Observations of polarization of moderately hard X-rays in solar flares are reviewed and compared with the predictions of recent detailed modeling of hard X-ray bremsstrahlung production by non-thermal electrons. The recent advances in the complexity of the modeling lead to substantially lower predicted polarizations than in earlier models and more fully highlight how various parameters play a role in determining the polarization of the radiation field. The new predicted polarizations are comparable to those predicted by thermal modeling of solar flare hard X-ray production, and both are in agreement with the observations. In the light of these results, new polarization observations with current generation instruments are proposed which could be used to discriminate between non-thermal and thermal models of hard X-ray production in solar flares

Emslie, A. G.

Leach, J.

Petrosian, V.

English

The significance of low hard X-ray polarization measurements for non-thermal models is discussed. Such a low polarization result, it is shown, can in fact occur in non-thermal models, and the ways in which the degree of X-ray polarization is correlated with the parameters of these models is discussed

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THE INTERPRETAT ION OF HARD X-RAY POLARIZATIMI
ft-ASUREMENTS IN SOLAR FLARES
J. LEACH
A. G. EASLIE
V. PETROSIAN
SEP 1983
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AUGUST 1983
SUIPR No. 959
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(Nw.wA-CHA^	 THE INTERPRETATI O N OF HARD	
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34874
^
I-RAY POLARIZATION MEASUREMENTS IN SOLAR
FLARES ( Stanford Univ.) 13 p HC A02CSCLA 03B 	 Unclas
G3/92 15056
INSTITUTE FOR PLASMA RESEARCH
STANFORD UNIVERSITY, STANFORD, CALIFORNIA
14
YA
ORIGINAL PAGE 19'
OF POOR QUALITY
The Interpretation of Hard X-ray Polarisation
Measurements in Solar Flares
J. Leach, # .A. G. Emslie, t
 & V. Petrosian.#
Tramiel et al. 1 have recently reported observations of polarization in moder-
ately hard ( 5 - 20 keV) X-rays  occuring in solar flares. In contrast with earlier
observations 2-7 ,  these new measurements exhibit low degrees of polarization
(< 5%). In this letter we comment on the significance of these new measurements
for models of hard X ray production in solar flares, in particular on the issue. Of
whether impulsive, solar flare hard X-ray  emission is predominantly a thermal 8-10
or a non-thermal 
11 — 14
process. Low polarizations are generally considered to
be indicative of a near isotropy of the distribution of bremsstrahlung-producing
electrons, a situation which can arise more naturally in thermal models. Here
we shall discuss the significance of low hard X-ray polarization measurements for
non-thermal models. We shall show that such a low polarization result can in fact
occur in non-thermal models, and we shall discuss the ways in which the degree
of X-ray polarization is correlated with the parameters of these models.
The characteristics of the hard X-ray  emission from solar flares can give im-
portant information about the underlying population of energetic electrons and
I Institute for Plasma Research and Department of Applied Physics, Stanford University, Stanford,
California 94305
,( Department of Physics, The University of Alabama in Huntsville, Huntsville, Alabama 35899
1
ORIGINAL PAGE W
OF POOR QUALITY
hence, indirectly, about the mechanisms by which that electron , 'Upulation is
created. It has been clearly demonstrated 15 that we cannot discriminate between
Clio non-thermal and thermal models on the sole basis of the hard X-ray spectral
form. General attention, therefore, has been turned to other characteristics of
the hard X-ray field, such as its spatial structure, directionality and, most impor-
taut, its polarization. In the early 1070'x, observations of hard X-rays  in flares
2-7,16
found evidence for large polarizations (up to 40%) . A large polarization
implies a non-isotropic distribution for the electrons and therefore favors a non-
thermal model over a thermal model. These measurements have been challenged 17
however, and the resulting dispute 
18 
has not clearly been resolved. The new obs-er-
vations of Tramiel et at, 
1 
are on a more solid observational footing and so should
be able to provide a better diagnostic into the nature of the energetic electron
population.
For isotropic electron distributions such as are expected on the basis of the
thermal models, the polarization of the emitted radiation should, of course, be
zero. However, the presence of temperature gradients can lead to slight electron
anisotropies and hence to low degrees of polarization 19. In addition a small polariza-
tion can arise from the consideration of those photons which are backscattered
by the pliotospher,, 20
 - .
Early studies with non-thermal models, with 23,27 or without 
24-27 
photos-
pheric albedo effects, were all based upon highly simplified angular distributions
