In a previous paper Bhat, et al., assess the evidence for the continuing acceleration of cosmic rays in the Loop I supernova remnant. The enhanced gamma-ray emission is found consistent with the Blandford and Cowie model for particle acceleration at the remnant shock wave. The contributions of other supernovae remnants to the galactic cosmic ray energy density are now considered, paying anisotropy of cosmic rays accelerated by local supernovae ( 100 pc). The results are compared with geophysical data on the fluctuations in the cosmic ray intensity over the previous one billion years

Bhat, C. L.

Houston, B. P.

Mayer, C. J.

Wolfendale, A. W.

English

NASA Technical Reports Server

345
OG 3.1-11
LO__NGTERM VARIABILITY OF THE COSMIC RAY INTENSITY
C.L.Bhat _ , B.P. Houston, C.J. Hayer
and A.W. Wolfendale
Un./versi_.y of Duz'ham, Phys.fcs
Deparbmenb, Durham DHI 3LE, England. (_
On lea ve fz'om Bhabha 2 t.omic Research
Centre, Sz'inagar-190006, Kashmir, India)
1. Introduction, In a previous paper Bhat et al.(1) assess
the evidence for the continuing acceleration of cosmic rays
in the Loop I supernova remnant. The enhanced gamma-ray
emission is found consistent with the Bland£ord and Cowie
(2) model for particle acceleration at the remnant shock
wave. We now consider the contributions of other supernovae
remnants to the Galactic cosmic ray energy density, paying
particular attention to variations in the energy density and
anisotropy of cosmic rays accelerated by local supernovae
(<100pc). The results are compared with geophysical data on
the fluctuations in the cosmic ray intensity over the
previous one billion years.
2. Shock Acceleration I_9_nSupernova Remnants, Blandford and
Cowie have applied shock acceleration considerations to
supernovae remnants exploding in the hot ISH. Assuming a
proton/electron ratio 10:1, a preshock factor -_I and an ISM
magnetic field of _I_ gauss, we get from Blandford and Cowie
the total energy in relativistic particles E within the
remnant as _s
R,
where the inital supernova energy _10 _ ergs and R, is the
remnant radius in units of 10 pc. During the Sedov phase of
the expansion the radius of the remnant is related to its
age t by _._
where t is in units of 10 _ years. This is consistent with
the previous assumptions about Loop I having an age of 4x10 f
yr and a radius of 110 pc. The efficiency of the mechanism
, increases with radius, provided the shock is strong. Beyond
this size the remnant continues to expand and the particles
are assumed to lose their energy adiabatically. We consider
three cut-off radii for the acceleration: 50,75 and 100 pc ;
" corresponding to I0%, 38% and 50% conversion e£ficiency-into
cosmic rays.
3 5 
OG 3.1-11 
LONG TE  RIABILITY O  TH  ~ C RA  IN SITY 
. . hat-, . . H uston, C. . Mayer 
and . . olfendale 
lI i v rsi t  f P rham, P ysi  
P artment, P r am P J .llE, E ql nd. (* 
On leave from 8haiJha Atomic Reselirch 
C ntre, Srinaq J 0 06, K hmir, In i ) 
~ I duction. In a p ious p r at e  a l) a ss 
th  e i nce fo  th  c ti uing a leration of co ic ra  
in th  L  I su r ova re nant. T  e nced ga ma-ray 
e ission is found consistent with the Blandford and Co ie 
(2) del fo  p rticle a eleration at th  re nant sh  
w e. We no  c sider th  c tributions of ot r su rnovae 
re nants to th  G lactic co ic ra  en r y d sity, p i g 
p rticular a tion to v ri tions in th  e y d sity an  
a tropy o  co ic ra  a lerated by lo l su rnovae 
«10 pc). T  r lts a  co pared wit  g physical d t  on 
th  flu t ations in th  co ic ra  in sity o r th  
p i us on  b n y rs. 
~ S k cceleration In S ernova R nants. Bl dford an  
C ie ha  a li d sh  a eleration c siderations to 
su r ovae re nants e l ding in th  h t ISM. A ing a 
p t n/electron r  1 : , a pr ck fa r ~1 an  an ISM 
magnetic fiel  of ~1~ gauss, we get from Blandford and Co ie 
th  to l e y in r tivistic p rticles E it in th  
