A galactic magnetic field reversal near the Sagittarius spiral arm may be responsible for the southern excess (or northern shortage) of cosmic rays near 10 to the 18th power eV. The north-south asymmetry produced by such a reversal would increase with energy in the same manner as the observed asymmetry. The existence of a reversal has been inferred from analyses of Faraday rotation measures

Elbert, J. W.

Sommers, P.

English

NASA Technical Reports Server

MODELING COSMIC RAY ANISOTROPIES NEAR l o L 8  eV 
P. Sommers and J. W. E l b e r t  
Un i ve rs i t y  o f  Utah, Department o f  Physics 
201 JFB, S a l t  Lake City, UT 84112 USA 
ABSTRACT 
A g a l a c t i c  magnetic f i e 1  d reversa l  near the S a g i t t a r i u s  
s p i r a l  arm may be responsib le  f o r  the southern excess 
( o r  nor thern shortage) of cos~nic rays near l o L 8  eV. The 
north-south asymmetry produced by such a reversa l  would 
increase w i t h  energy i n  the  same manner as the  observed 
asymmetry [1,2]. The ex is tence o f  a reversa l  has been 
i n f e r r e d  from analyses o f  Faraday r o t a t i o n  measures [3,4]. 
I. The puzzle. Cosmic ray  f l uxes  i n  the EeV range ( 1  EeV=10L8 eV) 
d isp lay  a prominent an isot ropy.  The f l ux  i s  suppressed a t  nor thern 
g a l a c t i c  l a t i t u d e s ,  and the  e f fec t  increases w i t h  energy through t he  
decade .5-5 EeV [1,21. This measured an i  sotropy should be inst rumenta l  
i n  any at tempt t o  p iece together  a p i c t u r e  o f  t he  Galaxy's magnetic 
f i e l d  and the sources o f  h i gh  energy cosmic rays. Other pieces o f  
t h i s  puzzle are the f o l l ow ing :  
1. The cosmic rays a t  t h i s  energy a re  probably most ly  protons. 
This i s  based main ly  on s tud ies  o f  the  depth o f  maximum o f  a i r  showers 
and the var iance i n  t he  depths o f  maximum L51. 
2. The mean g a l a c t i c  magnetic f i e l d  near the  sun has a 
magnitude o f  about 2.2 pG, and a t  l e a s t  near the sun i t  i s  d i r ec ted  
clockwise about the  g a l a c t i c  center  as viewed from n o r t h  o f  the Galaxy 
[6]. Protons moving perpendicular t o  the f i e l d  1 ines have o r b i t  
diameters D = E, where E i s  the  energy i n  EeV and D i s  i n  kpc. The 
energy decade .5-5 EeV the re fo re  provides probes up t o  distances o f  5 
kpc. 
3. The sources of these cosmic rays a re  probably ga lac t i c .  By 
v i r t u e  o f  L i o u v i l  l e '  s theorem, the  an iso t rop ic  observed f l u x  cannot 
come from an i s o t r o p i c  ex t raga lac t i c  f l u x .  I f  the  ex t raga lac t i c  f l u x  
i s  no t  i s o t r o p i c  b u t  i s  coming p r i m a r i l y  from the  Vi rgo c l u s t e r ,  then 
i t  i s  very d i f f i c u l t  t o  exp la i n  how the an isot ropy cou ld  be turned i n t o  A 
a southern excess over a whole decade o f  energies. It i s  conceivable, 
though, t h a t  some o f  the  cosmic rays i n  t h i s  energy decade are coming 
from the  southern s i de  o f  the  Galaxy ( r a t h e r  than from the  Virgo 
c l u s t e r )  . For exampl e, acce le ra t ion  by gal a c t i c  wind te rmina t ion  
shock [71 might  occur between the  Galaxy and the  Magel lanic clouds 
and could p r e f e r e n t i a l l y  f i l l  the southern ha1 f of an extended halo. 