for the beam electrons. These early studies all ignored the effects arising from
the geometry or the magnetic field and most of them (except Brown 2S ) also ig-
nnred the Coulomb scattering of the electrons within the target. Hence early non-
A	 (S.
a
,t
2
ORIGINAL PAGE l^'
OF POOR QUALIT-Y
thermal studies tended to derive somewhat higher polarizations than did studies
with thermal models.
The most recent study 
29,30 
uses a rokker-Planck treatment to follow the evolu-
tion of an electron beam in the solar atmosphere and evaluates the characteristics
of the bremsstrahlung hard X-rays produced in such non-thermal models. This
technique is a substantial improvement upon the previous theoretical analyses, and
the results show that low polarizations can arise naturally in non-thermal models.
flc;e we shall compare some of these recent results with the new observations )
 and
then we shall discuss why the calculated X-ray  polarizations are lower than one
would have expected on the basis of earlier models.
The three parameters by which Leach and Petrosian 29 describe their _models
are is (= d In Bids, where B is the magnetic field strength and a is the distance
along the loop), and 6 and ap, which describe the energy (E) and pitch angle
(a) distribution of the injected electrons, viz, f (B, a) , E_s exp(—al/ap). One of
the effects which would normally reduce the polarization of the X-rays  and which
has not been included in previous theoretical studies is the curvature of the flare
magnetic field. Since the orientations of the polarization vectors from different
parts of a curved loop will differ, observations with low spatial resolution will
measure a degree of polarization which is lower than that derived from smaller
(and straighter) portions of the loop. Here, following beach and Petrosian 29, we
shall be using flare loops which are semi-circular, Clearly, more complicated loop
geometries could give rise to an even greater reduction in the degree of polarization.
For one of the observed flares ) (designated as flare 21) we have information
about the hard X-ray  spectrum (Kane, private communication). This data allows
3	 {'
ORIGINAL PAGE E4a
OF POOR QUALITY
us to select a value for 6, thus leaving us with two free parameters, We therefore
compare the observed degree of polarization for this flare with the calculated
polarization curves for three models having different values of a g and tc (figure
1). There are two observational effects to be considered which would reduce the
degree of polarization measured from that which would otherwise be obtained:
(t) At these low X-ray  energies there may be a significant contribution from
an unpolarized thermal background 31 , A clear indication of such contamination
would be an increase in the polarization with increasing X-ray  energy, There may
1
be some evidence for this in the data .
(it) Any variation in the flare characteristics over the relatively long (,^- 2
minutes) integration times of the observations will give .rise to a lower observed
polarization than would be expected from a typical isolated elementary burst of
duration 10 seconds, especially if different elementary bursts are due to the
energization of different loops 
32.
In addition, there is a substantial error bar on the observation and some un-
certainty inherent in the calibration procedure followed l . Consequently we cannot	 }t
set strict limits on the values of the model parameters. However, as we clearly
show in figure 1, a low degree of polarization does not necessarily militate against
non-thermal models.
The reasons for the polarization estimates of reference 30 being lower than the
earlier estimates 
23-28 
are as follows. As seen in a full Fokker-Planck analysis of
the beam dynamics, any injected electron beam becomes increasingly isotropized
as it penetrates further down through the solar atmosphere. Since the rate at
which the electrons diffuse in pitch angle is comparable to the rate at which they
4
01R0G3`IAL V a*; p 
of pooR QUALV
lose energy 
33 
the bulk of the observed hard X-rays are emitted only after the
electron beam has undergone much of this isotropization. Thus the integrated X-
ray emission fror,.i the whole source will have the character of the emission from
a highly broadened electron beam, no matter what the original degree of electron
beaming was at injection. A spatially unresolved measurement of the hard X-ray
polari zation must then give rise to a low value. Certainly, the stronger the initial
beaming of the electrons is, the higher will be the X-ray  polarization, though we
stress that this is no more than a weak effect once the Coulomb collisions have
been properly incorporated into the analysis. Calculations from a variety of flare
models show that X-ray polarizations of around 25% are the most that can be
expected from reasonable model parameters such as those given in Table I, even
from a highly beamed (low ao) model with a uniform magnetic field. The effect of
any non-uniformity in the magnetic field (ic 34
 
