The extragalactic charged particles are reflecting from the Galaxy by its magnetic field. Assuming magnetic field in the Galaxy as quasilongitudinal, the mean transparency of Galaxy has been evaluated for extragalactic protons defined as a fraction of particles at a given energy from a given direction passing by the galactic plane. The anisotropy caused by the Galactic magnetic field reflection of protons can explain observed arrival directions of extensive air showers at large angle to the galactic plane. Our analysis shows that the increase with energy observed in  sin b sup 11  is self-consistent with changing in the cosmic ray energy spectrum at high energy (E  10 to the 19th power eV) in the case when extragalactic cosmic ray source with spectral index -2.2 is at the position of the Virgo Cluster

Karakula, S.

Tkaczyk, W.

English

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VIRGO CLUSTER AS A HIGH ENERGY COSMIC RAYS SOURCE 
S. Karakda and W. Tkaczyk 
Institute of Physics, University of L6di, Poland 
ABSTRACT 
The extragalactic charged particles a re  reflecting from the 
Galaxy by its magnetic field. Assuming magnetic field in the Ga- 
laxy as quasilongitudinal we have evaluated mean transparency of 
Galaxy for extragalactic protons defined as a fraction of particles 
at a given energy from a given direction passing by the galactic 
plane. The anisotropy caused by the Galactic magnetic field re- 
flection of protons can explain observed arrival directions of EAS 
at large angle to the galactic plane. Our analysis shows that the 
increase with energy observed in &in bl'> i s  self-consistent 
with changing in the cosmic ray energy spectrum a t  high energy 
(E > 10'' e ~ )  in the case  when extragalactic cosmic ray source 
with spectral index -2.2 i s  a t  the position of the Virgo Cluster. 
I. INTRODUCTION 
The measurements of energy spectrum and anisotropy of cos- 
mic rays are  the basic source of information about its origin. The 
main difficulty to identify the cosmic rays sources i s  the Galactic 
magnetic field. In the past we analized propagations of cosmic rays 
protons emmited by Galactic sources distributed as Galactic matter 
( ~ a r a k d a  et al., 1972 ). The comparison of the calculated and ob- 
served extensive air showers (EAS) anisotropy shows that if pro- 
tons are the primary cosmic rays of energy greater than 1018 eV 
they should be predominantly extragalactic. The study of EAS (i.e. 
Watson, 1980: Linsley and Watson, 1981) shown that cosmic rays  
at energies above lo1' eV are  likly to be of extragalactic origin. 
The anisotropy of arrival directions of the highest energy cosmic 
rays is  observed from the directions of the large angle to the ga- 
lactic plane (bu s 74O) (~unningham et al., 1980 and 1983). The 
experimental data confirmed the flattening of the cosmic ray energy 
spectrum at energy greater than loL9  eV and the exponent of the 
integral energy spectrum i s  -1.4 2 0.1 (~unningham et al., 1980 and 
1983: Bower et al., 1983). 
In this paper we have considered the cluster or supercluster 
ori in of high energy cosmic rays model, but for lower energy Es 
loP8 eV we assumed Galactic location of cosmic ray sources. For 
the quasilongitudinal magnetic field in the Galaxy we have evalua- 
ted the mean transparency of the Galaxy for extragalactic protons. 
Our analysis shows that the increase with energy observed in 
<sin bl'> (~unningham et  al., 1980 ) i s  self -consistent with l%han- 
ging in the cosmic ray energy spectrum a t  high energy (210 e ~ )  
in the case  when extragalactic cosmic ray source with spectral 
index -2.2 i s  at the position of the Virgo Cluster (bl1 = 74O). 
300 OG 5.4-8 
I     I   S I  S  
. arakula and  acz  
Institute o  sics, niversit  o  6dz, land 
 
