Gold and Venkatesan report observations of periods during 1974-1976 when extended regions of heliolongitude that emitted lower than average solar wind velocities at 1 AU also exhibited higher than average cosmic ray intensities as measured by the E  35 MeV CPME anti-coincidence scintillator (28 sq cm omnidirectional geometric factor) on IMP-8. Their observations reproduced by a simple model, based on the observed steady solar wind structure, wherein there is little modulation of cosmic rays in the inner heliosphere until they reach the shocked plasma beyond the stream interactions in the outer heliosphere (similar to 5 to 10 AU). Beyond the interaction boundary, the intensity exhibits a constant radial gradient (similar to 2%/AU). The model also offers an explanation for the irregular behavior of the rotation averaged radial gradients observed by inside 10 AU, as well as the significant, but often ephemeral, latitude gradients observed by Voyagers 1 and 2 and IMP-8

Roelof, E. C.

English

NASA Technical Reports Server

417
SH 4.1-21
EVIDENCE FOR REGIONS OF NEGLIGIBLE COSMIC-RAY MODULATION
IN THE INNER HELIOSPHERE (< 10 AU)
E. C. Roelof
The Johns Hopkins University, Applied Physics Laboratory
Laurel, Maryland, 20707, U.S.A.
ABSTRACT
Gold and Venkatesan [I] report observations of periods during
1974-1976 when extended regions of hellolongitude that emitted
lower-than-average solar wind velocities at i AU also exhibit-
ed higher-than-average cosmic-ray intensities as measured b_
the E > 35 MeV CPME anti-coincldence scintillator (28 cm
omnidirectional geometric factor) on IMP-8. Their observa-
tions can be reproduced by a simple model, based on the
observed steady solar wind structure, wherein there is little
modulation of cosmic rays in the inner heliosphere until they
reach the shocked plasma beyond the stream interactions in the
outer heliosphere (_ 5-10 AU). Beyond the interaction bound-
ary, the intensity exhibits a constant radial gradient (N 2%/
AU). The model also offers an explanation for the irregular
behavior of the rotation-averaged radial gradients observed by
inside I0 AU, as well as the significant, but often ephemeral,
latitude gradients observed by Voyagers I and 2 and IMP-8 [2].
I. Introduction. Gold and Venkatesan [I] present correlated IMP-8
observations of integral cosmic ray intensity (> 35 MeV) and solar wind
velocity during the previous minimum in solar activity (1974-6). The
use of the anti-coincidence scintillator of the JHU/APL Charged Particle
Measurements Experiment (CPME) as a cosmic ray detector was described in
detail by Roelof, Decker and Krlmigis [2]. They note that long-lived
recurrent regions of enhanced cosmic ray intensity fall within recurrent
regions of low speed solar wind (although they state that the converse
is not necessarily so). They offer a qualitative explanation based on a
sketch (reproduced here in Panel (b) of the Figure) of the quasl-stable
solar wind structure deduced by extrapolating solar wind velocities out-
ward with constant speed from IMP-8 and Pioneer-ll, a technique observa-
tionally validated for this period in the study of Mitchell, Roelof and
Wolfe [3]. The cosmic ray intensity enhancement of May 1974 occurred on
extrapolated stream lines that intersected the furthest reaches of the
"cavity" formed by the reverse shock of the preceding co-rotatlng inter-
action region (CIR) and the forward shock of the succeeding CIR. Gold
and Venkatesan therefore suggest that the modulation is weaker in the
"cavity" than in the shocked plasma beyond its boundary.
2. Analysis. Suppose the cosmic ray modulation beyond the cavities
formed by the CIR's is described by a uniform radial gradient g (%/AU)
so that the intensity J may be written j = Jo exp (gr). Here Jo would
be the intensity at the sun if the modulation region extended uniformly
inward to r = 0. However, we shall assume that g = 0 inside the
17 
 . 
I E E I S F EGLI I E S IC- Y ODULATION 
I I ELI ERE « ) 
. . oelof 
he Johns opkins niversity, pplied hysics aboratory 
aurel, aryland, 20707, .S. . 
S CT 
ol a enkatesan [1] r ort bservati ns f eri s ri 
1974-1976 hen e te ed re i s of eli l git de t t e itterl 
lo er-than-average s lar ind elocities at 1 AU also e hibit-
ed higher-than-average cosmic-ray intensities as measured b2 e t i ce i til t r 
nidirectional etric f t r) I P-8. heir ser a-
ti s can be reproduced by a si ple odel, based on the 
observed stea s lar ind str t r , herein t ere is littl 
odulation f c s ic r s i t i r eli s here til t 
reach the shocked plas a beyond the strea i teracti s in the 
ter heliosphere (~ 5-10 ). eyond the i teracti bound-
ar , the i te sit e hibits a constant ra ial gradient (~ 2 / 
U). odel l f r l nati n t i lar 
behavior of the r tatio -a era ed ra ial ra ie ts observed by 
i si e 10 , as ell as the si ificant, but fte ephe eral, 
latitu e gradients observed by oyagers 1 and 2 and I P-8 [2]. 
1. Introduction. old and enkatesan [1] present correlated I P-8 
observations of i te ral cos ic ray i te sit (> 35 e ) and s lar ind 
el cit during the previous inimu i s lar acti it (1974-6). he 
se f t e ti-c i i ce i till t r f t e J / harged arti l 
easurements Experi ent (CP E) as a cos ic ray detector as degcribed in 
detail by Roelof, Decker and Kri igis [2]. They note that long-lived 
recurrent regions of enhanced cosmic ray intensity fall within recurrent 
regions of low speed solar wind (although they state that the converse 
is not necessarily so). They offer a qualitative explanation based on a 
sketch (reproduced here in Panel (b) of the Figure) of the quasi-stable 
solar ind structure deduced by extrapolating so]ar ind velocities out-
ard it c sta t speed from I -8 and i eer-II, a tec i e ser a-
tionally validated for this period in the study of itchell, Roelof and 
olfe [3]. The cos ic ray intensity enhance ent of ay 1974 occurred on 
extrapolated stream lines that intersected the furthest reaches of the 
"cavity" formed by the reverse shock of the preceding co-rotating inter-
action region (CIR) and the for ard shock of the succeeding CIR. old 
and enkatesan therefore suggest that the odulation is eaker in the 
"caVity" than in the shocked plas a beyond its boundary. 
2. Analysis. Suppose the cosmic ray modulation beyond the cavities 
formed by the CIR's is described by a unifor radial gradient g (%/AU) 
so that the intensity j may be written j = jo exp (gr). Here jo would 
be the intensity at the sun if the odulation region extended unifor ly 
in ar to r O. ever, e s ll assume t t g insid the 
https://ntrs.nasa.gov/search.jsp?R=19850026527 2020-03-20T17:00:42+00:00Z
418
SH 4.1-21
cavities; we could chose a small, but non-zero value of g inside the
shocks, but the simplicity of the suggested model calls for a simple
treatment. We assume that the cosmic ray populations are ordered along
field lines in the inner heliosphere, as was demonstrated by the Voya-
ger/IMP comparisons in 1977-8 [2]. In a steady solar wind structure,
the large-scale interplanetary magnetic field lines follow the solar
wind stream-llnes, as viewed in a frame co-rotating with the sun. Then
the intensity at the Earth when its heliolongitude is _ should be the
intensity at the cavity boundary where the solar wind stream, extrapo-
lated outward from 1 AU, intersects the forward or reverse shock
bounding a CIR. Call the helioradlal distance of this intersection
rs(_). Then the cosmic ray intensity at Earth at heliolongltude _ is
simply j(_) = Jo exp [rs(_)].
The calculation of rs(_) is not difficult; the values could
actually just be scaled off Panel (b) of the Figure. An extrapolated
