the form
Qeq (Z,p) = Z * (1- exp(-125 p / Z2/3),
(1)
where P = v/c, and c is the speed of light. The functional
form of the exponent in (1) is based on the interactions
of heavy ions with the electrons of the atoms of the
target material. Note that the factor Z2/3/137 is the
electron velocity PTF = VTF/C in the Thomas-Fermi atom
318
model, in units of the speed of light (see e.g. Northcliff
and Schilling, 1970, and references therein).
With the argument based on earlier work by Luhn and
Hovestadt (1987) that in a plasma environment ionizing
interactions will depend on the relative velocity Prei of
the ion and the thermal electrons, Reames et al. (1999)
estimated the mean ionic charge of heavy ions for the
limiting case of equilibrium mean charge states due to
stripping by replacing P in equation (1) by Prei = pion
+ Pe,th> where Pion and Pe?th are the ion speed and the
thermal speed of the electrons, respectively, in units of
the speed of light. The dotted line in Fig. 1 illustrates
the resulting energy dependence of the equilibrium ionic
charge of iron for a coronal temperature of 1.3 MK,
using the approximation of Reames et al. (1999). Figure
1 shows that, both, the functional dependence of the
increase of the mean ionic charge of Fe as observed in
the Nov 6, 1997 SEP event and the absolute values in
the energy range 0.2 - 0.5 MeV/nuc can be reasonable
well reproduced. The requirements on electron density,
Ne, and resident time, T, to achieve this equilibrium
ionic charge depend on energy and are at ~ 1 MeV/nuc
Ne t > 1010 cm"3s (Reames et al. 1999, Kocharov et al.,
2000). This corresponds, for acceleration times of ~ 10
to 10000 s, to electron densities of 109 to 106 cm"3, i.e.
to radial distances at the Sun significantly below 2 solar
radii. However, at higher energies the equilibrium ionic
charge of Fe is significantly higher than the mean ionic
charge of Fe inferred by Cohen et al. (1999) for the
Nov 6, 1997 event. Whether this could be due to nonequilibrium effects as discussed below needs detailed
model calculations and is beyond the scope of this
paper.
The stripping process will also work for somewhat
lower values of Ne t, with the difference that charge
stripping equilibrium will not be reached and the mean
ionic charge will be somewhat smaller than the
equilibrium value and has to be computed by using the
appropriate ionization and recombination cross sections.
Models including the effects of shock acceleration,
statistical acceleration and charge exchange reactions
have been used to investigate the implications of charge
exchange reactions on ionic charge states in gradual
(Barghouty and Mewaldt, 1999, 2000; Kartavykh and
Ostryakov, 1999) and impulsive solar energetic particle
events (Ostryakov et al., 2000). The results showed that
the mean ionic charge and the charge distribution in the
energy range 0.20 - 0.50 MeV/nuc as observed in the
Nov 6, 1997 event can be reproduced reasonably well
(e.g. Stovpyuk and Ostryakov, 2001). However, these
authors did not try to simultaneously fit the ionic charge
of Fe at higher energies as inferred for this event by
Cohen etal. (1999).
However, some events, in particular those showing
large intensity enhancements at low energy at an interplanetary shock, consistent with local acceleration in
interplanetary space, exhibit also small, but significant
increases of the mean ionic charge of heavy ions with
energy (Bogdanov et al, 2000, Klecker et al, 2000, see
also Fig. 1). For acceleration in interplanetary space
stripping will not work because of the small density, and
other processes may play an important role.
the ionic charge composition and the elemental
composition will vary with velocity, as shown below.
Deviations from the simple power law energy
dependence of the energy spectra can be expected if at
least one of the above assumptions is violated. Non
steady state conditions, particle losses, or finite shock
size will generally result in a high-energy roll-over,
with particle spectra falling off more steeply than
described by a power law (e.g. Forman, 1981; Ellison
and Ramaty, 1985, and references therein). Energetic
particle spectra similar to steady state solutions of a
planar shock model with exponential roll-over from
losses and finite shock size have been described, for
example, by Ellison and Ramaty (1985). They find for a
diffusion coefficient Kof the form K ~ |3 R
Local Shock Acceleration and Energy
Dependence of the Mean Ionic Charge
In the test particle limit of diffusive shock acceleration
at a quasi-parallel, planar shock, steady state conditions,
and no losses, the distribution function of ions with
mass, M, and ionic charge, Q, is given by
j(E) = j0 E^ exp (-n0), with
(3)
Eo(A/Q)~E 0 , p * Q / A ,
(4)
where E0?p is the e-folding energy of protons. Spectra of
this form have been reported recently for large, gradual
events by Tylka et al. (2000). The observed spectra have
been fitted using the spectral shape (3) and showed
systematic differences of the e-folding energy E0 for
particles of different mass per charge ratio that could be
approximated by E0 (A/Q) ~ E0? p* (Q/A)6, with 8 in the
range 0.8 - 2.3. In fact, Tylka et al. (2000) successfully
used these systematic differences to infer mean ionic
charge states of heavy ions for 2 large, gradual events in
1998.