0) is to further reduce the degree
of polarization for the highly beamed models.
The parameter 6 (the spectral index of the injected electron beam) exercises a
R
strong influence upon the hard X-ray  polarization. (This parameter was fixed in our
above comparison with the flare of reference jij by independent observations ). The
two cross sections for linearly polarized bremsstrahlung production are functions
of the photon to electron energy ratio and the two cross sections behave differently
as funct;,,.ons of that energy ratio 34 . A flux of "hard" photons, i.e, photons each
having an energy close to that of the emitting electron, will, in general, be more
highly polarized than a flux of "soft" ones (i.e. photons each having an energy
much less than that of the emitting electron). Injected electrons with a flat energy
spectrum (i.e. low 6) will give rise to X-rays  in which a greater proportion of
5
Of IGMIAL FAGt'^* l9
OF POOR 01 1AUTY
the photons are soft and, therefore, the X-rays  gill be less polarized. Conversely,
electron distributions which are steep (large 6) produce generally harder photons
and thereby result in a more highly polarized emission (cf., for example, figure [3b)
in reference 23). As demonstrated in Table I, 6 has a very substantial influence upon
the observed polarization, and is at least as significant as the degree of electron
beaming at injection. This effect has received little attention in the literature to
date.
In summary, the observations of low hard X-ray polarization in solar flared
are in fact quite consistent with both thermal and non-thermal models of hard
X-ray production. Our hope of using polarization data as a discriminant rests
upon our being able to observe the coronal component of the emission in isolation,
for then any strong beaming of the non-thermal electrons, not yet having been
smoothed away by collisions in the thick target, should result in a quite high
0
polarization signature30, easily in excess of that produced in thermal models2y.
Spatially resolved polarization measurements are not yet possible. However, by
looking at flares occuring just past the edge of the solar limb 35 , it should be
possible to observe the emission from the upper part of the flare loop without
that emission 'being contaminated by the signal from the less polarized component
which is formed in the lower parts of the flare loop -,nd is absorbed in the intevening
photospheric layers. Unfortunately, by the same token, the emission from this
upper part of the loop will generally be no more than a small fraction of the total
flare emission, thus presenting problems with statistical noise unless the observed
flare is very large. Currently available instruments, such as the one used by Tramiel
6
ei al. W, should be capable of observing the coronal signal from the large, flares
that can be expected to occur during the next solar maximum.
We would like to thank G. A. Chanan for discussing and communicating the
data prior to publication. During the course of this work A. G. E, held a von
Braun fellowship at U. A. H. fie also expresses his thanks to P. A. Sturrock for his
hospitality at Stanford. J. L. and V. P, were supported by NASA grant NSG-7002
and NSF grant ATM-8218125. A. G. E. was supported by NASA grant NAGW-204
and NSF grant ATM-8303172,
N
7
F
4 j^
{ !j
Table I
The variation of the maximum percentage polarization at 16 keV
with .6 and ao, for ec = 0.0
ao
b oot 0.4 0.04 0.01
3 <5 <5 <5 6
4 8 8 11 13
5 10 11 20 1	 21
6 10 16 26 26
T Giectrons injected isotropically at the top of the loop
8
Fig. L A comparison between the polarization measured for Aare 21 of °Il amiel
et al. 
t 
and the polarizations calculated for three of the models of Leach and
Petrosian . The solid line is for a model with ag = 0.4 and k = 0,0, the dashed
line is for a model with ao = 0.4 and rc == 1.5 X 10- 9 , and the dotted line is for
