On 16 February 1984 a flare on the Sun's invisible disk produced a large, highly anisotropic solar particle event. A technique, in which interplanetary scattering parameters are determined purely from the form of the particle anisotropy, is applied to energetic particle data from neutron monitors and the ICE spacecraft

Bieber, J. W.

Evenson, P. A.

Pomerantz, M. A.

English

NASA Technical Reports Server

335 SH 3.2-1
EXPONENTIALANISOTROPYOF SOLARCOSMICRAYS
J. W. B1eber, P. A. Evenson, and M. A. Pomerantz
Bartol Research Foundation of The Franklln Institute
Unlversity of Delaware, Newark, Delaware 19716
ABSTRACT
On 16 February 1984 a flare on the sun's Invislble
dlsk produced a large, hlghly anlsotroplc solar
particle event. A novel technique, in whlch inter-
planetary scattering parameters are determined purely
from the form of the partlcle anlsotropy, is here
applled to energetlc partlcle data from neutron
monitors and the ICE spacecraft.
i. Introductlon. Recent theoretlcal investigations (Roelof, 1969;
Kunstmann, 1979; Earl, 1981) Indlcate that the cosmlc ray anisotropy
may appropriately be expressed as an exponentlal functlon of pitch
angle:
f = Co + ClB exp {!J_-_ _Jull-q} • (1)
Here, f is the phase space denslty, cO and cI are constants, _ is
the coslne of pitch angle, B is the magnetlc field magnitude, _ is the
scattering mean free path, L is the magnetlc fleld scale length, and q
is a parameter which, according to quas111near theory (Jokip11, 1971),
is related to the slope of the power spectrum of magnetlc fleld
fluctuatlons. Provided that q and the ratlo x/L do not change with
distance, (i) is an exact solution of the steady-state Boltzmann
equation in arbltrary gulding field configuratlons, includlng the
Parker fleld. Solar partlcle anisotroples are, of course, not
preclsely steady-state. Nonetheless, it mlght reasonably be expected
that (I) constitutes a better approxlmatlon to actual anlsotroples than
the often utillzed first-order anlsotropy (f : co'+ c1'_) which is
a solution of neither the steady-state nor the tlme-dependent Boltzmann
equation.
On 16 February 1984, a flare on the invislble disk of the sun
produced an unusual solar partlcle event that was recorded by neutron
monltors on Earth (Pomerantz et al., 1984) and by the MEHinstrument
aboard ICE, which at that time was located on nearly the same nomnal
Parker fleld llne as Earth at a distance of 0.07 AU upstream. The best
tlming of the parent flare is given by the sudden onset of radio
emisslon at 0858 UT (Earth-recelved tlme) from beyond the western limb
of the sun. This hlghly anlsotroplc event provides an ideal
observatlonal basls for testlng whlch of the alternate forms of pltch
angle dlstributlon -- flrst-order or exponential -- best descrlbes
energetic solar particle anlsotroples.
335 S  3.2-1 
E ENTIAL ANI ROPY O  S R C IC R  
J. W. B1eber, P. A. Evenson, an  M. A. Pomerantz 
Bartol Research Foundation of The Frankl1n Institute 
Un1versity of Delaware, e ark, elaware 19716 
AB ACT 
On 16 February 1984 a flare on the sun's 1nvis1ble 
d1Sk produced a large, hlghly an1sotrop1c solar 
particle event.  novel technique, 1n Wh1Ch 1nter-
planetary scatter1ng parameters are deter ined purely 
fro  the for  of the part1cle lsotropy, is ere 
appl1ed to energet1c partlcle data fro  neutron 
onitors a  the IC  s acecraft. 
1. Introduct1on. ece t theoret1cal 1nvestigat10ns ( oelof, ; 
unst ann, 1979; arl, 1981) 1nd1cate that the cos 1C ray anisotropy 
may appropriately be expressed as an exponent1al functlon of pitch 
angle: 
(1) 
ere, f 1S the phase space dens1ty, Co and cl are constants, ~ 1S 
the COS1ne of pitch angle, B 1S the agnet1c field agnitude, A 1S the 
scattering mean free path, L 1S the magnetlc f1eld scale length, and q 
is a parameter which, according to quas1l1near theory (Jokip11, 1971), 
is related to the slope of the po er spectru  of agnetlc f1eld 
fluctuat1ons. r ided t at  a  t e rat10 AI  do t c a e ith 
distance, (1) 1S an exact solution of the steady-state Boltzmann 
equation 1n arb1trary gU1ding field configurat1ons, includ1ng the 
Parker f1eld. Solar part1cle anisotrop1es are, of course, not 
prec1sely steady-state. Nonetheless, 1t m1ght reasonably be expected 
that (1) constitutes a better approx1mat1on to actual an1sotrop1es than 
t e ften til1zed first-order a 1sotropy (f = CO I + C11~) Wh1Ch 1S 
a solution of neither the steady-state nor the t1 e-dependent oltz ann 
equation. 