re nant as ( "t'i ~-s E ~) ~ J.-o x '0 R} t , ) 
w ere th  in l su r ova en  ~1 sl er  an  R is th  
re nant ra s in u its of 10 p  D ri g th  Se ~ p se of 
th  e ansion th  ra i s o  th  re ant is re d to its 
ag  t by R 1,S" f "') 
t:; :::: J . ..l. II , ,'" 
w ere t is in u it  of lOs y rs. T is is c sistent wit  
th  p ious as ptions a t L  I h i g an ag  of 4xl ~ 
y  an  a ra s of 11  p  T  ef cy of th  m hanism 
in ases i  ra s, p ided th  sh  is stro g. B d 
th  siz  th  re nant c ti ues to ex d an  th  p rticles 
ar  assu ed to lo  th ir en y a batically. W  c sider 
th  c ff ra ii fo  th  a leration: 5  an  100 p  ; 
rresponding to 10 , 30% and-50% co ersion ef ncy-into 
co ic ra . 
https://ntrs.nasa.gov/search.jsp?R=19850025686 2020-03-20T18:04:13+00:00Z
348
OG 3.1-11
_L The Monte-Carlo ModelL We consider a spherical region
(r_100pc) around the Sun and calculate the cosmic ray energy
density at the centre due to supernovae events occuring
randomly in time and space. For type II supernovae we adopt
a mean Galactic rate of I per 100 yr. This corresponds to a
mean explosion rate of 0.066 per 10 _ yr within the local
volume. Each simulation covers a 10 q yr period, with a
temporal resolution of 10 _ yr. We do not consider here
possible variations in the rate due to motions of the Solar
system through spiral arms.
In each time interval the number of supernovae
occurring within 100pc is sampled from a Poisson
distribution and these are assigned random positions. The
mean local energy density is derived from Eq. I allowing for
the Sedov phase propagation of the remnant, Eq. 2. The three
cases A,B,C (corresponding to efficiency values 10, 30 and
50% respectively) are e_h simulated 10 times and average
energy densities derived. The baseline energy densities are
initally assumed to be zero, permitting an absolute
determination of the local contributions.
Mean energy densities are derived over time-scales from
0.1 to 100 Myr, and long-term averages for models A,B,C are
found to be 0.1, 0.5, 1.0 eV cm-'3 respectively. The local
Galactic energy density is generally taken to be _1.0 eV
cm "3, based on present observation of the cosmic ray and
synchrotron spectra. To derive the fluctuation in the local
energy density we first require the long-term mean to be 1.0
eV cm -_ . To achieve this, the baselines in each model are
increased to a corresponding constant level.
We also derive the expected cosmic ray anisotropy as a
function of time due to the local supernovae. During the
acceleration phase the particles are essentially limited to
the downstream region, behind the shock front. The
anisotropy amplitude % is thus determined when the remnant
sweeps past the Sun, and is given by
4. Results. The probability of fluctuations on different
time-scales, about a mean of 1.0 eV cm'_ are given in Figure
I. The upward and downward probabilities are given
separately for models A,B,C. It is apparent that in all
cases there is a greater probability of a downward
excursion: a reflection of the low probability for a local "
supernova event in a given time bin. For model A the
probability of upward fluctuations is relatively small,
whereas downward excursions, of a statistically small c
magnitude (<10_), are more prevalent. Model C is considered
unrealistic, in that it is very difficult to explain the
inferred cosmic ray grammage (E_few GeV) of 6 g cm-_if the
particles originate within 100 pc. This extreme case is
included to illustrate overall effect of increasing the net
acceleration efficiency.
46 
 . - 1 
~  he onte-Carlo odelL e nsider  herical ion 
~1 0pc) und e n  lculate e s ic  ergy 
ensity t t  ntre e t  pernovae ents ccuring 
ra domly i  ti e a d s ace. or t e II s pernovae e opt 
 ean alactic te f 1 er  r. his rresponds   
ean plosion r te f . 6 er ~ r ithin t  l al 
lume. ach I ulation vers  ~ r eriod, ith  
t poral r solution f ~ r. e  ot nsider re 