a model with ad 0.1 and K = 1.5 X 10-9. K = 1.5 X 10"9 corresponds to a
twentyfold increase in the magnetic field strength from the top of the Aare coronal
loop to the transition region, a distance of 2 X 109cm. All three models have a
coronal density of 5 X 109cm-3 . For a pare at disk center the viewing angle would
be 0°, for one on the solar limb it would be 90°.
9
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OF POOR QUALM
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References
(1) Damiel, L. J., Chanan, G. A., and Novick, R., Astrophysical Journal, sub-
mitted (1983).
(2) Tindo, I. P,, Ivanov, V. D., Mandel'stam, S. L., and Shuryghin, A. I., Solar
Physics, 14, 204 - 207 (1070).
(3) Tindo, I, P,, Ivanov, V. D., Mandel'stam, S. L., and Shuryghin, A. I., Solar
Phy,iics, 24 )
 429 - 433 (1972).
(4) Tindo, 1 P., Ivanov, V. D., Valni6ek, B., and Livshits, M. A., Solar Physics,
27, 120 - 435 (1972).
(5) 'Tindo, I, P., Mandel'stam, S. L., and Shuryghin, A. I., Solar Physics, 32, 4160
- 475 (1973).
(6) Na! a.da, M, P., Neupert, W, M., and Thomas, R. J., Solar Physics, 37, 429 -
435 (1074).
(7) Tindo, I. P,, Shuryghin, A. I., and Steffen, W,, Solar Physics, 48, 210 - 227
(1976).
(8) Crannell, C. J., Frost, K, J,, Miitzler, C., Ohki, K., and Saba, J. L., Astro-
physical Journal, 223, 620- 637 (1978).
(9) Brown, J. C., Melrose, D. B., and Spicer, D. S., Astrophysical Journal, 223,
592 - 597 (1979).
(10) Smith, D. F., and Lilliequist, C. G., Astrophysical Journal, 232, 582 - 589
(1079).
Y
10
*,	 6
(11) Lin, R. P.., and fludson, 11, S., Solar Physics, 17, 412 - 435 (1471).
(12) Brown, A. C., Solar Physics, 18, 484 502 (1971),
(13)Petrosian, V., Astrophysical Journal, 186, 201 304 (1473).
(14) Kane, S. R., in IAU Symposium No. 57, Coronal Disturbances, ed, G. A.
Newkirk, Jr., Reidel, Dordrecht, 105 - 141 (1974),
(15) Brown, J. C., in /AU Symposium No. 68, Solar Gamma, X, and PUV Radia-
lion, ed. S. R. Kane, Reidel, Dordrecht, 245 - 282 (1475).
(16) Somov, B. V., and Tindo, I. P., Cosmic Research, 16, 555 - 564 (1978).
x,7) Brown, J. C., McClymont, A. N., and McLean, I. S., Nature, 247, 448 - 449
(1074).
(18)Mandel'stam, S. L,, Beigman,1. L., and Tindo, I, P., Nature, 254, 462 (1975).
(19) Emshe, A. G., and Brown, J. C,, Astrophysical Journal, 237, 1015 - 1023
(1980).
(20)Tomblin, F. F., Astrophysical Journal, 171, 377 - 389 (1472).
(21)Santengelo, N., horseman, H., and Horstman -Moretti, E., Solar Physics, 29,
143 - 148 (1973).
(22)1Ienoux, J. -C., Solar Physics, 42, 2119- 233 (1975).
(23)Langer, S. I-i., and Petrosian, V., Astrophysical Journal, 115, 666 - 676 (1977).
(24) Elwert, G,, in IAU Symposium No. 35, Structure and Development of Solar
Active Regions, ed. K. O. Kiepenheuer, Reidel, Dordrecht, 444- 448 (1468).
11
(25)Elwert, G., and Haug, E., Solar Physics, 20, 413 - 421 (1971).
(26)Haug, C., Solar Physics, 25, 425 - 434 (1472).
(27)Bai, T., and Ramaty, R,, ,Astrophysical Journal, 219, 705 - 726 (1978).
(28)Brown, J. C., Solar Physics, 28, 441 - 459 (1972).
(29)Leach, J., and Petrosian, V., Astrophysical Journal, 251, 781 791 (198.1).
(30)Leach, J., and Petrosian, V., Astrophysical Journal, 289, 715 - 727 (1983).
(31)Emslie, A. G., and Vlahos, L., Astrophysical Journal, 242, 359 - 373 (1980).
(32)de Jager, C., and de Jon g-c- G., Solar Physics, 58, 127 - 137 (1978).
(33) Krall, N. A., and Trivelpiece, A. W., Principles of Plasma Physics, McGraw-
Mill, New York, § 6,4 (1973).
34) Tsena, I1. K., and Pratt, R. H., Physical Review, A7, 1502 - 1515 (1973).
(35) Kane, S. R,, Fenimore, E, E., Klebesadel, R. W., and Laros, J. G., Astro-
physical Journal (Letters), 254, 1,53 - 57 (1982).
(36) Lemen, J. R,., Chanan, G, A., Hughes, J. P., Laser, M. R., Novick, R.,
Rochwarger, I. T., Sackson, M., and "Framiel, L. J., Solar Physics, 80,
333 - 349 (1982).
s
12


