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 association 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 coming from the heart of the flare itself. If this is true, then we can

sidestep the difficulties associated with interpreting other signatures 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 densities, optical depths, magnetic field strengths, energies of fast electrons 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 distributions, then a single parameter would characterize those distributions, namely, the local electron temperature. With this assumption, 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 temperature. We refer to this as an "ionization temperature", rt

.

Of course, if this were to be a physically meaningful temperature 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 "temperature" is not physically meaningful.

We proposed that the charge distribution would be seriously

affected by X-rays from the flare. Hence, rather than characterizing 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 basically two plateaus, one chromospheric (at T = 9500 K), the other

coronal (at T=2xio8A" ). Between these two plateaus, there is a transition 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 emission measure of the X-ray source. Here, we are interested in onedimensional 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 comparison, 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-

5

cm2, 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 Xray 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 conditions 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 predominant 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 temperature 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 magnesium 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 complicated: 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 Xrays 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 general, 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 ionization 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 reproduce 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 quantitative 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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