he e tragalactic c ar ed rticles re refl ti  fr  t e 
alaxy y its agnetic field. ssu i  agnetic field i  the 
laxy as quasilongitudinal e ave evaluated ea  transparency o  
alaxy for extragalactic r t s defined as a fraction o articles 
at a gi e  energy fr  a given directi  assi  y the alactic 
l he anisotropy ca sed  t e alactic agnetic field r
flecti  o  r tons can explai  observed arrival irections o S 
at large angle to the galactic l . ur analysis sho s that the 
increase it  energy observed in <.s  b ll  is self-
it  changing in the cos ic ray energy spectru  at high energy 
(E > 1019 eV) i  the case hen extragalactic cos ic ray source 
it  spectral index -  is at the positi  o the irgo l st r. 
I. I TI  
he easure ents o energy spectru  and anisotropy o c
ic rays are the basic source o infor ation about its ori i . he 
ai  difficulty to identify the cos ic rays sources is the alactic 
agnetic field. I  the past e analized ropagations o cos ic rays 
protons e ited b  alactic sources distri t  as alactic atter 
(K arakula et al. 19 ) he co parison of the calculated and o
served extensive air sho ers ( anisotropy sho s that i  pr
tons are the pri ar  cos ic rays o energy greater than 1018 e  
they should be predo ina tl  extra l t he study o S (i.
atson, 1980: insley and atson, 1981) sho n that cos ic rays 
at energies above 1019 e  are likl  to be o  extragalactic ori i . 
he anisotropy o arrival directions o  the ighest energy cos ic 
rays is observed fr  the directions o  the large angle to the 
lactic plane (bll ~ 7 0 ) (Cunningham et al., 1980 and 1983). he 
experi ental data confir ed the flattening o the cos ic ray energy 
spectru  at energy greater than 1019 e  and the exponent o the 
integral energy spectru  is -  ± 0. (Cunningham et al. 1980 and 
1983: o er et al., 1983). 
I  this paper e have considere  the cluster or supercluster 
origin o  hi  energy cos ic rays odel, but for lo er energy ~ 
10:L e e assu ed alactic location of cos ic ray sources. For 
the quasilongitudi al agnetic field in the alaxy e have eval -
ted the ean transparency o the alaxy for extragalactic protons. 
ur analysis shows that the increase ith energy observed in 
<sin b ll  (Cunningham et al., 1980) is s l - i ith cg -
ging in the cos ic ray energy spectru  at high energy (~101 eV) 
in the case hen extragalactic cos ic ray source ith spectral 
index -  is at the positi  of the irgo luster (bll = 740 ). 
https://ntrs.nasa.gov/search.jsp?R=19850025772 2020-03-20T17:59:54+00:00Z
2. THE TRANSPARENCY OF THE GALAXY FOR EXTRA- 
GALACTIC PROTONS 
The trajectory of arriving protons from the particular extraga- 
lactic directions were calculated assuming the mathematical model 
of the magnetic field in the Galaxy. In our calculations the magne 
tic field in the Galaxy was assumed a s  the quasilongitudinal model 
of Thielheim and Langhoff (1968). In this model the field lines a r e  
parallel to the spiral arms but with opposite orientation above and 
below the galactic plane. The strength of the component of the field 
parallel to the arms in details was  described in our paper Karakuka 
et al., (1972). The galactic disc, where the trajectories of protons 
were calculated, was defined by lzl 5 0.4 kpc (distance perpendi- 
cular to the galactic plane) and R 5 15 kpc (radius from the Ga- 
lactic center) .  The equation of motion of the protons in the Galac- 
tic magnetic field was  solved numerically. Our calculations indicated 
that some of the extragalactic particles a r e  reflecting from the Ga- 
laxy by its magnetic field. Only extragalactic particles entering the 
Galaxy on the observing level can be registrated as a n  EAS. We 
have evaluated the mean transparency of the Galaxy which was  
defined as a fraction of the number of particles at  a given energy 
from a given position of source passing through the plane located 
a t  a Solar System and perpendicular to the direction of the extra- 
galactic source (observer plane). In practice for large bu this pfa- 
ne i s  the galactic disc plane ( z = 0 ) .  We have followed large number 
of the protons trajectories for selected energies. The positions of 
the starting point of the protons trajectories was  at  random selected 
on the plane outside the Galactic disc. The real magnetic field in 
the Galaxy has  a regular and irregular components (magnetic clouds). 
Our model of the magnetic field in large scale describes the regular 
component. The nature and feature of irregular component a r e  not 
known up to now. For our considerations we also assume that the 
general properties of this component should be weaker than the 
regular component and shoulcl follow the last one in whole Galaxy. 
So  from the point of view of our considerations there i s  no differer 
ce  between randomoccuring irregularities of magnetic field in the 
time of grotons propagation and at  random selected positions of the 
starting point of the proton traiectory for the model of regular Ga- 
lactic magnetic field. Moreover in that case  we evoid the problem 
lo0 of focusing of particles in 
quasilongitudinal magnetic 
field. The mean transpa- 
3 rency parameter defined 
above i s  characteristic 
lo-' for the whole Galaxy. 
Figure 1 shows the mean 
transparency of Galaxy 
for extragalactic' protons 