I f  the  ordered magnetic f i e l d  Mere conf ined t o  a t h i n  enough d isk,  then 
a southern excess would be expected as these p a r t i c l e s  d i f f u s e  nor th-  
ward. Any such model would be r a t h e r  cont r ived,  however, s ince i t  - 
would requ i re  a southern source t o  be prominent on ly  i n  a l i m i t e d  
energy band where no remarkable spect ra l  bump i s  observed. I n  t he  
f o l l ow ing  we w i l l  assume t h a t  EeV cosmic rays are o f  g a l a c t i c  o r i g i n .  
. 
304 
ODELING COSMIC RAY I PIES NEAR 101~ eV 
P. Sommers and J. lbert 
i rsity of t , partment of Physics 
201 JFB, Salt Lake it , UT 84112 USA 
A STRACT 
 galactic agnetic fi ld reversal near the Sagit arius 
spiral arm ay be responsible for the southern ex ss 
OG 5.4-9 
(or northern shortage) of cosmi c rays near 10 1 ~ eV. The 
nort -south asymmetry produced by such a reversal ould 
i r ase ith energy in the same anner as the observed 
asymmetry [ ]. The existence of a reversal has been 
i ferred from analyses of Faraday rotation asures [ ]. 
I. The puzzl . osmic ray fl xes in the EeV range (1 EeV=10 1e eV) 
display a pro i nt anisotropy. The fl x is suppr ssed at northern 
galactic l ti , and the ef i ses ith energy through the 
decade .5 EeV [ ,2]. his asured anisotropy should be i strumental 
in any at empt to piece to ether a picture of the laxy's agnetic 
field and the sources of high energy cosmic ray . ther pi ces of 
this puzzle are the f llo i g: 
1. The cosmic rays at this energy are robably stly pr t . 
is is sed ainly on studies of the depth of axi um of air showers 
and the v ri nce in the depths of aximum [5]. 
2. The ean galactic gnetic field near the sun has a 
gnitude of about 2. ~G, and at l ast near the sun it is dir cted 
clock ise about the galactic center as vi ed from orth of the alaxy 
[ . rotons oving perpendicul r to the field lines have rbit 
di t rs  , re  is the energy in EeV and  is in k . The 
energy decade .  EeV therefore provi es probes up to di t s of 5 
k . 
3. e sour s of t se cosmic rays are probably l cti  B
irt e f 's t r the anisotropic observed flux cannot 
co e from an isotropic extr galactic fl . If the extr galactic flux 
is ot isotropic ut is co ing ri arily from the rgo cl t r, then 
it is very ifficult to explain how the anisotropy could be turned into 
a southern ex ss ver a ole ecade f ener i . It is co c i l  
t , that so e of the cosmic rays in this energy decade are coming 
from the southern side of the alaxy (rather than from the irgo 
cl t r). or ex acceleration by l ctic i d ter ination 
shock [ ] i ht ccur etween the alaxy and the l anic cl s 
and could r ferential y fill the southern l f an extended l . 
If the ordered gnetic field were confined to a thin enough i  then 
a southern ex ss uld be expected as t se articl s iff se north-
y such odel uld be rather c tri  since it 
uld require a southern source to be ro i nt nly in a li ited 
energy and re no re arkable spectral bu p is er In the 
f l owing  il  assume t at eV osmic rays are f alactic ri i
https://ntrs.nasa.gov/search.jsp?R=19850025773 2020-03-20T17:59:57+00:00Z
4. The magnitude o f  t he  disordered p a r t  o f  t he  g a l a c t i c  magnetic 
f i e l d  i s  n o t  much greater  than the mean (ordered) f i e l d  s t rength,  even 
i n  dense clouds [8,91. An abrupt large-angle  change i n  a  p a r t i c l e ' s  
d i r e c t i o n  i s  therefore rare.  The sca le  of magnetic i r r e g u l  a r i  t i e s  
probably does n o t  exceed 150 pc [ l o ] .  For EeV protons whose o r b i t  
c i rcu~nferences a re  several k i loparsecs,  t he  o r b i t s  the re fo re  sense 
p r i m a r i l y  t h e  mean f i e l d  b u t  s u f f e r  f requent  small de f l ec t i ons  f rom 
magnetic i r r e g u l a r i t i e s .  