(2)
with particle velocity, v, and injection velocity, v0,
respectively. In this ideal case the spectral index y is
determined by the shock compression ratio (e.g. Axford
et al., 1977; Blandford and Ostriker, 1978) and is
independent of mass and ionic charge, i.e. no variations
of the ionic charge (and elemental) composition with
energy would be expected. However, if the energy
spectra depend on both, velocity and mass per charge,
104
102
10D
QMeV
"i
1
I
10-"
10"'
10U
10'
10a
E (MeV/nuc)
E (MeV/nuc)
FIGURE 3. Mean ionic charge of Fe and Fe/O ratio as
a function of energy, computed for 3 different values of
the e-folding energy E0?p.
FIGURE 2. Model energy spectra of selected ionic
charge states of Fe for power law spectra with an
exponential cutoff of the form j(E) = j0 E~T exp (-E/E0),
with E 0 ( A/Q) ~E 0 ,p * Q / A .
319
If this spectral form holds for individual charge states, a
moderate energy dependence of the mean ionic charge
is a natural consequence. To illustrate this effect we
computed in Fig. 2 the differential energy spectra of
iron with ionic charge states of 6, 10, 14, and 18, using
equations (3) and (4), 8 = 1 , and y = 2.
The effect of the rigidity dependent cutoff that varies
systematically with ionic charge state is evident. A M/Q
dependent cutoff of the form described above will result
in a suppression of low ionic charge states, i.e. in an
increase of the mean ionic charge with energy. At the
same time, also the relative abundances of elements
with different M/Q will vary with energy.
In Fig. 3 we computed the mean ionic charge of Fe for
three values of the e-folding energy of protons (30
MeV, 10 MeV and 1 MeV), assuming solar wind abundances of the individual Fe charge states as reported for
the May 1, 1998 Interplanetary Shock event (Klecker et
al. 2000). Figure 3 demonstrates that values of E0?p in
the range of ~ 10-30 MeV as observed by Tylka et al
(2000) result, for this simple model, in an almost constant mean ionic charge at energies < 3 MeV/nuc, with
an increase to QFe ~ 15-17 at 50 MeV/nuc. For E0jp =
30 MeV, this functional dependence is very similar to
the SAMPEX observations in the October 30 to
November 6, 1992 event. This is illustrated by the
dashed line in Fig. 1, where EO,P = 30 MeV and the same
parameters have been used as in Fig. 3. Smaller values
of E0 will result in an increase of the mean ionic charge
starting at lower energies, as demonstrated for E0,p = 1
MeV in Fig. 3. This example shows that small increases
of the mean ionic charge of Fe by 1 - 2 charge units in
the energy range 0.1-1 MeV/nuc could also be caused
by a mass per charge dependent cutoff in the energy
spectra. The small increase of the mean ionic charge of
Fe from ~ 10 to 12.5 in the energy range 0.03 - 0.4
MeV/nuc as observed by SOHO and ACE in the May 1,
1998 SEP event (Fig. 1) would be consistent with such a
model. For a quantitative comparison detailed spectral
information from several instruments on ACE will be
needed. This investigation is planned as an extension of
the present study in a future paper.
A rigidity dependent cutoff of the energy spectra would
also result in systematic variations of elemental
abundances with particle velocity. This is illustrated in
Fig. 3, where the Fe/O-ratio is computed from the Fe
spectra for individual ionic charge states, assuming
ionic charge abundances as measured in the solar wind
during the May 1, 1998 event, as described above,
summed over all charge states, and an oxygen spectrum
computed also with equations (3) and (4). For oxygen a
charge state of 6 and the same parameters have been
used as for iron, and the Fe/O-ratio has been normalized
to 1 at 0.01 MeV/nuc. Figure 3 illustrates that the
320
increase of the mean ionic charge and the decrease of
the Fe/O ratio are directly related, as expected. Values
of E0,p in the range 10-30 will result in a decrease of
the Fe/O-ratio in the energy range ~ 0.5 - 20 MeV/nuc
by a factor of ~ 10. In case of the October 30 and Nov 2,
1992 events a decrease of the Fe/O-ratio from 0.41 ±
0.03 near 1 MeV/nuc (Mason et al., 1995) to 0.031 ±
0.007 and 0.071 ± 0.006 at - 28 - 65 MeV/nuc has been
observed, indeed (Selesnick et al., 1993). Thus, the
rigidity dependent cutoff effect seems to be a promising
candidate for the interpretation of ionic charge
variations with energy of the type observed in the Nov
2, 1992 event that are difficult to understand otherwise
(s. a. discussion in Oetliker et al., 1997), or for only
small increases of the mean ionic charge with energy at
energies < 1 MeV/nuc.
In this mechanism, the variation of the mean ionic
charge with energy is limited to the range of ionic
charge states available in the source, i.e. there is the
additional requirement that the initial ionic charge
distributions consist of at least two ionic charge states.
Therefore the largest effect can be expected for ions
with a broad solar wind ionic charge distribution as
observed for Fe, consistent with observations.
DISCUSSION AND SUMMARY
An increase of the mean ionic charge of heavy ions with
energy has been observed in many solar energetic
particle events. There is a large event-to-event
variability of this energy dependence.
