Recent data indicating that the solar modulation effects are propagated outward in the heliospheric cavity suggest that the 11-year cosmic ray modulation can best be described by a dynamic time dependent model. In this context an understanding of the recovery characteristics of large transient Forbush type decreases is important. This includes the typical recovery time at a fixed energy at 1 AU as well as at large heliocentric radial distances, the energy dependence of the recovery time at 1 Au, and the dependence of the time for the intensity to decrease to the minimum in the transient decreases as a function of distance. These transient decreases are characterized by their asymmetrical decrease and recovery times, generally 1 to 2 days and 3 to 10 days respectively at approx. 1 AU. Near earth these are referred to as Forbush decreases, associated witha shock or blast wave passage. At R equal to or greater than + or - 10 AU, these transient decreases may represent the combined effects of several shock waves that have merged together

Jokipii, J. R.

Lockwood, J. A.

Webber, W. R.

English

NASA Technical Reports Server

388
SH4.1-9
THE INTENSITY RECOVERY OF FORBUSH-TYPE DECREASES AS A FUNCTION OF
HELIOCENTRIC DISTANCE AND ITS RELATIONSHIP TO THE II-YEAR VARIATION
Lockwood, J. A. and W. R. Webber
Space Sclence Center, Unlverslty of New Hampshire
Durham, New Hampshire 03824 USA
Jokapli, J. R.
Department of Planetary Sciences, Unlverslty of Arizona
Tucson, Arizona 95721 USA
I. Introduction. Recent observations of the cosmlc-ray modulation,
includlng partlcularly interplanetary radial gradient studies, have
helped to identify two key questions which need to be answered in order
to understand the cosmlc-ray modulation process. One question is
related to the Importance of cosmlc-ray particle drifts in both the
short-term and ll-year modulation process. The other question is
related to the degree to which the ll-year modulation process repre-
sents a superpositlon of transient (Forbush) decreases. Recent data
Indicating that the solar modulation effects are propagated outward In
the heliospherlc cavity [i,2,3,4] suggest that the ll-year cosmlc-ray
modulatlon can best be described by a dynamic tlme-dependent model.
In thls context an understanding of the recovery characterlstlcs
of large translent Forbush-type decreases is important. Th_s includes
the typical recovery tlme at a fixed energy at 1 AU as well as at
larger hellocentrlc radlal distances, the energy dependence of the
recovery tlme at 1 AU, and the dependence of the tlme for the intenslty
to decrease to the minimum in the transient decrease as a function of
distance. We characterize these transient decreases by their
asymmetrical decrease and recovery times, generally 1-2 days and 3-10
days respectively at _ 1 AU. Near earth these are referred to as
_orbush decreases, associated with a shock or blast wave passage. At R
- I0 AU, these translent decreases may represent the comblned effects
of several shock waves that have merged together.
2. Observations. About thirty transient decreases from 1972-1984
observed at 1 AU (Fig. I) for whlch data were available from the IMP
spacecraft (P median _ 1.7 GV) and the Mt. Washington neutron monitor
(P median % 5 GV) were analyzed to determine the characteristic reco-
very tlme t at earth. Certain selectlon crlterla were applled too
these decreases: a) magnitude - 3% as seen in daily average count rate
of the Mr. Washington neutron monitor; and, b) effects of solar
partlcles in the IMP cosmlc-ray data should be small or negligible.
The fractional decrease (AN/N) was calculated from the logarlthmlc
difference of the daily average counting rates recorded for three days
before the decrease and at the minimum. For the recovery it Is assumed
that n = n exp (-t/to),where n = £n N - £n N and n = £n N - £n N .
No is the _-day average intensity befor°ethe event, _ Is the°intensl_y
on day t and N is the mznlmum intensity (for details see [5]). In all
m
cases the recovery could be fltted well by thls form.