On 16 February 1984, a flare on the invis1ble disk of the sun 
produced an unusual solar part1cle event that was recorded by neutron 
on1tors on Earth (Po erantz et al., 1984) and by the MEH 1nstrument 
aboard ICE, hich at that ti e was located on nearly the same no 1nal 
r r f1eld 11ne as rt  t  istance f .  U str . e st 
t1ming of the parent flare is given by the sudden onset of radio 
e iss10n at 0858 UT ( arth-rece1ved t1 e) fro  beyond the estern li b 
of the sun. This h1ghly an1sotrop1c event provides an 1deal 
observat1onal bas1s for test1ng Wh1Ch of the alternate for s of p1tch 
angle d1stribut1on -- f1rst-order or exponential -- best descr1bes 
energet1c solar particle an1sotrop1es. 
https://ntrs.nasa.gov/search.jsp?R=19850026504 2020-03-20T17:01:48+00:00Z
336 SH 3.2-1
2. Neutron Monitor Observatlons. To determlne the form of solar
particle anisotropy in this event, the fractional increases recorded by
8 polar neutron monitors during the interval 0900-1000 UT were
corrected to sea level pressure. An effectlve value of _ was
calculated for each statlon. The data were then fltted to a
first-order anlsotropy and to the exponential anlsotropy (1) wlth the
parameter q set equal to unity. Separate determinatlon of q from the
avaulable neutron monutor data was not feasible for thus event.
40
Results of thus analysis appear
un Figure i. It is immeduately ap- (a)
parent that 'the exponential anisot-
ropy provides a substantually better 20
descruption of the data than the __flrst-order anlsotropy. The
goodness-of-fit parameter ×2, is ®' m 0
nearly 10 times larger for the
first-order fit than for the expo- ®
nentlal fit, Even this poor fit for u
the furst-order case us accomplushed _ 40 _l::l:_IIlIII::_:
only by resort to the unphysical
artifice of assuming negatlve densl- m (b)
ties for u less than -0.4. Changes
m 20in p appear between the two fits be-
cause the best-flt symmetry axis
differs slughtly for the two
assumptions, 0
The value of x/L corresponding
to the exponential plotted in Figure
1 is 2.8. However, comparable
agreement was obtained for _/L in -1.0 -0.5 0 +0.5 +1.0
the range 2-10. The value of L at
this time, as calculated for a
Parker magnetic field corresponding Fig. 1. Two alternate forms of
to the ICE-observed solar wind speed pitchangle distribution are fitted
of 280 km/s, was 1.4 AU. Hence, at to hourly-averagedneutron monitor
neutron monitor energies (> 400 MeV) data from Thule (o), McMurdo (e),
the scattering mean free path in • Alert(o), Inuvik (m), Goose Bay (&),
this event was 3 AU or larger. Mawson (_), Apatlty (0), Oulu (0).
3. Spacecraft Observatlons. Measurements of the flux of protons wlth
energles 35-145 MeV from eight equally spaced arrival directions are
made every 97 seconds by the MEH instrument on the ICE (formerly
ISEE-3) spacecraft (Meyer and Evenson 1978). Since the magnetlc fleld
is also measured at the spacecraft (E. Smith, private communicationvla
ISEE common datapool tape), a representatuvepitch angle for each
viewing direction can be computed durectly by averaglng the magnetic
field observatlons over the period of the particle flux measurement.
This is in contrast to the neutron monitor analysis wherein the
direction of the field was a free parameter. Figure 2 shows the
35-145 MeV ICE data (10 minute average) at approximately0955 UT on
16 February 1984, near the maximum of the event at these energies. The
336 SH 3.2-1 
2. Neutron Monitor Observatlons. To determlne the form of solar 
particle anisotropy ln tfilS event, the fractional increases recorded by 
8 polar neutron monltors durlng the interval 0900-1000 UT were 
corrected to sea level pressure. An effectlve value of ~ was 
calculated for each statlon. The data were then f1tted to a 
first-order an1sotropy and to the exponential an1sotropy (1) w1th the 
parameter q set equal to unity. Separate determinat10n of q from the 
ava1lable neutron mon1tor data was not feasible for th1S event. 