The interpretation of hard X-ray polarization measurements in solar flares

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 This document has been reproduced from the best copy furnished by the 
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furnished in this condition by the organizational source and is the best copy 
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which have been reproduced in black and white. 
 
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 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
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Produced by the NASA Center for Aerospace Information (CASI) 
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^T ' *
THE INTERPRETATION OF HARD X-RAY POLARIZATION
MEASUREMENTS IN SOAR ,FLARES
John Leachl
Center for Space Science and Astrophysics
ctanford University
A. Gordon Emslie
Department of Physics
University of Alabama in Huntsville
Vahfi Petrosiani
Center for Space Science and Astrophysics
Stanford University
	
(NASA-CR-172.790) THE ZNTEEPHETATION OF HARD	 N84- 10142
X-RAY POLARIZATION MEASUEZMENIS IN SOLAR
ZIABES < Staof ord Univ.) 13 p HC A02/MF A01
	
CSLL 03B	 Umc:las
G3j92 18473
ai'lA".^
IAlso Department of Applied Physics, Stanford University
r
t
i
1
t
ii.	 f
i^v
ABSTRACT
We review recent observations of polarization of moderately hard X-rays
in solar flares and compare them with the predictions of recent detailed
modeling of hard X-ray bremsstrahlung production by non-thermal electrons. We
find that the recent advances in the complexity of the modeling lead to
h
substantially lower predicted polarizations than in earlier models and more
i
fully highlight now various parameters play a role in determining the polari-	 . a
i
zation of the radiation field. The new predicted polarizations are comparable
to those predicted by thermal modeling of solar flare hard X-ray production,
and both are in agreement with the observations. In the light of these
results, we propose new polarization observations with current generation
fi
instruments which could be used to discriminate between non-thermal and
thermal models of hard X-ray production in solar flares,
Subiect Headings	 Sun: flares - Sun: X-rays X-rays: bursts.4
k
2
I. INTRODUCTION
Tramiel,	 Chnnan =W Novick (71984),, or TCN for short, 	 have recently
reported observaLLons of polarization in moderately hard ( ,5-20 keV) X-rays
occurring in solar flares.	 In contrast with earlier observations (Tindo et
A_1. 1970, 1972a, 4972b; Tindo, Mandel'stam and Shuryghin 1973; Nakada, Neupert
and Thomas 1974; Tindo, 	 Shuryghin and Steffen ,1976), these new measurements
exhibit low degrees of polarization 01v5%).	 In this article we comment on the
significance of these new measurements for models of hard X-ray production in
solar flares, in particular', on the issue of whether imp^,ilsive, solar flare
hard X-ray emission is predominantly a thermal ( e.g. Crannell et a1.1978;
Brown, Melrose and Spicer 1979; Smith and Lilliequist 1979) or non-thermal
(Lin and Hudson 1971; Brown 1971; Petrosian 1973; Kane; 1974) process.	 Low
polarizations are generally considered to be indicative of a near isotropy of
the distribution of bremsstrahlung-producing electrons,	 a situaL	 .	 hitherto
thought to arise more natu^^ally in thermal models.	 Here we shall discuss the
significance of such low hard X -ray polarization measurements of non-thermal
d	 ll	 h	 h	 h	 1	 1	 t'	 l	 -mo els. we sha	 s ow t at suc a ow po ariza on resu t can occur ^n non
thermal models, and we shall discuss the ways in which the degree of X-ray
polarization is correlated with the parameters of these models.
The characteristics of the hard X-ray emission from solar flares can give
important information about the underlying populatio; :. of, energetic electrons«
and hence, indirectly, about the mechanisms by which that electron population
is created. It has been clearly demonstrated (e.g. Brown 1975) that we cannot
discriminate between non-thermal and thermal models on Rohe sole basis of the
hard X-ray spectral form. General attention, therefore, has been turned to j
other characteristics of the hard X-ray emission, such as its spatial
structure, directionality and polarization.	 The large (up to 40%)
f
i
3,
t
r
polarization observed in the early 1970 fs (,see Somov and Tindo 1978, and
references therein) implies a non-isotropic distribution for the electrons and
therefore favors a non-thermal model over a thermal model. These early
measurements have,however, been challenged. (Brown, McClymont and McLean
1974), and the resulting dispute (Mandel'stam, Beigman and Tindo 1975) has not
r
caearly been resolved. The new observations of TCH (1984) are on a more solid
observational footing and so should be able to provide a better diagnostic
into the nature of the energetic electron population.
	