In Flg. 2 we have plotted the characteristic recovery tlme, to,derived in the manner described above for the IMP detector versus that
for the neutron monitor at Mr. Washington. Clearly the data are fitted
by t (MW) = t (IMP) wlth an average s 5 days which Implies that the
deca_ tlme in° these events is on the average the same for the two
388 
SH4.1-9 
THE INTENSITY RECOVERY OF FORBUSH-TYPE DECREASES AS A FUNCTION OF 
HELIOCENTRIC DISTANCE AND ITS RELATIONSHIP TO THE II-YEAR VARIATION 
Lockwood, J. A. and W. R. Webber 
Space Sc~ nc  Center, Un~vers~ty of New Hampsh~re 
Durham, New Hampsh~re 03824 USA 
Jok~p~i, J  R. 
Department of Planetary Sc~ences, Un~vers~ty of Ar~zona 
Tucson, Arizona 95721 USA 
1. Introduct~on. Recent observat~ons of the cosm~c-ray modulat~on, 
~nclud~ng part~cularly ~nterplanetary radial grad~ent stud~es, have 
h lped to identify two key quest~ons w ~ch need to be answered ~n o der 
to understand the cosm~c-ray modulat~on process. One question ~s 
related to the ~mportance of cosm~c-ray part~cle dr~fts ~n both the 
short-term and II-year modulat~on process. The other quest~on ~s 
related to the d gree to w ~ch the II-year modulat~on process epre-
sents a su erposi t~on of trans~ent (Forbush) d cr ases. Recent data 
~nd~cat~ng hat the solar modulat~on ffects are ropagated outward ~n 
the heliospher~c cav~ ty [1,2,3,4] suggest hat the II-year cosm~c-ray 
modulat~on can best b  descr~bed by a dynam~c t~me-dependent model. 
In th~s con ext an understand~ng of the recovery character~st~cs 
of large trans~ent Forbush-type d creases ~s ~mportant. Th~s includes 
the typ~cal recovery t~me t a f~xed energy at 1 AU as well as at 
larger hel~ocentr~c r d~al d~stances, th  energy dependence of the 
recovery t~me at 1 AU, and th  dep ndence of the t~me for the i tens~ty 
to decrease to the m~nimum ~n the trans~ent decrease as a funct~on of 
distance. We character~ze these trans~ent d cr ases by the~r 
asymmetrical d crease and recovery t~mes, generally 1-2 days and 3-10 
days r spect~vely at '\, 1 AU. Near earth these are referred to as 
forbush decreases, assoc~ated with a shock or blast wave passage. At R 
- 10 AU, these trans~ent d creases may epresent the comb~n d ffects 
of several shock waves hat hav  merged tog ther. 
2. Observat~ons. About th~rty trans~ent d creases from 1972-1984 
obs rved at 1 AU (F~g. 1) for w ~ch data were av ~lable from the IMP 
spacecraft (P med~an '\, 1.7 GV) and the Mt. Wash~ngton neutron mon~tor 
(P med~an '\, 5 GV) were analyzed to determ~ne the character~st~c reco-
very t~me t at earth. Cert~~n select~on cr~ter~a were appl~ed to 
thes  d crea~es: a) magn~tude - 3% as see  in da~ly average count rate 
of the Mt. Wash~ngto  neutron mon~tor; and, b) ffects of solar 
part~cles ~n the IMP cosm~c-ray data should be small or ne l~g~ble. 
The fract~onal d cr ase (ll /N) was a culated from the logar~thm~c 
d~fference of the daily average cou ting rates recorded for three days 
before th  d crease and at the m~n~mum. For th  recovery it ~  assumed 
that n = n exp (-tit ), where n = tn N - tn Nand n = tn N - tn N • 
N is the ~-day avera~e intens~ty befor~ the event, & ~s theO~ntens~~y 
oR day t and N ~s the ~n~ um ~ tensity (for deta~ls see [5]). In all 
m 
cases th  recovery could be f~tted well by th~s form. 