idealized field llne has the equation r(__) = a + V(_) (_ - _)/Q, where
is the heliolongitude of the line at 1 AU (r = a), V(_) is the veloc-
ity there, and Q is the solar sidereal rotation rate. The CIR bound-
aries can be parametrlzed by a pseudo-field line with the velocities of
the forward (VF) or reverse (RR) shock and the extrapolated crossings of
those lines at 1 AU ( _ and _.). The lines in the rarefaction between
high (VH) and low (VL) speed regions can be idealized as a "dwell" in
which the lines appear to emanate from a single coronal longit..de
(__): r(_')= a (_o -_)/_o -_)" We computers(_)for the four regions
of°the idealized stream structure shown in Panel (c) of the Figure: I,
V(@) = VH, intersection of high speed solar wind with reverse shock V =
VR; II and III, rarefaction,as shown in Panel (b); and IV, V(@)= VL,
intersection of low speed solar wind with forward shock V = VF. The
resulting formulas are:
_R-_
rs(#) = a + (VHVR/Q) VH -Vm Region I
1 + (VR/Qa)(# R -@o )
r (_) = a Region II
s 1 - (VR/Qa)(#o -@)
The corresponding formulas for Regions III and IV are obtained by
replacing VR with VF, VH with V and _R with __. The result of the cal-
culation is plotted in Panel (L) of t]he Figu{e with dashed lines indi-
cating the regions where the over-simplification of the model is most
extreme.
3. Comments. As could have been seen directly from Panel (b), the
cosmic ray enhancement falls in the longitudes of high values of
rs(@) shown in Panel (a); not so evident in Panel (a) is the sharpness
of the peak within the rarefaction region. Since d_/dt = -Q', the
synodic rotation rate, the rs(@) plot is just a time plot running
backwards (see lower scale). The intensity history, if treated as a
fractional change, is in (J/jl) = g(rs - a) where Jl would be the
minimum intensity predicted by the model. A peak radial distance of 9
8 
SH 4.1-21 
cavities; we could chose a s all, but non-zero value of g inside the 
shocks, but the simplicity of the suggested model calls for a simple 
treatment. We assume that the cosmic ray populations are ordered along 
field lines in the inner heliosphere, as was demonstrated by the Voya-
ger/IMP comparisons in 1977-8 [2]. In a steady solar wind structure, 
the larg -s l interpla t r agnetic field lines follow the s l r 
ind strea -lines, as viewed in a frame co-rotating ith the sun. Then 
the inte sit at the arth hen its heliolongi tude is should be the 
intensity at the cavity boundary where the solar wind stream, extrapo-
lated t r from 1 , i t r t the forw r r re r sh 
i a I . ll th li r ial istan f this inter ti 
r s (<1». Then the cos ic ray intensity at arth at heliolongitude is 
simply j(<I» = j exp [r (<1»]. 
 s 
The calculation of rs(<I» is not difficult; the values could 
actually just be scaled off Panel (b) of the Figure. An extrapolated 
idealized field line has the equation r(<!>') a + V(<I» ( - <1>' )/Q, here 
 is the heliolongitude of the line at 1 AU (r a), V(<I» is the veloc-
t s h d l io e d-
i r etri do-fiel lin it th l citi f 
the forward (V ) or reverse (RR) shock and the extrapolated crossings of 
those lines at 1 AU ( <l>F and <l>R). The lines in the rarefaction bet een 
high (V ) and low (V ) speed regions can be idealized as a "dwell" in 
which the lines appear to emanate from a single coronal longit"de 
(<1»: r(') = a ( -<1>')/<1> -<1». We compute rs(<I» for the four regions 
000 
of the idealized stream structure shown in Panel (c) of the Figure: I, 
(<I» ' i t r ti f i s l r i it r rs s 
V ; II and III, rarefaction, as shown in Panel (b); and IV, V(<p) = V1' 
intersection of low speed solar wind with forward shock V = V • The 
lt ulas r : 
r (<I» 
s 
r (<I» = a 
s 
1 + (VR/Qa) (R - 0) 
1 - (VR/Qa)(o -<1» 
Region I 
Region II 
The corresponding formulas for Regions III and IV are obtained by 
replacing V with V ' V with VL and with <l>F. The result of the cal-
ulati n i l tt i anel (a) f tte i r it as e li i i-
cating the regions here the over-si plification of the odel is ost 
tr e. 
3. Comments. As could have been seen directly from Panel (b), the 
cos ic ray enhancement falls in the longitudes of high values of 
rs(<I» shown in Panel (a); not so evident in Panel (a) is the sharpness 
of the peak ithin the rarefaction region. Since d<l>/dt = -g', the 
synodic rotation rate, the rs(<p) plot is just a time plot running 
backwards (see lo er scale). The i tensity history, if treated as a 
fractional change, is In (j/j 1) = g(rs - a) where j 1 would he the 
mini um i tensity predicted by the odel. A peak radial ista ce of 9 
419
SH 4.I-21
AU beyond the Earth with a radial gradient of 2%/AU would give a frac-
tional enhancement oE ]/Jl = 1.20. This is within the range of
maximum/mlnimum intensities presented in Figure 2 of [I]; note that
Figure 2 and Figure 3 of that paper are from different years. Also, the
longitude used in Figure 2 of [I] is not the Earth heliolongltude used
here, but rather the estimated source longitude of the observed solar
wind stream. The latter longitude is inappropriate for galactic cosmic
ray studies - for example, it would compress the entire rarefaction
region of Panel (a), with its attendant intensity enhancementg, into a
glngle longitude on their plot. A more appropriate longitude for
labelling field lines in the outer hellosphere is the heliolongitude of
the innermost spacecraft being used, as was done here and was discussed
in [2].
The exercise of this paper is intended mainly to illustrate
the very plausible circumstance that cosmic ray modulation in the inner
heliosphere (r ! I0 AU) may be quite variable (_ependlng on stream
structure evolution) with radial gradients much smaller than in the very
different plasma/field regimes of the outer hellosphere. An extremely
significant result from the VGR/IMP high time resolution (i h) intensity
comparisons [2] was that there were entire solar rotations devoid of
significant gradients between i and 3-5 AU! Equally important were the
ephemeral latitudinal gradients _ l%/deg lasting _ I rotation (which
would go essentially undetected if gradients are computed from 25-day
averages as in other measurements done with less sensitive instruments).
Our present study suggests an intr]_ulng explanation for latitude gradi-
ents in the inner hellosphere. Suppose we compare intensities on two
field lines passing through the same longitude (_) at 1 AU, but at
different latitudes (e); this was the technique by which fleld-aligned
latitudinal gradients were found in [2]. If the boundaries of the
"cavity" were inclined to the solar equatorial plane owing to latitudi-
nal shears described by terms like (DV/Se) or (5#o/De) in solar wind
velocity structure, then we would have a latitudinal intensity gradi-
ent D(in j)/De = g[(Sr /DV.)(_V_/58) + (Dr /D__)(D__/Se)] where, for
example, Vi = VH' VR a_d #i = _j, # . A she_r o_ 5V/{_ = (I00 kin/s)/(10
deg) is not unreasonable _3], and _rom Panel (a), we see that Dr /SV =
(5 AU)/tlO0 km/s) in the peak. Consequently, a latitudinal g£adient
D(In j)De = (2%/AU)[(5 AU)/(100 km/s)][(lO0 km/s)/(10 deg)] = l%/deg, as
observed [2], could be produced by shears in the stream/shock structure.
4. Acknowledgements. This work was encouraged by my valued colleagues
R. E. Gold and D. Venkatesan, and supported in part by the Air Force
Geophysics Laboratory under Task ZFIO of Contract N00024-85-C-5301
between The Johns Hopkins University and the Department of the Navy.
5. References.
I. Gold, R. E., and D. Venkatesan, (1985), Proc. Int. Conf. Cosmic
Rays, 19th, Paper SH 4.1-14.
2. Roelof, E. C., Decker, R. B. and S. M. Krlmigis, (1983), J. Geophys.
Res__.__.,88, 9889.
 