Results of th1S analysis appear 
1n F1gure 1. It is i med1ately ap-
parent that the exponential anisot-
ropy provides a substant1ally better 
descr1ption of the data than the 
f1rst-order an1sotropy. The 
goodness-of-fit parameter, x2, is 
nearly 10 times larger for the 
first-order fit than for the expo-
nent1al fit. Even this poor fit for 
the f1rst-order case 1S accompl1shed 
only by resort to the unphysical 
artifice of assuming negat1ve denS1-
t1es for ~ less than -0.4. Changes 
1n ~ appear between the two f1tS be-
cause the best-f1t symmetry axis 
differs Sllghtly for the two 
assumptions. 
The value of AIL corresponding 
to the exponential plotted in Figure 
1 is 2.8. However, comparable 
agreement was obtained for AIL in 
CD 
II) 
o 
CD 
I-
(J 
C 
-c 
CD 
(J 
I-
CD 
a.. 
40 ~""""""....-r'-,..,.....,...,.....""'-"-rr"T'TT"T1 
20 
o 
(a) 
• 
0. 0 
c • 
40 1-+-l+++++!-H-1H-t-+t+++-H 
(b) 
20 
a 
-1.0 -0.5 a +0.5 + 1.0 
the range 2-10. The value of L at JL 
thlS time, as calculated for a 
Parker magnetic field corresponding Fig. 1. Two alternate forms of 
to the ICE-observed solar wind speed pitch angle distribution are fitted 
of 280 kmls, was 1.4 AU. Hence, at to hourly-averaged neutron monitor 
neutron mon1tor energ1es (> 400 MeV) data fro  Thule (0), McMurdo (e), 
the scattering mean fr e path in ' Alert (0), Inuvik (-), Goose Bay (A), 
this event was 3 AU or larger. Mawson (6), Apatlty (t), Oulu (0). 
3. Spacecraft Observat1ons. Measurements of the flux of protons w1th 
energ1es 35-145 MeV fro  eight equally spaced arrival directions are 
made every 97 seconds by the MEH instru ent on the ICE (formerly 
ISEE-3) spacecraft (Meyer and Evenson 1978). Since the magnet1c f1eld 
is also measured at the spacecraft (E. Smith, private co mun1cat1on Vla 
ISEE co mon datapool tape), a representat1ve pitch angle for each 
viewing direction can be computed d1rectly by averaglng the magnetlc 
field observat1ons over the period of the particle flux measurement. 
This 1S in contrast to the neutron monitor analysis wherein the 
direction of the field was a fr e param ter. Figure 2 shows the 
35-145 MeV ICE data (10 minute average) at approx1mately 0955 UT on 
16 February 1984, near the maximum of the event at these energies. The 
337 SH 3.2-i
sectoreddataobviouslydo not followa straightllne(flrst-order
anisotropy) but the exponential (1), with a choice of q=1.2 and
L/L=2.8,providesan excellentfit, as shownby the plottedcurve.
I I I I I I I I i
_P
o BOO- 1984 February 16 _
n- ICE-MEH 09:55 UT /'-'
.-i.-
r- 6o0 Protons 35-
-i
0
0 400
c-
O
,4,-
o 20o
I,.
o- f
- -.5 o .5 .o
Cosine of PJfch Angle
Fig. 2. SectoredICE partlcledata (circles)are comparedto an
exponentialanisotropy(curve)with L/L = 2.8 and q = 1.2.
The persistenthigh anisotropyof the eventand the longmean free
pathdeterminedfrom the shapeof the pitch angled]strlbutlonsuggest
thatthe entiretime proflleis a reflectionof contlnuedinjectionat
or nearthe sun. We havemodeledthe t]me profi]euslngcoronal
diffusion(Reid,1964) and interplanetaryfocuseddiffuslon(B1eberet
al.,1980) and flnd excellentagreement. A key resultof this analysis
is that the flow at the posltionof the spacecraftis at all tlmes
approximatelysteadystate. Changeswlth time are nearlyall due to
changesin the sourcestrengthat the sun.