o sible ariations i  t  te e t  otions f t e olar 
st  t ugh iral r s. 
 ch e t rval  ber f pernovae 
ccurring ithin 100pc is sa pled fro  a oisson 
istribution a d t se r  ssi ned ra om ositions. e 
ean cal ergy ensity  erived fro  q. 1 ll ing r 
t  edov hase ropagation f t  nant, q. . he ree 
ases , ,C (c rresponding t  fficiency alues , 30 a d 
50  r spectively) re eQch i ulated  ti es d erage 
ergy ens ties erived. e aseline ergy ens ties r  
i itally assu ed t  be zero, ermitting an a solute 
etermination f e al ntributions. 
ean ergy ens ties re erived er e-scales  
.  t  0 yr, d ng-~erm erages f r odels , ,C r  
f nd t   . , . , .  e  -3 spectively. he l cal 
alactic e ergy ensity is enerally ta en t  be ~ .0 e  
-3 , ased  resent servation f t e s ic r  d 
s nchrotron ectra.  erive t e fl ctuation i  t  l cal 
ergy ensity e st quire t  l g-term ean t   .  
e  -3 •  hieve t is, t  aselines i  ch odel r  
i reased t  a rresponding nstant l el. 
e lso erive t  pected s ic  isotropy s  
f ction f ti e due t  t e l cal s ernovae. uring t e 
cceleration hase t e articles r  sentially li ited t  
t e wnstream r ion, hind t  ck nt. he 
isotropy plitude ~ i  t us etermined hen t  r nant 
s eeps ast t e un, a d is i en by 
(' -It- -o~1o l3) 
<:) -: 7" .,. Ie C 
~ esults, The probability of fluctuations on ifferent 
ti e-scales, out  ean f .   -~  i en i  igure 
1. The upward and do nward robabilities are given 
sepnrately f r odels ,B,C. It is apparent t at in ll 
cases t ere is a reater robability f a do nward 
cursion;  flection f t  l  robability f r  l cal 
supernova event in a given ti e in. or odel  t e 
robability f ard fl ctuations i  r latively all, 
hereas nward cursions, f a t tistically s all 
agnitude «1 %), are ore revalent. odel  is c nsidered 
nrealistic, i  t at it i  ery ifficult t  plain t  
inferred cos ic ray gra mage (E~few e ) of 6 g cm-~if the 
articles riginate ithin  c. his extreme se i  
luded  strate verall ffect f reasing e et 
celeration fficiency. 
.. 
• 
347
OG 3.1-11
FRACTIONALENERGYDENSITY,
..L.. IN'REdES ' D_CREASES'
29!'""'." _>o'"-->_%\ '_
lo lo(mx.) 60 3+............
_ ,A , _ _ 32
/ "" _ 28 LOCALENER6Y OENSITY:leVcm:
< ' _,,_-'--"10% <
8 30 / , - m _
20 i .... "_-_ so%u_..,
0_
_ 0 , , , B , ,
_0
................... "_>10% _'_30%30 0%",,
20 "._ , _ ?0 2 4 6 8 10 12
0 Anisofmpy Amptifude _(xl04)
10 C 3i i
10s 106 1_ 10B 106 1_ 10B
_ERASIN6 TIME(YEARS) Fi6ure 2
Figure 1
In Figure 2 we show the variation of anisotropies on 10 _
yr time bins, derived from averaging over 10 Monte-Carlo
samples of the supernovae spatial distributions. The
absolute anisotropies are normalized for the case of I eV
cm-_local contribution (model C).The absolute values for the
other two cases can be derived by scaling to the appropriate
mean local energy density.
5. Conclusions, Model B, and to a lesser extent A, predict
significant (>20_) increases in cosmic ray energy density on
time-scales of a few million years. These results are in
agreement with the experimental studies of cosmogenic
nuclides by Tokar and Povinec (3) and Voshage (4). However,
model B predicts a large decrease in intensity on
time-scales of 10 _ yr, suggesting that the presently
measured energy density is likely to be less than the true
• long-term average by up to 50%. While this possibility can
not be completly ruled out at present, it seems difficult to
reconcile it with the results of high energy (El > 100MeV)
gamma-ray observations. From the stand-point of the mean
Galactic energy density being _ 1.0 eV cm "% model A is more
consistent with the observations. If the Blandford and Cowie
model is appropriate for the bulk of Galactic supernovae
then no more than _10% of the observed cosmic rays can
originate from within 100pc.
29 
10 
10 
~ 7 
FRACTIONAL ENERGY DENSITY , 
0 
60 
>-
5O~ 
60 a5 
<! 
>30% 
CO 
40 ~ 
50% t-(Max) 20 ~ 
W 
0:: 
 IJ,.J Q. 
 