Large increases of the mean ionic charge in the energy
range 0.03 to 0.5 MeV/nuc with a further increase at
higher energies could be explained by additional
stripping of electrons low in the corona (e.g. Qm (Fe)
~ 15 at 1 MeV/nuc), if the density is sufficiently high to
establish charge stripping equilibrium.
Moderate increases of the mean ionic charge at
energies < 10 MeV/nuc (e.g. Qm (Fe) - 13 at 10 MeV/
nuc) with a further increase at higher energies could be
explained by the stripping mechanism and nonequilibrium conditions (e.g. Ostryakov and Stovpyuk,
1999).
A constant mean ionic charge of Fe at energies < 1
MeV/nuc with a large increase at higher energies could
be explained by an exponential, M/Q dependent, cutoff
in the energy spectra.
A moderate increase of the mean ionic charge of Fe
from ~ 9 - 10 (Solar Wind source) by ~ 1 - 3 charge
units in the energy range < 1 MeV/nuc would also be
consistent with a rigidity dependent exponential cutoff
of the energy spectra, provided the e-folding energy E0
is sufficiently small.
11. Hovestadt, D. et al., The SOHO Mission (editors: Fleck,
B. et al.), Solar Physics 162, 441 - 481 (1995).
12. Kartavykh, Y.Y. and V.M. Ostryakov, 26th ICRC 6, 272 275 (1999).
13. Klecker, B. et al., ACE 2000 Symposium, AIP Conf.
Proc. 528, 135-138 (2000).
14. Kocharov, L. et al., Astron. & Astrophys. 357, 716 - 724
(2000).
15. Lee, M. A., ACE 2000 Symposium, AIP Conf. Proc. 528,
3-18 (2000).
16. Leske et al., Astrophys. J. Lett. 452, L149 - L152 (1995).
17. Luhn, A. et al., Proc. 19th ICRC, 4, 241 - 248 (1985).
18. Luhn, A., and D. Hovestadt, 1987, Astrophys. J. 317, 852
- 857 (1987).
19. Mason, G.M., et al., Astrophys. J. 452, 901 (1995).
20. Mazur, I.E., G.M. Mason, M.D. Looper, et al., Geophys.
Res. Lett. 26, 173 - 176 (1999).
21. Mobius, E., et al., Space Science Reviews 86, 449 - 495
(1998).
22. Mobius, E., M. Popecki, B. Klecker, D. Hovestadt, et al.,
Geophys. Res. Lett. 26, 145 - 148 (1999).
23. Northcliffe, L.C., and R.F. Schilling, Nuclear Data
Tables, A7, 233 - 463 (1970).
24. Oetliker, M., B. Klecker, D. Hovestadt, et al., Astrophys.
J. 477, 495 - 501 (1997).
25. Ostryakov, V.M and Stovpyuk, M.F., Solar Physics 189,
357-372 (1999).
26. Ostryakov, V.M., Kartavykh, Y.Y., Ruffolo, D., et al, J.
Geophys. Res. 105, A12, 27315 - 27322 (2000).
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Lett. 26, 3585 - 3588 (1999).
28. Selesnick, R.S., et al., Astrophys. J., 418, L45 - L48
(1993).
29. Stovpyuk, M.F. and V.M. Ostryakov, Solar Physics 198,
163 - 167 (2001).
30. Tylka, AJ. et al., ACE 2000 Symposium, AIP Conf.
Proc. 528, 147 - 152 (2000).
31. Ziegler, J.F., Handbook of stopping cross-sections for
energetic loss in all elements, Vol. 5, Editor J.F. Ziegler,
Pergamon Press, (1980).
So far we discussed the two limiting cases, i.e. (1)
stripping low in the corona, and (2) M/Q dependent
acceleration effects in interplanetary space. In principle,
a combination of the two effects could also occur. In
both cases, the large variability of the energy
dependence could be explained by the variability of the
acceleration parameters and, in case of acceleration
close to the Sun, by the variability of the electron
density. In order to determine which of the mechanisms
is important in individual SEP events, a precise
determination of the ionic charge dependence on energy
and the determination of the energy spectra over a wide
energy range are essential. In the case of stripping, for a
large range of coronal temperatures of - 106 to 107 K a
relatively steep increase of the mean ionic charge in the
energy range 0.1-1 MeV/nuc is expected (Kocharov et
al., 2000), i.e. in the energy range where measurements
from SAMPEX and ACE are available. For M/Q
dependent cutoff effects and an exponential cutoff, on
the other hand, at E < 1 MeV/nuc no energy
dependence, or only a gradual increase, accompanied by
compositional variations, would be expected. However,
the approximation of an exponential cutoff may be too
simplistic and not be a good fit for all cases. As has
been shown by Lee (2000) in a model combining shock
acceleration with interplanetary transport and upstream
escape, the exponential cutoff could show a much more
involved dependence on particle and shock parameters.
In any case, the precise determination of the ionic
charge distribution in the energy range - 0.1 to 10
MeV/nuc provides a powerful tool for the investigation
of source locations and acceleration processes of solar
energetic particles in CME or interplanetary shock
related events.
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