For isotropic electron distributions such as are expected on the basis of	 f
thermal models, the, polarization of the emitted radiation should, of course,
	
be zero. However, the presence of temperature gradients can lead to slight	 «
electron anisotropies and hence to low degrees of polarization ( Emslie and
	
Brown 1980). In addition, a small polarization can arise from the	 I^,
consideration of those photons which are backscattered by the photosphere Al
(Tomblin 1972; Santangelo, Horstm an and Hors tman-Moretti 1973; Knoux 1975;
Langer and Petrosian 1977; Bai and Ramaty 1978)..
Early studies	 with non-- thermal models, with (Langer and Petrosisn 1977;
^M
Bas and Ramaty 1978) or without (Elwert 1968; Elwe . t and Ha1!g 1971; Haug 1972;
Bai and Ramaty 1978) photospheric altedo effects, 	 were all based upon highly
1
simplified angular distributions for the beam electrons. 	 These early studies
all ignored the effects arising from the geometry of the magnetic field and
most of them ( except Brown 1972) also ignored the Coulomb scattering of the
electrons within the target.
	 Hence, earl} non-thermal studies tended to
derive somewhat higher polarizations than did studies with thermal models.
More recent studies (Leach and' Oetrosian 1981, 1983) have used a Fokker-Planck
treatment to follow the evolution of an electron beam in the solar atmosphere
and evaluate the characteristics of the bremsstrIablong
	 hard X-rays produced
4
in such non-thermal models, This technique is a substantial improvement upon
the previous theoretical analyses and permits us to assess more realistically
the expected polarization in such models.
In RI we shall discuss the Fokker-Planck model results and
compare them with the observations of TCN (1984). In §IIX we discuss
why the predicted polarizations are substantially lower than those in earlier
simpler models. Here also we discuss the influence of various parameters of
the injected electron distribution and the target atmosphere which .affect the
polarization of the emergent bremsstrahlung radiation. Finally, we describe
scenarios where high polarizations are still possible, with a view toward
future observational efforts in this area.
11. POLARIZATION IN NON-THERMAL MODELS AND
COMPARISON WITH OBSERVATIONS
In their Fokker-Planck studies, Leach and Petrosian (1981, 1983) assume
the injection of a beam of non-thermal electrons at the top of a flare loop.
They then investigate the evolution of this non-thermal, electron population
under the influence of the Coulomb collisions it suffers with ambient plasma
particles. The essential three parameters used by Leach and Petrosian in
their analyses are the reciprocal magnetic field scale length K (R dlnB/ds,
where B is the strength of the guiding magnetic field and s distance from
the top of the loop), and S and ao, which describe the energy (E) and
pitch angle (a) distribution of	 the inected electrons, viz f(E,a) «
F_6 exp(-a2 /aa ). One of the effects which would normally reduce the
polarization of the X-rays and which has not been included in previous
theoretical studies is the spatial curvature of the flare magnetic field.
Since the orientations of the polarization vectors from different parts of
a c ,a__'rved loop will differ, observations which do not resolve the loop will
5
^• 1
4
i xF; 1 x
i
tmeasure a degree of polarization which is lower than that derived from smaller
(and straighter) portions of the loop. Here, following Leach and Petrosian,
we shall use flar:'e loops which are semi-circular. Clearly, more complicated
loop geometries could give rise to an even greater reduction in the degree of
polarization.
For one of the flares observed by TCN (designated by theee authors as
flare 21), we have information about the hard X-ray spectrum tS.K. Kane,
private communication). These data allow us to fix the value for d, thus
{
leaving us with only two free parameters. We therefore in Figure 1 compare