60 
>30% 
100% 
(Max) 
( ~----JO 
07 08 06 07 
AVERAG G I E S) 
igure  
OG 3 -11 
36 
32 
 LOCAL ENERGY DENSITY,leVe";' 
~24 
>. 
~ 20 
.0 
(j 
e 16 
£l. 
12 
8 
4 
0 2 4 6 8 10 12 
Anisotropy Amplitude ~(x 10') 
Figure 2 
In i ure 2 e sho  t  ariation f isotropies on lOS 
r ti e ins, erived fr  eraging ver  onte-Carlo 
am~les f t e s pernovae atial istributions. he 
bsolute nisotropies re rmalized r e ase f 1  
-llocal ontribution odel ).The bsolute alues r e 
ther t o ases n e erived  aling t  t e ppropriate 
ean cal nergy ensity. 
~ onclusions. odel , and t  a lesser extent , redict 
significant ()20%) i creases i  cosmic ray e ergy ensity on 
t e-scales f  f  illion ears. hese sults re  
agreement ith t e experimental st dies of cosmogenic 
uclides by okar, and ovinec (3) and oshage ( ). owever, 
odel  redicts a large decrease in i tensity on 
ti e-scales f 0~ yr, suggesting that the presently 
easured energy ensity  l ely t  e l s t an t e t e 
l ng-term average by up t  50 . hile t is ossibility can 
not be completly r led out at resent, it seems i ficult t  
reconcile it with the results of high energy (E r > 100MeV) ga ma-ray bservations. Fro  t e t nd-point f t e ean 
alacti c energy ensi ty eing "-  . 0 e  e  -"1 odel  i  ore 
con istent ith t e bservations. If t e landford and Cowie 
odel is propriate for t e bulk f alactic supernovae 
t en no more t an - 0% f t e observed cosmic rays can 
riginate fr  ithin 0pc. 
348
OC 3.1-11
Re£erences,
(1) Bhat,C.L., et al., 1985, Proc. 19 _ ICRC, OG 3.1-10
(2) Blandford,R.D., and Cowie,J.P., 1980, Astrophys. J.,
237, 793
73--) Tokar,S., and Povinec,P., 1983, Proc 18 _ ICRC,
Bangalore, 2, 381
(4) Voshage,H., 1984, Earth and Planetary Sci. Lett., 71,
181
48 
OG . -11 
eferences. 
(1) hat,C.L., t l., 985, roc. 9 c \oo, JCRC, O  . -10 
(2) landford,R.D., and owie,J.P., 1980, strophys. J., 
137, 93 t:h 
(3) okar,S., and ovinec,P., 1983, Proc 18 JCRC, 
angalore, 1, 381 
(4) oshage,H., 984, arth nd lanetary ci. ett., 71, 
181 


Long term variability of the cosmic ray intensity

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