Such a steadystateflowmay be used to lookfor changesin the
scatteringparameterswhich determinethe shapeof the pltch angle
distribution.A relatedanalysisconductedby Bieberand Pomerantz
(1985)uses longterm averagesof neutronmonitordata. The shape of
the pltch angledistributionmay be characterizedmany ways,one of
which is to considerratiosof the amplitudesof harmoniccomponents
determinedby Fourieranalysisof the countingrate as a functlonof
arrivaldirection. Figure3 showsthe averageflux,ratioof secondto
first harmon]cr2/rl,and ratioof third to firstharmonicr3/r1
as a functlonof time. Note the dlstinctlydifferentvaluesof the
harmonicratiosbeforeand afterthe datagap. Thls jump impliesa
reductionin the mean free path for scatteringby almosta factorof
two,while q remainsnearlyunchanged. It is likelythatthis change
is relatedto the changein the propertiesof the solarwind whlch is
indicatedby the increasein the magneticfieldmagnitudealso shown in
Figure3.
337 SH 3.2-1 
sectored data obviously do not follow a straight llne (flrst-order 
anisotropy) but the exponential (1), with a choice of q=1.2 and 
A/L=2.8, provides an excellent fit, as shown by the plotted curve. 
Q) 
-o 800 
a::: 
-C 600 
:J 
o 
U 400 
C 
o 
-0200 ~ 
a.. 
-1 
1984 February 16t 
ICE -MEH 09:55 UT 
Protons 35 -145 MeV 
-.5 0 .5 
Cosine of Pitch Angle 
1.0 
Fig. 2. Sectored ICE partlcle data (circles) are compared to an 
exponential anisotropy (curve) with AIL = 2.8 and q = 1.2. 
The persistent high anisotropy of the event and the long mean free 
path determined from the shape of the pitch angle dlstrlbutlon suggest 
that the entire time proflle is a reflection of contlnued injectlon at 
or near the sun. We have modeled the tlme profile uSlng coronal 
diffusion (Reid, 1964) and interplanetary focused diffuslon (Bleber et 
al., 1980) and flnd excellent agreement. A key result of this analysis 
is that the flow at the posltion of the spacecraft is at all tlmes 
approximately steady state. Changes wlth time are nearly all due to 
changes in the source strength at the sun. 
Such a steady state flow may be used to look for changes in the 
scattering parameters which determine the shape of the pltch angle 
distribution. A related analysis conducted by Bieber and Pomerantz 
(1985) uses long term averages of neutron monitor data. The shape of 
the pltch angle distribution may be characterized many ways, one of 
which is to consider ratios of the amplitudes of harmonic components 
determined by Fourier analysis of the counting rate as a functlon of 
arrival direction. Flgure 3 shows the average flux, ratio of second to 
first harmonlC r2/r1, and ratio of third to first harmonic r3/r1 
as a functlon of time. Note the dlstinctly different values of the 
harmonic ratios before and after the data gap. ThlS jump implies a 
reductlon in the mean free path for scattering by almost a factor of 
two, while q remains nearly unchanged. It is likely that this change 
is related to the change in the properties of the solar wind WhlCh is 
indicated by the increase in the magnetic field magnitude also shown ln 
Flgure 3. . 
$ 3 8 sh 3.2-1
300 .... 4. Conclusions.Local
_. - ' _-'_'_' - measurementsof important200 parametersof interplane ary
100 _." _,_ partlclepropagationcan be made
with hightimeresolutionif
i 4 _ anisotropiescan beI ! !
measuredwith sufflcientIE
.50- _,m#__ statisticalaccuracy. Analysis
_- _ ._T,_ of energeticparticledatafor
-..4o
_-_ the eventof 16 February1984
.50 from neutronmonitorsand from
_ _ l _ _ _ ICE leadsto the following
f:_TI"#h_ conclusions:(1)Particle
.15- _ - anisotropiesare better
"_ 10 _ - des ribedby an exponential
.05- _±__3J-_ functlonof pitchanglethan by
_r the commonlyassumedfirst-order
t i t _ i i I anisotropy.(2) Fittingto the
12- ,_D__ exponentialanlsotropyallows
_ boththe scatterlngmean free
m 11 _,_L-_ _ path x and the parameterq,
_ whlch characterlzesthe
, , , , , . . dependenceof the scatterlng
09:00 09:50 10:00 10:30 I :00 rate upon pitchangle,to be
1984 February 16 (UT) determlned.For thisevent,itis foundthatx is greaterthan
3 AU and q is approximately1.2.
Fig.3. Time profilesof average (3) An apparentchangein the
particleflux,harmonicratios scatterlngmean freepath
r /r and r /r (seetext),and occurredin connectionwith a2 I 3 1
magneticfieldB observedat ICE. smallchangein the magnitudeof
the interplanetarymagnetic
fleld.