the observed degree of polarization for this flare with the calculated
polarization curves for three models having different values of 
a0 and k .
We note at this point, however, that there are two further effects to be
considered which would reduce the degree of polarization measured from that
predicted by the model;,'
(i) At 'these low X-ray energies there may be a significant contribution
from a relatively unpolarized thermal background (Emslie and Vlahos 1980). A
clear indication of such contamination would be an increase in the
polarization with increasing X--ray energy. There may be some evidence of this
in the data (TCN 1984).
(ii) Any variation in the flare characteristics over the relatively
long ( 2 minutes) integra.t!i.on times of the observations will give rise to a
lower observed polarization than would be expected from a typical isolated
elementary burst of duration 10 seconds, especially if different elementary
bursts are due to the ` energization of different loops (de Jager and de Jonge
1978; Emslie 1983; Kipl.inger, et al. 1983).
	 -"
In addition, there are substantial error 5ars on the observations and
some uncertainty inherent in the calibration procedure followed (TCN 1984).
Consequently, we cannot set strict limits on the, values of the model
.	 1}
parameters. However, the main point here is that, as we clearly show in
Figure 1, a low degree of polarization does not necessarily militate against
non-thermal models.
III. DISCUSSION AND SUMMARY
The reasons that the polarization estimates cf Leach and Petrosian (1983)
are lower than the ear'iier modeling estimates are as follows. As seen in a
full Fokker-Planck analysis of the beam dynamics, any injected electron beam
becomes increasingly isotropized as it penetrates further down through the
solar atmosphere (Leach and Petrosian 1981). The rate at which the electrons
diffuse in pitch angle is comparable to the rate at wh -v ch they lose energy
(Emslie 1978), and the bremsstrahlung cross-section is a decreasing function
of electron energy (e.g. Koch and Motz 1959). Consequently, the bulk of the
o-1 is er.;ed hard X-rays are emitted only after the electron beam has undergone
much of this isotropization. Thus the integrated X-ray emission from the
whole source will have the character of the emissiott from a highly broadened
electron beam, independent of the original de ree of electron .beaming at
injection. A spatially unresolved measurement of the hard X-ray polarization
must then give rise to a low value. Certainly, the stronger the initial
beaming of the electrons is, the higher will be the X-ray polarization, though
we stress that this is no more than a weak effect once the Coulomb collisionsM
have been properly incorporated into the analysis. Calculations for a variety
of flare model parameters (Leach and Petrosian 1'983) show that X-ray
polarizarione of around 2,5%. are the most that can be -expected, even from a
highly beamed (low as ) model with a uniform magnetic field. The effect of any
non-uniformity in the magnetic field (K 0 0) is to further reduce the degree
of polarization for the highly beamed models.
We now consider the influence of the parameter 8 (the spectral index of
7
i}
the injected electron beam) upon the hard X-ray polarization.	 (This parameter
was fixed in our above comparison with flare 21 of TCN 1984 by independent
observations.)	 The	 two cross sections for	 linearly polarized br.emsstrahlung
production are functions of the photon to electron energy ratio (k/E). 	 These
functional dependences are such that photons with larger k/E	 ("hard" photons)
are, in general, more highly polarized than those witf) smaller k/E ("soft"
photons) (Tseng and Pratt	 1973).	 Injected electrons with a flat energy
.spectrum ( i.e. small 6) will give rise to X-rays in which a greater proporton I
of the photons have low values of k/E 	 ( i.e. are "soft") ,and, therefore, the
r
t
^	 4
X-rays will be less polarized.	 Conversely,	 electron distributions which are
steep
	