In F~g. 2 we have plotted the characterl.stl.c recovery tl.me, t , 
derived in the manner descrl.bed above for the IMP detector versus h~t 
for th  neutron monl.tor at Mt. Washl.ngton. Clearly the data are fl.tted 
by t (MW) = t (IMP) wl.th n average ;;; 5 days w ~ch ~mpll.es hat the 
o 0 decay t~me ~n these events ~s on the average the same for the two 
https://ntrs.nasa.gov/search.jsp?R=19850026519 2020-03-20T17:01:22+00:00Z
389
SH4.i-9
instruments dlfferlng by a factor of 3 in the rlgldlty of thelr mean
responses. We also observe that: i) there is no slgnlflcant dlfference
in recovery tlmes for events classed as Co-rotatlng Interactlon Reglons
(CIR), having a more symmetrlcal decrease and recovery tlme, and the
classlcal Forbush-type translents; 2) t does not depend upon the
magnltude of the decrease; 3) t does no_ change slgnlflcantly before
and after the solar magnetlc fl_Id reversal in 1980; and 4) t is the
same in the decreaslng phase of the solar cycle (before 1981-i_82) and
in the recovery part of the cycle.
we have investlgated the hel_ocentrlc radial dependence of t foro
19 translent decreases, of whlch 16 were included _n the analysls of
the energy dependence of t above, utlllzlng addltlonal data from
cosmlc-ray telescopes (E > 60°MeV) on Voyagers 1 and 2, and Pioneer i0.
An additlonal crlterlo_ Imposed for this latter study is that (AN/N) of
the transient must be _ 10% as seen In the dally average count rate of
the IMP detector at 1 AU. Th_s latter crlterlon enables the translent
events to be more clearly identlfled _s they move outward and posslbly
coalesce w_th other decreases at R - i0 AU [6]. For 13 of the 19
events examlned we belleve that there is llttle doubt about the asso-
clat_on at various radlal d_stances. For only one transient decrease
is t less at larger R. In Fig. 3 we show an example of a translento
decrease whlch has been traced from 1 AU to 21 AU. The dependence of
t upon hellocentric radlal dlstance for the ensemble of all 16 eventso
is shown In Flg. 4. It is evldent that on the average the magnitude of
t becomes much longer as R increases [see 7]. The data shown is Flg. 4
o
can be fltted by to(R)/to(1) = 1.26 exp (0.090R),where R is the radialdlstance in AU.
From a comparlson of the magnltude of the "same" event (AN/N) at
dlfferent R we flnd no strong dependence of (AN/N) upon R. A posslble
reason for thls behavlor as opposed to a more rapld decrease in
magnltude expected for 9 sangle shock is that, as suggested by [6], the
translents seen at R - i0 AU probably represent the coalescence of
several smaller translents seen at 1 AU.
For i0 out of 19 translent decreases we also determlned the t_me T
from onset to the mlnlmum intens_ty as a functlon of R. We f_nd
T(R)/T(1) = i.i0 exp (0.055R)where T(R) Is the value at R and T(1) at
earth. This means that at R _ i0 AU zt takes about twlce as long to
reach mlnlmum. We f_nd that from 1 to 30 AU the ratio (t /T) increases
slowly, due to the longer recovery tlme at larger R. _he fact that
thls ratlo Is >> 1 clearly Indicates that we are observlng asymmetrlcal
transient decreases at large R, however.
3. Ph_slcal Model for the Observed Energy and Spatlal Dependence of
the Recovery Time. A physlcal model based upon a tlme-dependent,
two-dlmenslonal numerical solution to the cosmlc-ray transport wlth a
single shock weakening wlth dlstance has been developed by one of us
(JRJ) to study these translent events [8]. The transient is
represented by a dlsturbance propagated into the steady-state cosmic-
ray d_strlbutlon. The _ntensltaes at several rad_l and energies are
studied. Thls model predlcts that there should be only a small depend-
ence of t upon energy at a glven R as is observed. The varlatlon ofu
Intensity wath R depends mainly on the decay of the disturbance as it
propagates through the hellosphere. For an e-foldlng distance of 5-7
AU for the weakenlng of the shock, the varlatlon of the recovery tlme
wlth energy and heliocentric radlus is glven in Table i.