5. The ordered g a l a c t i c  magnetic f i e l d  i s  probably n o t  con f ined  
t o  a  t h i n  d isk ,  b u t  may extend 3 kpc o r  more t o  e i t h e r  s ide  of t h e  
plane. I f  t he  ordered f i e l d  were conf ined t o  a  t h i n  d isk  o f  1 kpc 
f u l l  th ickness, f o r  example, then a t  energies above 1 EeV no p ro ton  
o r b i t i n g  perpendicu lar  t o  the f i e l d  d i r e c t i o n  cou ld  be conf ined. A t  
several EeV a pronounced excess would be detected from d i r e c t i o n s  
nea r l y  para1 l e l  o r  a n t i - p a r a l l e l  t o  the f i e l d  d i r e c t i o n .  Moreover, 
j u s t  below 1 EeV, protons o r b i t i n g  perpendicu lar  t o  the  f i e l d  1  i nes  
would be conf ined on ly  i f  t h e i r  o r b i t s  met the  g a l a c t i c  plane nea r l y  
perpendicu lar ly .  In p a r t i c u l a r ,  a r r i v a l  s  from t h e  g a l a c t i c  cen te r  
and a n t i  -center  d i r e c t i o n s  would he s t rong ly  suppressed. I n  eva lua t i ng  
the  th ickness o f  the  ordered magnetic f i e l d ,  i t  would be he1 p f u l  t o  
have n o t  on l y  t he  observed dependence of f l u x  ( a t  var ious energ ies)  on 
the  north-south va r i ab l e  ( g a l a c t i c  l a t i t u d e )  b u t  a1 so t he  mean f l u x  
values p ro jec ted  onto the g a l a c t i c  cen te r -an t i - cen te r  ax i s  as w e l l  as 
f l u x  values p ro jec ted  onto the  ax i s  p a r a l l e l  t o  t he  mean f i e l d  d i r e c t i o n .  
6. Analyses o f  Faraday r o t a t i o n  measures [3,4]  suggest t h a t  a  
reversa l  o f  the  ordered f i e l d  occurs between t he  sun and t he  g a l a c t i c  
center .  Various est imates e x i s t  f o r  the d is tance t o  the  reversa l ,  b u t  
a  d is tance o f  2 kpc may be rea l  i s t i c .  F i e l d  reversa ls  o f  t h i s  t ype  
a re  seen i n  o ther  s p i r a l  ga lax ies (M51, F133, k181, NGC 6946, NGC 4258) 
[11,12]. Arnong the  s p i r a l  ga lax ies whose f i e l d s  have been mapped, M31 
i s  except ional  i n  n o t  showing a f i e l d  reversa l  [13,141. 
11. Assembling a  p i c t u re .  P u t t i n g  together  pieces 4 and 5 one 
f i n d s  t h a t  EeV cosmic rays a re  governed by a  la rge-sca le  ordered mag- 
n e t i c  f i e l d .  I n  t h i s  con tex t  H i l l a s  [ I 5 1  has made t he  f o l l ow ing  cogent 
argument t h a t  a  southern excess a t  Ear th  imp1 i e s  t he  ex is tence o f  a- 
r a d i a l  g rad ien t  i n  the  cosmic r ay  dens i t y :  L i o u v i l l e ' s  theorem 
requ i res  t h a t  the  i n t e n s i t y  (per  u n i t  area and so l  i d  angle) from the  
south a t  p o i n t  P i n  f i g u r e  1 must equal the  i n t e n s i t y  from the  n o r t h  a t  
ea r th .  The observed southern excess a t  e a r t h  then imp l i es  t h a t  t he  
i n t e n s i t y  from the  south a t  ea r t h  exceeds the  i n t e n s i t y  from the  south 
a t  P. S i m i l a r l y ,  t he  i n t e n s i t y  from the n o r t h  a t  3 exceeds t he  i n t e n s i t y  
from t h e  no r t h  a t  ear th .  Therefore the  nor thern  and southern i n t e n s i t i e s  
increase w i t h  g a l a c t i c  rad ius.  It can a1 so be shown t h a t  i f  t he  dens i t y  
of cosmic r a y  o r b i t  centers  increases l i n e a r l y  w i t h  g a l a c t i c  r a d i u s  
near t he  sun, then the  observed north-south asymmetry should increase 
l i n e a r l y  w i t h  energy ( i  .e. o r b i t  s i ze ) .  