for the selected directions 
of the group of galaxies. 
The transparency of Ga- 
10" 1018 10' E Lev] loZ0 laxy increases with ener- 
Fig. 1. The mean transparency of gy. We can also notice 
Galaxy as a function of that the energy of pro - 
proton energy. tons, when galactic mag- 
301 
OG 5.4-8 
2. T E T S  F T  L  F  
LACTIC P S 
he traject r  o arriving protons fr  the articular e tr
lactic directions ere calculated assu ing the athe atical odel 
o the agnetic field in the alaxy. In our calculations the agn~ 
tic field in the alaxy as assu ed as the quasilongit i al odel 
o  hielhei  and angh ff (1968). In this odel the field lines are 
parallel to the spiral ar s but ith opposite orientation above and 
bel  the galactic pla . he strength o the co ponent o the field 
arallel to the ar s in details as described in our paper r la 
et al., (1972). he galactic disc, mere the trajectories o protons 
ere calculated, as defined by Izl ~ 0. kpc (distance per
cular to the galactic plane) and R::: 15 kpc (radius fro  the 
lactic C r). he equation o  otion o  the protons i  the al -
tic agnetic field as solved nu ericall . ur calculations indicated 
that so e o the extragalactic particles are refl ti  fr  the 
laxy  its agnetic field. nly extragalactic articles entering the 
alaxy on the observing level can be registrated as an . e 
have evaluated the ean transparency o  the alaxy hic  as 
defined as a fraction of the nu ber o  particles at a given energy 
fro  a given positi  o source passing through the plane located 
at a olar Syste  and er e ic lar to the direction o the e tr
galactic source (observer lane). I  ractice for large bll this l
ne is the alactic disc pla e (z=O). e ave f ll ed large er 
o the protons trajectories for selected ener ies. r.f' e siti s o
the starting point o the protons trajectories as at ra do  selected 
on the plane outside the alactic disc. he real agnetic field i  
the alaxy as a regular and irregular co ponents ( agnetic clouds). 
ur odel o the agnetic field i  large scale describes the regular 
co po e t. he nature and feature o  irre lar co p e t are t 
 up to n . r r c nsiderations e also assu e t at the 
general properties o this co ponent should be eaker than the 
re l r co ponent and s d foll  the last one i  hole ala . 
o fro  the p i t o  vie  o our considerations there is no dif erel2. 
ce bet  rando  ri  irregularities o agnetic field i  the 
ti e o  protons r a ati  and at r  selected siti s o the 
starti g p i t o  t e r t  traiect r  for the odel o r l r 
lactic agnetic fiel . ore r i  t at ase e e oid t e r l  
10° o focusing o articles i  
quasilongitudinal agnetic 
fiel . he ea  tr
re cy ra eter efined 
above is c aracteristic 
for the hole alaxy. 
igure 1 sho s t  ean 
tra sparency o alaxy 
for extragalactic' rotons 
for the selected directions 
o the roup o  l i
he transparency o
1 '9  [eY] 10 20 laxy i creases it  
i 1. he  tr r   
alaxy as a function of 
r t  e r
gy. e can also notice 
t at the e ergy of ro -
t ns, e  alactic 
netic field h a s  a small influence on particles, strongly depends on 
the arriving positions relative to the Galactic plane. 
3. THE EXPECTED FLUX OF THE COSMIC RAYS FROM 
THE VIRGO CLUSTER 
The base  of our analysis was  the Haverah Park EAS data 
(cunningham et al., 1980) indicating that the mean value of <sin bl1> 
increases with energy. 
In this paper we want to examine if the observed changes in 
energy spectrum of cosmic rays  and &in bll> a r e  self- consistent, 
as far as our simple assumptions allow: 
i )  the galactic cosmic ray differential energy spectrum (IG) for 
energy greater than 1019 eV has  a power index -3.1, 
ii) some extragalactic sou ces with an unknow spectrum (IEx) fi located at  a position bo can give contribution to the observed 
flux, 
iii) the probability of the registration of the extragalactic charged 
particles depends on its energy, because of the influence of 
the Galactic magnetic field. 
In such case the mean value of sin bu can be expressed by: 
11 11 P (bl1) sin bl'- db + w (bo ) lEX * ~ ( b g ) -  sin b 11 
11 0 
sin b = 9 
where: 
p (bU)  - the probability ~ l~ reg i s t r a t i on  by Haverah Park array as 
the function of b , 
w(bl') - the transparency of the Galaxy versus  energy for extra- 
galactic protons. 
The integral in the numerator of above expression gives the con - 
tribution from the galactic cosmic ray flux. The second component 
of this sum represents the cont 'bution from the extragalactic point 
'ii 
source located a t  the position bo, after integration over the galactic 
latitzde with the delta Dirac function. The denominator expresses  
Nn 10 the normalization coef- 
3 ficient in the definition of .. 
'L the mean value sin b 11 . 
V) 11 
- The dependence of <sin b > 
:v) on the energy observed 
IE by Haverah Park was 
u used to calculate the ra- 
g tio of IEx/IG for extra- 
C 
o galactic source which i s  
C 
- located a t  the position of 
n 
the Virgo Cluster. The ra- - 
tio rtot/IG i s  a constant 
10" 1ol8 I O ' ~ E [ ~ V I  loz0 
3 for energy E < 10'' e V  
Fig. 2. The total flux (multiplied by E ) and increases for the 
calculated from &in bl%as a greater energy. Fig. 2 * 
function of energy. shows the differential to- 
tal ( I ~ ~ ~  = IG+lEX) cosmic 
302 OG 5.4-8 
  