389 
SH4.1-9 
1nstruments d1ffer1ng by a factor of 3 1n the r1g1d1ty of the1r mean 
responses. We also observe that: 1) there 1S no s1gn1f1cant d1fference 
1n recovery t1mes for events classed as Co-rotat1ng Interact10n Reg10ns 
(CIR), having a more symmetr1cal decrease and recovery t1me, and the 
class1cal Forbush-type trans1ents; 2) t does not depend upon the 
magn1tude of the decrease; 3) t does no€ change s1gn1f1cantly before 
o 
and after the solar magnet1c f1eld reversal 1n 1980; and 4) t 1S the 
same in the decreas1ng phase of the solar cycle (before 1981-l~82) and 
1n the recovery part of the cycle. 
We have 1nvest1qated the he110centr1c rad1al dependence of t for 
o 19 tranS1ent decreases, of wh1ch 16 were 1ncluded 1n the analys1s of 
the energy dependence of t above, ut1l1z1ng add1 t10nal data from 
o 
cosm1c-ray telescopes (E > 60 MeV) on Voyagers 1 and 2, and P10neer 10. 
An addit10nal cr1ter10g 1mposed for this latter study 1S that (AN/N) of 
the transient must be ~ 10% as seen 1n the da1ly average count rate of 
the IMP detector at 1 AU. Th1S latter cr1ter10n enables the tranS1ent 
events to be more clearly ident1fled ~s they move outward and poss1bly 
coalesce w1th other decreases at R - 10 AU [6]. For 13 of the 19 
events exam1ned we belleve that there 1S l1ttle doubt about the asso-
c1at1on at var10US rad1al d1stances. For only one tranS1ent decrease 
is t less at larger R. In F1g. 3 we show an example of a tranS1ent 
o decrease wh1ch has been traced from 1 AU to 21 AU. The dependence of 
t upon he110centric rad1al d1stance for the ensemble of all 16 events 
1~ shown 1n F1g. 4. It 1S eV1dent that on the average the magnitude of 
t becomes much longer as R 1ncreases [see 71. The data shown 1S F1g. 4 
o 
can be f1tted by t (R)/t (1) = 1.26 exp (0.090R), where R 1S the rad1al 
d1stance 1n AU. 0 0 
From a compar1son of the magn1tude of the "same" event (AN/N) at 
d1fferent R we f1nd no strong dependence of (AN/N) upon R. A poss1ble 
reason for th1S behav10r as opposed to a more rap1d decrease In 
magn1tude expected for ~ s1ngle shock 1S that, as suggested by [6], the 
tranS1ents seen at R - 10 AU probably represent the coalescence of 
several smaller tranS1ents seen at 1 AU. 
For 10 out of 19 tranS1ent decreases we also determ1ned the t1me T 
from onset to the m1n1mum 1ntens1ty as a funct10n of R. We f1nd 
T(R)/T(l) = 1.10 exp (0.055R) where T(R) 1S the value at Rand T(l) at 
earth. This means that at R ~ 10 AU 1t takes about tW1ce as long to 
reach m1n1mum. We f1nd that from 1 to 30 AU the rat10 (t /T) 1ncreases 
slowly, due to the longer recovery t1me at larger R. <;fhe fact that 
th1s rat10 1S » 1 clearly 1nd1cates that we are observ1ng asymmetr1cal 
transient decreases at large R, however. 
3. Phys1cal Model for the Observed Energy and Spat1al Dependence of 
the Recovery T1me. A phys1cal model based upon a t1me-dependent, 
two-d1mens10nal numer1cal solut10n to the cosm1c-ray transport w1th a 
s1ngle shock weaken1ng W1 th d1stance has been developed by one of us 
(JRJ) to study these trans1ent events [81. The trans1ent 15 
represented by a d1sturbance propagated 1nto the steady-state cosmic-
ray d1str1but10n. The 1ntens1t1es at several rad11 and energ1es are 
studied. Th1S model pred1cts that there should be only a small depend-
ence of t upon energy at a g1ven R as is observed. The var1at10n of 
o 1ntens1ty w1th R depends ma1nly on the decay of the d1sturbance as 1t 
propagates through the he110sphere. For an e-fold1ng distance of 5-7 
AU for the weaken1ng of the shock, the var1at1on of the recovery t1me 
w1th enerqy and he11ocentr1c rad1us 1S g1ven 1n Table 1. 