(large d) generally produce photone with k/E near unity ("harder"
photons) and, thereby, result in a more highly polarized emission ( cf. e.g.,
Figure 3b of Langer and Petrosian 1977):	 As demonstrated in Table 1, the f
spectral,	 index d
	
has	 a	 very	 substantial	 influence	 upon	 the	 observed
polarization, and is at least as significant as the cle ree of electron beaming
SLY R'A
at ig.jection. This effect has received little attention in the
	 literature
	 to
da ..
In summary, the observations by TCN (1984) of low hard X-ray polarization *;*'
in solar flares are, in fact, consistent with both thermal and non-thermal
models of hard X-ray production. 	 Our hope of using polarization data as a
discriminant rests upon our being able to observe the 'coronal component of the
emission	 in isolation,	 for	 then	 any strong beaming of the non-t(ierm.al
electrons, not yet having been smoothed away by collisions in the thick
target,	 should result in quite a high polarization signature ( Leach and
Petrosian 198?),	 easily in ,excess of that predicted by thermal models (Emilie
and Brown 1980).
Spatially resolved polarization measurements 	 are not yet possible.
8
NHowever, by looking at flares occurring just past the edge of the sober limb
(Kane etal. 1982), it should be possible to observe th e emission from the
upper part of the flare loop without that emission being contaminated by the
less polarized component from the eclipsed lower parts. Unfortunately, by the
same token, the emJ1 9sion from this upper part of the loop will generally be no
more than a small fraction of the total flare emission, thus presenting
problems with statistical noise unless the observed flare is very large.
Currently available instruments, such as the one used b ;°r TCN (1984), should,
however, be capable (Lemen et al. 1982) of observing the coronal signal from
the large flares which can be expected to occur during the next solar maximum.
We would like to thank G .A. Chanan for discussing and communicating the
data prior to publication? During the course of this work A.G.E. held a von
Braun fellowship at U.A.H. He also expresses his thanks to P.A. Sturrock for
his hospi:ality at Stanford. J.L. and V.P.`were supported by NASA grant NSG-
7092 and NSF grant ATM-8218125; A.G.E. was supported by NASA grant NAGW-294
and NSF grant ATM-8303172.
Y
!M
^J
i
li
r;.
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Phvs. Rev., A7, 1502.
0
FIGURE CAPTION
r.
i
s
i
p.
r Gx
1
1
r
^l
Figure 1. A comparison between the polarization measured for flare 21 of
Tramiel, Chanan and Novick (1984) and the polarizations calculated for three
of the models of Leach and Petrosian ( 1983). The solid line is for a model
With a2
0
	 0.4 and k = 0.0, the dashed line ika for a model with a' - 0.4
and K = 1.5 x 10" 9 , and the dotted line is for a model with a20 	 0.1 and
K = 1.5 x 10" 9 . (K = 1.5 x 10" 9
 corresponds to a twentyfold increase in the
magnetic field strength f rom the top of the flare curonal loop to the
transition region, a distance of 2 x 10 9
 cm.) All three models have a coronal
density of 5 x 10 cm
-3 For a flare at disk center the viewing angle would be
00 0
 for one on the solar limb it would be 900.
.
12
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ORIGINAL PAGE 18
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The interpretation of hard X-ray polarization measurements in solar flares

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