305 OG 5.4-9 
 it e f  r d rt f  l ctic tic 
ld s t ch t r n  an r d) i ld tr n 
n e l  ,9]. r t l   n  ti 's 
i ti  s  l  tic s 
r ably s t d 50 c [10]. r eV t s  r it 
i mferences r  everal t  it  t r f r   
ri rily  an i ld t ff r nt al  fl ti  rom 
etic 
 r d l ctic tic i ld s ably t fi d 
  in t y t nd  c r r   it r i   
f  r d i ld  fi d o  in i k f  c 
ll es r n t r i s v    o ton 
r iting r ndicul r   l  i ction uld  t 
v ral   ced  ld  t ct d  ti  
arly l l r ti r ll l   ld 
 low  t  iting r ndicul r o  ld li s 
ld  fi  ly f ir i  t  l cti   arly 
r i n rti  rri ls  l cti  t r 
nd ti- ti  l  b  tr ngl  . n l ting 
  f  r  tic t l   l ful o 
 t ly  rv d nce t i  r i )  
 l  l ti  ti ) t ls  n l x 
 t d t   l ti   i   l   
x  t d t   i  r llel   n ld 
 f r y t tion  ] t t  
rsal f  r  ld r  t n  n nd  l ti  
 ti  i t r   o  t 
  f c y   i ld l  f i   
r  n n r iral l  M M ,   ) 
,12]. ~non  ir l l   l  ve n 1 
s ti l n t o i   ld rsal ,14]. 
II. li   tting r   d   
 t  i   r     r  
tic n i  t t  1 ]    ll i  t 
r t t  t rn  t rth pl    f  
ial i t n  i  y sit :  re  
i  t  sity r it  d id l )   
th t i t n   t l  sity   rth t 
 r  t r   t rth   t  
sity   t  t rt    sity   t  
t i  it    rth t Q   ity 
  rth t f   rn  t r  iti s 
  l ti    ls  hO\'m t f  it  
i  y it   rly h l ti  i s 
r  n  r  y tr  uld  
rly h rgy i . it i
Figure 1 
I f  t he  o r b i t s  shown i n  H i l l a s '  f i g u r e  are p ro ton  o r b i t s  a t  4 EeV 
(where t he  southern excess i s  very prominent), then po in t s  P and Q a re  
separated by 8 kpc. Even i f  one considers t r a j e c t o r i e s  o f  median p i t c h  
angle, t he  i n f e r r e d  r a d i a l  g rad ien t  p e r s i s t s  over 4 kpc. A source 
dens i t y  v a r i a t i o n  over such l a r g e  distances would n o t  be due simply t o ,  
v a r i a t i o n  w i t h i n  o r  between s p i r a l '  ams.  We know o f  no reason why h i gh  
energy cosmic ray  sources should be more abundant a t  l a r g e r  g a l a c t i c  
r a d i i  . 