Table 1: Var la t lon  of Recovery Tlme t Wlth Enerqy and H e l i o c e n t r l c  
0 Radlus. 
Energy Distance 1.7 3.3 5.0 
IGeVl [AUI 
1 .3  5.3 7.5 9.7 
3.6 5.0 7.0 8.6 
9.1 4.5 5.9 7.6 
These p r o p e r t i e s  a r e  i n  e x c e l l e n t  q u a l l t a t l v e  agreement wl th  t h e  
observa t ions  repor ted  here.  P r e c l s e  quantitative agreement i s  n o t  
expected a t  t h l s  s t a g e  glven t h a t  t h e  model 1s only two-dlmenslonal and 
t h e  evolution of t h e  dxsturbance 1s q u i t e  slmple. 
We conclude that f o r  the translent decreases  observed here:  
1) t h e  average recovery t lme t from t r a n s i e n t  decreases  a t  1 AU i s  
0 
energy independent and t 1s % 5 days; 
0 
2) t i s  essentially t h e  same before  a s  a f t e r  t h e  s o l a r  magnetlc 
fPeld  reversed I n  1980; 
3) t 1s cons tan t  throughout t h e  s o l a r  modulation cycle ;  
4 )  tRe r a t l o  of recovery t lmes  t ( ~ ) / t  (1) i n c r e a s e s  wl th  R and IS 
about 5 t lmes  longer  a t  20 ~u ' than g t  1 AU; 
5 )  t h e  t lme f o r  t h e  decrease  t o  reach minimum, T, increases about 
10%/AU o u t  t o  20 AU; s o  t h a t  a t  20 AU lt 1s % 2 t lmes longer  than 
a t  1 AU; 
6 )  t h e s e  r e s u l t s  a r e  w e l l  descrxbed by a two-dimensional numerxcal 
s o l u t l o n  t o  t h e  cosmic-ray t r a n s p o r t  equat ion which i n c o r p o r a t e s  an 
outward movlng weakening shock. 
6. Acknowledgments. 
The au thors  want t o  thank F.B. McDonald and T. von Rosenvlnge f o r  
making d a t a  a v a i l a b l e  from Pioneer  and Voyager s p a c e c r a f t  and IMP 
satellite r e s p e c t i v e l y .  The s t u d i e s  by JAL, WRW and J R J  were suppor- 
t e d ,  i n  p a r t ,  by g r a n t s  from NSF (ATM-8304486), NASA/GSFC (NAS5-24354) 
and NSF (ATM-8317701) and NASA (NSG-7101) r e s p e c t i v e l y .  
References 
1. McDonald, F.B., e t  a l . ,  (1981),  Ap. J., 249, L71. 
2. Webber, W.R. and J.A. Lockwood, (1981),  J. Geophys. Res. 86, 11458. 
3.  McKlbben, R.B., e t  a l . ,  (1982),  Ap. J., 254, L23. 
4. Lockwood, J.A. and W.R. Webber, (1984),  J. Geophys. Res., 89, 17. 
5. Lockwood, J .A .  and W.R. Webber, (1985),  t o  be pub. J.Geophys. R e s .  
6. Burlaqa,  L., e t  a l . ,  (1984),  J. Geophys. Res., 89, 6579. 
7. Van Allen,  J.A.,  (1979),  Geophys. Res. L e t t . ,  5, 566. 
8. J o k i p l l ,  J . R . ,  and J. Kota, (1983),  Ap. J., 265, 573. 
Figure  Captions 
Fig. 1 M t .  Washington neutron monitor monthly average count r a t e .  
Upper pane l  xnd ica tes  t r a n s l e n t  decreases  > 3% observed a t  M t .  
Washington. 
Flg. 2 t f o r  IMP vs.  t f o r  M t .  Washington neutron monltor. 
Fig.  3 ~ 8 u n t  r a t e  of 1&8, Vl,V2, and PI0 f o r  t r a n s l e n t  decrease  
on J u l y  12,  1982. 
Fig. 4 Ra t lo  t o ( R ) / t o ( R  = 1) vs.  r a d l a l  d l s t a n c e  R. 
390 SH4.1-9 
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The intensity recovery of Forbush-type decreases as a function of heliocentric distance and its relationship to the 11-year variation

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