SH 4.1-21 
AU beyond the Earth ith a radial gra(Uent of 2 / AU ould give a frac-
tional enhance ent of j/j1 = 1.20. This is ithin the range of 
a i / i i int iti r s t in i r 2 f [1]; t th t 
i r a i r 3 f th t r r from iffer t rs. ls , the 
longitude used in igure 2 of [1] is not the arth heliolongitude used 
r , t rath r the stim t s r lo itu f the s r l r 
i tream. latt lo itu is in r priat fo l ti i 
ra tu i - for pl , it l press the tir r r f ti 
region of anel (a), ith its attendant inte sit enhance ents, into a 
si l lon itu t ir l t. r r pri t lo itu for 
labelling field lines in the outer heliosphere is the heliolongitude of 
th in r ost ecraft i , s s r s is 
 . 
he exercise of this paper is intended ainly to illustrate 
t si l ircu st i a odulati th r 
li s ere (r ~ 1 ) a e it ri l Q~ i stream 
structure evolution) ith radial gradients uch s aller than in the very 
iff r t l s a/fiel re i es f the t r li s ere. n e tre ely 
significant result from the VGR/I P high time resolution (1 h) intensity 
paris ns er ti o i 
significant gradients bet een 1 and 3-5 AU! qually i portant ere the 
ephemeral latitudinal gradients ~ l /deg lasting ~ 1 rotation (which 
oul ntiall detect i r i nts r c pute from - a 
r s s i t r easure ents e it l ss s siti i stru ents). 
ur present study suggests an intriguing explanation for latitude radi-
ents in the inner heliosphere. Suppose e co pare i te sities on t o 
fiel lines passing through the sa e longitude (<I» at 1 , but at 
different latitudes (a); this as the technique by hich field-aligned 
i al r i nts er ndari s 
"cavit " ere i cli e to the s lar e uatorial plane o ing t l tit i-
nal shears described by terms like ('OV /oa) or ('0<1> /'Oa) in solar wind 
 