I f  the  cosmic r ay  dens i t y  g rad ien t  i s  n o t  due t o  a  source 
grad ient ,  then i t  must be due t o  some propagat ion e f f e c t .  Ins tead o f  
excess sources ou t s i de  t he  sun's g a l a c t i c  o r b i t ,  one can look  f o r  a  
s ink  r eg ion  c l ose r  t o  t h e  g a l a c t i c  center.  A f i e l d  reversa l  reg ion i s  
an e f f e c t i v e  evacuat ipn s i t e  f o r  cosmic rays.  Figure 2 shows some o f  
t he  fas t -escapi  ng t r a j e c t o r i e s  near a  reversa l  . (The shaded regions 
a re  reg ions where grad1 81b 0.) 
The f i e l d  reversa l  zone i s  then a 
r eg ion  o f  low cosmic r ay  densi ty,  so 
a  dens i t y  g rad ien t  p o i n t s  away from 
t h a t  r eg ion  ( r a d i a l l y  outward a t  t h e  
' sun's  p o s i t i o n ) .  O r b i t s  o f  very h i gh  
energy cosmic rays  cou ld  be a f f ec ted  
d i r e c . t l y  by the  f i e l d  reversa l ,  
causing a pronounced shortage a t  
h i gh  nor thern  1  a t i  tudes. 
Our numerical s imu la t ions  con f i rm 
t h a t  the  energy dependence o f  t he  
nor thern shortage (southern excess) 
can a r i s e  from a un i fo rm source 
dens i t y  i f  there  i s  a  f i e 1  d  reversa l  
'r a t  about 2 kpc w i t h  a  g rad ien t  reg ion  o f  .5 kpc on e i t h e r  s i de  o f  i t  and i f  
6 = 0 t he re  i s  sorne admixture o f  i s o t r o p i c  
f l u x  from the  ha lo  o r  i n t e r g a l a c t i c  
F igure 2 space. 
111. Remarks. A d e f i n i t v e  exp lanat ion f o r  the  nor thern  shortage o f  
EeV cosmic rays  may n o t  be poss ib le  w i t hou t  more d e t a i l e d  knowledge o f  
t he  g a l a c t i c  magnetic f i e l d  and cosmic ray  sources. I f  ca re fu l  ana lys is  
determines t h a t  t h e  ordered magnetic f i e l d  i s ,  a f t e r  a l l ,  conf ined t o  a  
t h i n  d isk ,  then a p lanar  excess model [I61 ( i  .e., shortage a t  no r t h  - and 
306 
OG 5.4-9 
i re  
f  it  hown in ' re r  ton i  t  
r   out ern s s ry n i  nd  re 
eparated y . n f  i r  j t ri  f i n itch 
l t e i rred r dial r i t r i ts r   r  
nsity ri tion r uch l rge  ld t   i ply o 
ri ti n in r t en iral r    f  son i h 
ergy s ic y r s hould e re nt t r l ctic 
adi  . 
f t  s i  ay nsity i nt s t  o  r  
t en t t e e to  r gation f tead f 
ss o r s tside t e '  l ctic  an l ok f r  
sink r gion l r to t e l ctic t  fi ld r rsal r gion is 
n ff ctive v cuatipn ite f r s ic i re ho s o  f 
t e f t- scaping t j ctori s ar  r l. ( e haded gi s 
re r gi s r  radlBlfo  
1 
B = 0 
i ure 
 fi ld r rsal e is t en  
gion f l w s ic y i o 
 nsity r i t i ts y from 
t t gion (r dial y t rd t t e 
'  iti its f ry igh 
nergy s ic r ys uld e ff ted 
i tly y t e fi ld l
ausing  r ced short  t 
igh rthern latitud
ur rical i l ti s onfirm 
t t t e nergy n nce f t e 
rthern h rt  (southern x ss) 
an ri e from  iform ource 
nsity if t re is  fi ld r v rsal 
t about c ith  r di nt region 
f .5 pc n ither side f it and if 
t ere is some d ixture f i otropic 
flux from the alo r i t r alactic 
s
III. r .  efinitve explanation for the rthern short ge f 
eV cosmlC rays ay ot e ssible ut re tailed l ge f 
t e alactic netic field and cosmic ray so If careful nalysis 
deter i s t at the or ered gnetic field i , fter ll  onfined to  
thin di , then a l nar ex ss odel [16J (i. , shortage t orth and 
south po les)  might  be a complete explanat ion f o r  the anisotropy. O r  
perhaps i t  w i l l  be found t h a t  a s i g n i f i c a n t  f r a c t i o n  o f  EeV cosmic 
rays a re  heavy nuc le i ,  i n  which case a s p i r a l  ann source dens i ty  
g rad ien t  could be. the c o r r e c t  explanation. I n  f ac t ,  each puzzle p iece 
i s  r a t h e r  fuzzy. I n  support o f  the  f i e l d  reversa l  explanat ion, we 
o n l y  c l a im  t h a t  i t  i s  a p i c t u r e  which i s  composed o f  the  pieces descr i -  
bed above and which requ i res  no special  ad hoc pieces. 