5. Acknowledgments.This researchwas supportedby the National
ScienceFoundationundergrantsATM-8303758and DPP-8300544and by NASA
undergrantNAG-5-374.
References
Bieber,J. W., and M. A. Pomerantz,(1985),paperSH 4.5-21,this
conference.
Bieber,J. W. et al., (1980),J. Geophys.Res.,85, 2313.
Earl,J. A., (1981),Astrophys.J., 251,739-755.
Jokipii,J. R., (1971),Rev.Geophys.---S'pacePhys,9, 27-87.
Kunstmann,J. E , (1979),Astrophys.J., 229, 812-820.
Meyer,P. and PZ Evenson,(19/8),IEEETrY. Geosc1.Electronics,
GE-16,180.
Pomerantz,M. A. et al., (1984),Proc. Intl.S_mp.on C-R ModulationIn
the Heliosphere,pp. 437-443,Morioka,Japan.
Reid,G. C., (1964),J. Geoph_s.Res., 69, 2659.
Roelof,E C., (1969),Lecturesin High-_EnergyAstrophysics,NASA Spec.
PubIZ199, pp. 111-135,NASA,Washington,D. C.
38 sh 3.2-1 
300 
., 
.......... 200 . ., . 
c: . 
0 . 
.... 100 0 
~ . 
D. . . 
• 50 ~~ . ~ 
~ .40 
~ 
.30 
.15 ~ i/a.A""o..: -~ 
"}, .10 
~ 
.05 
t:' 12 
c: 
-CD 11 
• 
09: 0 09:30 10: 0 10:30 11 : 0 
1984 February 16 (UT) 
Fig. 3. Time profiles of average 
particle flux, harmonic ratios 
r2/r1 and r3/r1 (s e text), and 
magnetic field B observed at ICE. 
4. Conclusions. Local 
measurements of important 
parameters f interpla et  
partlcle propagation can be made 
with high time resolutl  if 
partlcle anisotropi  can be 
measured with sufflcient 
statistical accuracy. Analysis 
of energetlc particle data for 
th  event of 16 February 1984 
from neutron monitors and from 
ICE leads to the follo i  
conclusions: (1) Partlcle 
anisotropi  are better 
descrlbe  by an exponential 
functlon of pitch angle than by 
the co monly assumed first- r r 
anisotr . (2) Fltting to the 
exponential anlsotropy allows 
both the scatterl  mean fr e 
path A and the parameter q, 
WhlCh characterlzes the 
dependenc  of the scatterl  
rate upon pitch angle, to be 
determlned. For this event, it 
is found that A is greater than 
3 AU and q 1S approx1matel  1.2. 
(3) An apparent change ln the 
scatterl  mean fr e path 
occurred in connecti  with a 
small change in the magnltude of 
the interpl t ry magnetic 
fleld. 
5. Acknowledgment . ,This research wa  su porte  by the National 
Science Foundati  under grants ATM-830375  and DPP-83 05  and by NASA 
under grant NAG-5-374. 
References 
Bieber, J. W., and M. A. Pomerantz, (1985), paper SH 4.5-21, this 
conference. 
Bieber, J. W. et al., (1980), J. Geophys. Res., 85, 2313. 
Earl, J. A., (1981), Astrophys. J., 251, 739-7 5. 
Jokipii, J. R., (1971), Rev. Geophys: !pace Phys, ~, 27-87. 
Kunstma n, J. E., (1979), Astro)hYs. J., 229, 812-820. 
M yer, P. and P. Evenson, (1978 , I E Trans. GeOSC1. Electronics  
GE-16, 180. 
Pomerantz, M. A. et al., (1984), Proc. Intl. Symp. on C-R Modulati  ln 
the Helios~he  pp. 437- 43, Morioka, Japan. 
Reid, G. C., (1 64), J. Geophys. Res., 69, 2659. 
Roelof, E. C., (1969), Lectures in High- ergy Astrophysi  NASA Spec. 
Publ. 199, pp. 111-135, NASA, Washingto , D. C. 


Exponential anisotropy of solar cosmic rays

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