. 
 f 
C  , ) f  ll
f 
f  <si  11   t
 
  
   . ; 
 Iic l X) 
  
flux, 
 f f 
f f 
11 
   
f, (11 ) . 11 11 (1  ) ( il) . bll JIG·   • m  ·   o .I x·P b o ·sm 0 
 
 
P 11 ) 0 11 registration 
f   
ll )   
t s. 
 f  
  
f  t~but
  
u  
u , ~ 10 t  r li ti  f-, . 
=t f 
l ll  
': The dependence of <sin lP> I 1 N on the energy observed · 1025 
- tit, , 1..-1 se  to calc late the ra-
-
I I 
I I 
17 0 1 10'9 E [eV] 1020 
 .   3 
<.si ll> as  
f 
f  -
galactic source hich is 
located at the position of 
.  
! t/I G   
  19  
 i r  f r t  
 . i .  
 t  iff r ti l t -
Itot    )  
3 
ray flux multiplied by E calculated from Haverah Park measurements 
of <sin bl1> . 
4. DISCUSSION AND CONCLUSIONS 
From the comparisons of our results (Fig. 2 )  with experimen- 
tal data of cosmic ray energy spectrum (cunningham et al., 1980: 
HiUas, 1984) we can conclude good agreepent. We have made the 
same calculations for different positions (bo) of the extragalactic 
point sources but the best agreement we have got only for the po- 
sition of the Virgo Cluster. It can be strong indication that high 
energy cosmic rays (E > 1019 e ~ )  are originated from this cluster. 
We can also notice that the differential cosmic rays energy spect- 
rum of the Virgo Cluster has  the spectral. index = -2.2, and in the 
energy range s 1018 eV the intensity of the Galactic and extraga- 
lactic fluxes a re  equal. In the lower energy region the Galactic 
cosmic ray flux i s  dominand. 
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Bower, A.J. et al., 1983, J.Phys. G: Nucl. Phys. 9, L53. 
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Watson, A.A., 1980, Astrophys. J. ( ~ e t t e r s ) ,  236, L71. 
Cunningham, G., Lloyd-Evans, J., Reid, R.J.O., and Watson, A.A., 
1983, Proc. 18th Int. Cosmic Ray Conf.,  anga gal ore), 22, 157. 
Hillas, A.M., 1984, Ann. Rev. Astron. Astrophys., 22, 425. 
Karakda,  S., Osborne, J.L., Roberts, E., and Tkaczyk, W., 1972, 
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e l l ti s r i t iti  bo )   tr l tic 
r es  t  r  
i   i  l I   t  i t  t  
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Virgo cluster as a high energy cosmic rays source

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