Ack now1 edgement . 
This  research was supported by the United States National Science 
Foundation under g ran t  number PHY8415294. 
References 
1. Ast ley,  S.M. e t  a1 . Proc. I C R C  17 (Par is )  2, 156 (1981). 
2. Efimov, N.N. e t  a1 . Proc. I C R C  18 (Bangalore) 2, 149 (1983). 
3. Simard-Normandin, M. & Kronberg, P.P. Ap. J. 272, 74 (1980). 
4. Thomson, R.C. & Nelson, A.H. Mon. N o t . R . t c S o c .  - 191, 863 
(1980). 
5. Chant ler,  M.P. e t  a l .  J. Phys. G 9, L27 (1983). 
6. Manchester, R.N. Ap.J. (7974 ) . 
7. J o k i p i i ,  J.R. & ~~FWII:~~~:E!~&.J. 290, L1  (1985). 
8. Troland, T.H. & Heiles, C. A n 5 2 1 7 9  (1982). 
9. Fleck, R.C. Ap.J. 264, 139 TP98j)~ 
l o .  J o k i p i i  , J . R x  a1.Ap.J. 157, L119 (1969) 
11. Sawa, T. & Fujimoto, n u b r ~ s t r o n .  Soc. Japan - 32, 551 (1980) 
(and references t he re in )  . 
12. K le in ,  U. e t  a1 . Astron. Astrophys. 108, 176 (1982). 
13. Beck, R. Astron. Astrophys. 106, 1 2 1 7 9 8 2 ) .  
14. Sofue, Y. & Takano, T. Pub1 . T t r o n .  Soc. Japan 33, 47 (1981). 
15. Hi1 1 as, A.M. High Energy Astrophysics (Moriond M G t i  ng 1984, 
pp. 11-26) K i m  Hup Lee Co. (Singapore). 
16. ~dowczyk, J. & wolfendale, A.W. J . ~ h y s .  G - 10, 1453 (1984). 
307 OG 5.4-9 
t  ) t   ti    r 
  l    ti   i  
  v    i l   i
l    .   l   
     l  l . 
l  i        d f   
      i l   
ck o le  
 rch     l  
ti n   r 
 
s , ~·1. t l.    ,  
. . . t l  e   ,  .
. r andin, .  r .P. . 4 ,  
. .C.  .H. . t. . astr:-Soc.  . -
. .P. t     
 a e . . ~  188, 637 T  
 , .  MOrITll, G.E. Ap.J. 1 
. , . .  les . p.J::252:-T7  
. .C. p.J.  f91j3)-.-
10.  .R. et ~ .J.  l  ) 
 , .  Mr.lPub~As on.  1 ) 
d    • -
 l . t l. s s s.  
, . s . s s. -rf982)
, .  , . p l ~ o   , 
ill  .M.  r   eeti  
   . . 
Wd zyk,  Wolfendale, .W. .P s.  lQ  


Modeling cosmic ray anisotropies near 10(18) eV

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server