velocity structure, then we would have a latitudinal intensity gradi-
t 'O(l j)/o [('Or/'O i)('O i/'Oa) ('Ors/'Ok)('Ok/'Oa)] here, f r 
example, Vi = V ' V ana = <l>R' • A shear of 'Ov/'Oa ~ (100 km/s)/(10 deg) is not unreasonable f3], and Prom Panel (a), we see that 'Or /'OV ~ 
(5 U)/'100 k /s) in the peak. Consequently, a latitudinal g~adient 
'O(1n j)'Oa ~ (2 / U)[(5 U)/(100 /s)][(IOO /s)/(IO e )] 1 /deg, as 
bser ed , ul r ced ar i t trea / ck t t re. 
4. Acknowledgements. This work was encouraged by my valued colleagues 
R. E. old and D. enkatesan, and supported in part by the ir Force 
eophysics aboratory der ask FI0 f ontract 0 024-85-C-5301 
between The Johns Hopkins niversity and the Depart ent of the Navy. 
. eferences. 
1. old, . ., a . enkatesan, ( 85), r c. I t. onf. os ic 
ays, 9th, aper S . - 4. 
2. Roelof, E. C., Decker, R. B. and S. M. Krimigis, (1983), J. Geophys. 
Res.,~ 9889. 
420
SH 4.1-21
3. Mitchell, D. G., E. C. Roelof and J. H. Wolfe, (1981), J. Geophyq.
Re___s.,86, 165.
12
(a) R (AU)
-,-180 270 0
10
,!
Hehoradiusof
::) 8 stream/shock
_._ intersection
(AU)
-o 0
O
_- 6 After Gold and Venkatesan [1] -2
\
\
\
%
4 ,v ,,,/ ,_
LOWspeed / Rarefactlon_ Hlghspeed
+ forward / + reverseshock _+ reverseshock
shock // __
/ I '%,%%
2 .._, Rarefaction
+ forward shock "_..
_J
I I#"S I I I I I I I _ I I
(c) 90 180 270 360
IMP 8 cosmicray enhancement I IMP-8
,v ,° -Low-
Low Rarefractlon Highspeed
speed
0 I I I I I I | I
7 6 5 4 3 2 1 0 -1
_--Time (days)
Figure: (a) Outer helioradius rs(_) of intersection of interplanetary
field lines from IMP-8 heliolongitude (_) with "cavity" boundary formed
by interacting CIR's sketched in (b), as proposed in [I], for the steady
solar wind speed profile shown in (c). If there is no cosmic-ray radial
gradient within the "cavity" and a constant radial gradient (g) beyond
it, the intensity profile at r = a = I AU is j = Jl exp [grs(_) - a].
9 
 . 
3. itchell, D. ., E. C. Roelof and J. H. olfe, (1981), ~eoph~.!.. 
Res.,~, 165. 
2r---------------------------------------------------------, (a) 
 
