The effects which solar flare X-rays have on the charge states of solar cosmic rays is determined quantitatively. Rather than to characterize the charge distribution by temperature alone, it is proposed that the X-ray flux at the acceleration site also is used. The effects of flare X-rays are modeled mathematically

Mullan, D. J.

Waldron, W. L.

English

NASA Technical Reports Server

Semi-annual report for Grant NAG5-567 "Ionic Charge
Distributions of JSaergetic Particles from Solar Flares"
D. J. MuUan.
Bartol Research Foundatioa. University of Delaware. Newark. DE 19716
and
W. L. Waidron
Applied Research Corporation. Suite 650. 8401 Corporate Dr., Landover. MD
20785
This report covers the six-month period from July 1, 1985 to
December 31, 1985.
The purpose of this research is to determine quantitatively the
effects which solar flare X-rays have on the charge states of solar
cosmic rays.
The charge states of the ions which are accelerated in associa-
tion with solar flares have long been considered as of primary
importance in providing us with fundamental physical information
about conditions at the site of acceleration. The reason is obvious:
the energetic particles may be "pure flare material", perhaps com-
ing from the heart of the flare itself. If this is true, then we can
sidestep the difficulties associated with interpreting other signa-
tures of the flare, such as radiation in the visible, .UV, X-ray, and
radio portions of the spectrum. Those other signatures represent a
complicated Convolution of several factors, including local densi-
ties, optical depths, magnetic field strengths, energies of fast elec-
trons and their spectra, etc. In contrast to these, detection of
energetic particles allows us to "reach in" to the flare site and
pluck out. material which has experienced the flare phenomenon
itself, and has now arrived at the detector, essentially unaffected
by interrplanetary effects, carrying "first-hand" information about
the flare site.
The charge distributions of various ions contain information
about the temperature at the acceleration site. If collisional
processes were the only important determinant of the charge dis-
tributions, then a single parameter would characterize those distri-
butions, namely, the local electron temperature. With this assump-
tion, extensive tabular results have been compiled by several
authors, showing the (unique) charge state distribution for each
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particular element. At any given temperature, each element can be
characterized by a unique mean charge. Previous interpreters of
the charge states of solar energetic particles (SEP) have generally
adopted the approach of simply entering such tables with their
observed mean charge valueand reading off the appropriate tem-
perature. We refer to this as an "ionization temperature", rt.
Of course, if this were to be a physically meaningful tempera-
ture of the acceleration site, all of the elements whose charge
states were recorded would yield identical values of 7i.
The problem is, the data definitely do not yield identical values
of ?<. This problem has become especially acute with the extensive
data compiled by ISEE-3. Thus, in a study of three large flares,
Luhn et al (1984) reported rt=2xio8^r for the elements C, N, 0, Si,
and S; 7<=4xioaA'for Ne and-Fe; and ?;=7xio8A" for Mg. No stretching
of the tables can possibly yield identical values of Ti for the three
groups of elements. We therefore conclude that the straightforward
interpretation of the observed charge states in terms of a "tem-
perature" is not physically meaningful.
We proposed that the charge distribution would be seriously
affected by X-rays from the flare. Hence, rather than characteriz-
ing the charge distribution by a single parameter ("temperature"),
we proposed that a second parameter would be essential, namely,
the X-ray flux at the acceleration site. We proposed to calculate
quantitatively how the charge distributions would be altered in the
presence of realistic flare X-ray spectra.
To model the effects of flare X-rays, we proceed as follows. The
temperature structure of the solar atmosphere is taken to be basi-
cally two plateaus, one chromospheric (at T = 9500 K), the other
coronal (at T=2xio8A" ). Between these two plateaus, there is a tran-
sition region where the temperature varies linearly with height
over 25 km. In the, absence of X-rays, the ionization structure can
be calculated uniquely for each element in the corona. The flare is
modelled as a source of X-rays located in the transition region, at a
height of 5 km below the base of the corona. The temperature of
the flare X-ray source is taken, in the first instance , to be lO'A":
this is entirely consistent with the measured X-ray spectra of many
solar flares.
To model the effects of flares of varying size, we vary the emis-
sion measure of the X-ray source. Here, we are interested in one-
dimensional X-ray penetration through the solar atmosphere. Thus,
the emission parameter which we use here is a linear one, defined
as
where N, is the local electron density, and 5z is a linear thickness
of the X-ray emitting region. The values which we have explored for
- 3 -
logio EML so far range from 31.5 to 35.5 in steps of 0.25. For com-
parison, we note that the volumetric emission measures, EMV, of
many solar flares lie in the range Iog10 EMV = 48-50. Hence if the
area of flare emission is of order Iog10 area = I0is-5cm2, our choice of
linear emission measure is reasonable. Small solar flares have
dimensions of order 10a cm, and thus it appears that our choice of
area! factor is also empirically plausible. With a uniformly filled
flare volume of side length 108 cm, our choice of EML values
corresponds to electron densities in the range log10JV8 = l 1,75-13.75.
For purposes of calculating the charge distributions, we need
to know the flux of X-rays which pass through unit area of a volume
element in the solar corona near the flare. For this purpose, we
have chosen to consider, in the frist instance, a "target point"
situated in the corona at a distance of 1000 km from the X-ray