4 
2 
(c) 
"0 8l High r----..... 
c. 
'" 
"0 
c:: 
~ 
.... 
co 
(3 (/J 
ll r l 
trea /shock 
 
( ) 
'I 
'I 
'I , I 
, I 
, I 
, I 
, I 
, I 
, ' , \ 
, \ 
, \ 
, \ 
, \ 
I , 
I ' I 
IV 111/ 
Lowsp~ed / f r r I 
shock / 
 
,/ 
Rarefaction 
""""" r ck 
II 
180 
 ( ) 
2 
4 
6 
8 
1 
~gc~~~~~~~~12 
t r t san 
High speed 
+ reverse shock 
270 360 
IMP 8 cosmic ray enhancement IMP-8 
hellolongltude 
(deg) IV 
'_o 
s eed 
III II 
 a refraction igh speed 
o~----~----~------~----~----~------~----~----~--~ 
 o 
*- l e (days) 
Figure: (a) Outer helioradius rs(<I» of intersection of interplanetary 
fiel lines fro I P-8 heliolongitude (<I» ith "cavity" boundary formed 
by i teracti eI 's sketched i ( ), as proposed i [lJ, f r the stea 
s lar ind speed r file sho n in (c). If there is no cos ic-ray ra ial 
gradient ithin the "cavity" and a constant radial gradient (g) beyond 
it, the intensity profile at r = a = 1 AU is j = Jl exp [grs(<I» - aJ.

Evidence for regions of negligible cosmic-ray modulation in the inner heliosphere ( 10 AU)

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