source. The latter is treated as a point, although clearly, it is trival
to allow for the finite extent of the source, and to move the "target
point" to an arbitrary location. This choice of distance leads to X-
ray fluxes at the "target point" which lie in the range from 5xio7 to
In the equation of ionization balance, the ionization rate due to
photons is proportional to the first power of the density, whereas
the ionization rate due to collisions, and the recombination rate,
are both proportional to the square of the density. Thus, in a
steady state, where photoionizations are balanced by collisional
recombinations, the charge state will depend on the ratio of X-ray
flux to the local density. It is in terms of that ratio that we will
characterize our results.
However, for definiteness in the calculations, we choose a
coronal density of I012cm.-3. Hence, for the most part, the flare
plasma which we have chosen to model is denser than the ambient
corona, as we would expect.
The calculation proceeds as follows. The X-rays, with a thermal
bremsstrahlung spectrum, are allowed to propagate through the
ambient corona, ionizing the local material as they pass through.
After propagating 1000 km, the local charge distributions are
printed out for each of eight elements: H, He, C, N, 0, Ne, Mg, Si,
and S. For the first four of these elements, the quiet coronal condi-
tions are already such that each of them is essentially stripped of
its electrons. Thus, the dominant stages of ionization are H n, He
El, C VII, and N VIII, even without X-rays. Addition of flare X-rays
does not alter the ionization distribution in any qualitative way.
For oxygen, 0 VII and 0 Vffl are present in almost equal abundances
in the ambient corona: adding flare X-rays pushes the dominant
ionization stage higher, until 0 DC becomes dominant for
logio£jtfL=33.75 and greater.
-4 -
For the remaining four elements, we show in Figures 1-4 how
the relative abundance of the various charge states alters as the
X-ray flux builds up. For example, in the ambient corona, Ne is
predominantly Ne IX, but with increasing X-ray flux, the predom-
inant stage becomes Ne X and finally Ne XI (i.e. fully stripped),
within the range of X-ray fluxes which we have considered. Suppose
we tried to interpret the observation of completely stripped Ne in
terms of collisional processes alone: then according to the tables of
C. Jordan (1968), the "ionization temperature" would have to be at
least as high as 5xioaA". However, as Fig. 1 shows, we can make Ne XI
the dominant stage of ionization even when the ambient tempera-
ture is only 2xioa^r as long as the X-ray flux is large enough (but still
reasonable as far as solar flares are concerned).
In Fig. 2, we show the results for magnesium. Here, within the
range of X-ray fluxes which we have considered, we can drive mag-
nesium to such a state that the predominant ion becomes the fully
stripped one, Mg XIII. For this to occur by purely collisional
processes, Jordan's tables suggest that the temperature would
have to be at least I0xio8/f: and yet, our ambient medium is still at
only 2xioaJT. Thus, the interpretation of a charge state of Mg in such
conditions in terms of purely collisional processes would yield a
source temperature which would be in error by 500%.
In Figs. 3 and 4, we show the ionization states for silicon and
sulfur. Here, the presence of many competing levels of ionization
makes for peculiar charge state distributions: the dominant charge
state remains essentially unchanged in Si, for example, over a very
broad range of X-ray fluxes. For sulfur, the situation is also compli-
cated: the dominant charge state remains 9+ or 10+ over a broad
range of X-ray fluxes, and then changes abruptly to 14+.
In Fig. 5 we show the "apparent ionization temperature" for
four elements as a function of X-ray flux. The ordinate represents
the temperature which the ambient medium would need to have in
order to create the same predominant stage of ionization if the X-
rays were entirely absent. (Note that H, He, C, N, arid 0 would all
lie on a horizontal line at a temperature of 2xio6 in Fig. 5.) In gen-
eral, we can characterize the results by the statement that Mg is
the most sensitive element to the X-ray flux, Ne is next, and S/Si
(along with H, He, C, N, and 0) are the least sensitive.
In view of the empirical results of Luhn et al (1984), the results
in Fig. 5 are of great interest. Qualitatively, the results of Luhn et
al are in complete agreement with Fig. 5: the lowest "apparent ioni-
zation temperatures" are ascribed by Luhn et al to S, Si, C, N, and
0, the highest are ascribed by them to Mg, with Ne lying in
between. This is consistent with the right-hand side of Fig. 5.
Quantitatively, to reproduce the figure of 7xioaA" quoted by
Luhn et al for Mg, we would need to have an X-ray flux to electron
-5-
density ratio of order -0.5 (in the logarithm to base 10). To repro-
duce the figure of 4xio8A" quoted by Luhn et al for Ne, we would
need an X-ray flux to density ratio of order -1.0. And to reproduce
the figure of 2xioaA" quoted by Luhn et al for Si and S, we would
need an X-ray flux to density ratio of -1.5 or less. Thus, we cannot
claim that we yet have obtained quantitative agreement to better
than an order of magnitude with the results of Luhn et al. However,
we note that we have made no attempt yet to optimize the quanti-
tative agreement between our calculations and the results of Luhn
et al: the results in Figs. 1-5 are a first cut through the problem,
with values of solar coronal parameters which seemed plausible.
The fact that our first cut has yielded qualitative agreement
with the empirical results is encouraging. We now plan to do a more
detailed study of parameter space in order to discover whether or
not we can improve on our quantitative accuracy. In particular,
rather than depending solely on the mean charge state (as Luhn et
al prefer to do), we plan to calculate the actual charge distribution
to compare with the ISEE-3 data.
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Ionic charge distributions of energetic particles from solar flares

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